ovito.data — OVITO Python Reference 3.15.3-dev-HEAD-b1e9512d documentation

# `ovito.data`

This Python module defines various data object types, which are produced and processed within OVITO’s data pipeline system. It also provides the `DataCollection` class as a container for such data objects as well as several utility classes for computing neighbor lists and iterating over the bonds connected to a particle.

Data containers:

> - `DataObject` - base of all data object types in OVITO

> - `DataCollection` - a general container for data objects representing an entire dataset

> - `PropertyContainer` - manages a set of uniform `Property` arrays

> - `Particles` - a specialized `PropertyContainer` for particles

> - `Bonds` - specialized `PropertyContainer` for bonds

> - `VoxelGrid` - specialized `PropertyContainer` for 2d and 3d volumetric grids

> - `DataTable` - specialized `PropertyContainer` for tabulated data

> - `Lines` - set of 3d line segments

> - `Vectors` - set of vector glyphs

Data objects:

> - `Property` - uniform array of property values

> - `SimulationCell` - simulation box geometry and boundary conditions

> - `SurfaceMesh` - polyhedral mesh representing the boundaries of spatial regions

> - `TriangleMesh` - general mesh structure made of vertices and triangular faces

> - `DislocationNetwork` - set of discrete dislocation lines with Burgers vector information

Auxiliary data objects:

> - `ElementType` - base class for type descriptors used in typed properties

> - `ParticleType` - describes a single particle or atom type

> - `BondType` - describes a single bond type

Utility classes:

> - `CutoffNeighborFinder` - finds neighboring particles within a cutoff distance

> - `NearestNeighborFinder` - finds N nearest neighbor particles

> - `BondsEnumerator` - lets you efficiently iterate over the bonds connected to a particle

class ovito.data.BondType

  Base: `ovito.data.ElementType`

  Represents a bond type. This class inherits all its fields from the `ElementType` base class.

  You can enumerate the list of defined bond types by accessing the `bond_types` bond property object:

      bond_type_property = data.particles.bonds.bond_types
      for t in bond_type_property.types:
          print(t.id, t.name, t.color, t.radius)

  property radius: float

    This attribute controls the display radius of all bonds of this type.

    When set to zero, bonds of this type will be rendered using the standard width specified by the `BondsVis.radius` parameter. Furthermore, precedence is given to any per-bond widths assigned to the `Width` bond property if that property exists.

    Default:

      `0.0`

    Added in version 3.10.0.

class ovito.data.Bonds

  Base: `ovito.data.PropertyContainer`

  Stores the list of bonds and their properties. A `Bonds` object is always part of a parent `Particles` object. You can access it as follows:

      data = pipeline.compute()
      print("Number of bonds:", data.particles.bonds.count)

  The `Bonds` class inherits the `count` attribute from its `PropertyContainer` base class. This attribute returns the number of bonds.

  Bond properties

  Bonds can be associated with arbitrary bond properties, which are managed in the `Bonds` container as a set of `Property` data arrays. Each bond property has a unique name by which it can be looked up:

      print("Bond property names:")
      print(data.particles.bonds.keys())
      if 'Length' in data.particles.bonds:
          length_prop = data.particles.bonds['Length']
          assert(len(length_prop) == data.particles.bonds.count)

  New bond properties can be added using the `PropertyContainer.create_property()` method.

  Bond topology

  The `Topology` bond property, which is always present, defines the connectivity between particles in the form of a N x 2 array of indices into the `Particles` array. In other words, each bond is defined by a pair of particle indices.

      for a,b in data.particles.bonds.topology:
          print("Bond from particle %i to particle %i" % (a,b))

  Note that the bonds of a system are not stored in any particular order. If you need to enumerate all bonds connected to a certain particle, you can use the `BondsEnumerator` utility class for that.

  Bonds visualization

  The `Bonds` data object has a `BondsVis` element attached to it, which controls the visual appearance of the bonds in rendered images. It can be accessed through the `vis` attribute:

      data.particles.bonds.vis.enabled = True
      data.particles.bonds.vis.flat_shading = True
      data.particles.bonds.vis.width = 0.3

  Computing bond vectors

  Since each bond is defined by two indices into the particles array, we can use these indices to determine the corresponding spatial bond vectors connecting the particles. They can be computed from the positions of the particles:

      topology = data.particles.bonds.topology
      positions = data.particles.positions
      bond_vectors = positions[topology[:,1]] - positions[topology[:,0]]

  Here, the first and the second column of the bonds topology array are used to index into the particle positions array. The subtraction of the two indexed arrays yields the list of bond vectors. Each vector in this list points from the first particle to the second particle of the corresponding bond.

  Finally, we may have to correct for the effect of periodic boundary conditions when a bond connects two particles on opposite sides of the box. OVITO keeps track of such cases by means of the special `Periodic Image` bond property. It stores a shift vector for each bond, specifying the directions in which the bond crosses periodic boundaries. We make use of this information to correct the bond vectors computed above. This is done by adding the product of the cell matrix and the shift vectors from the `Periodic Image` bond property:

      bond_vectors += numpy.dot(data.cell[:3,:3], data.particles.bonds.pbc_vectors.T).T

  The shift vectors array is transposed here to facilitate the transformation of the entire array of vectors with a single 3x3 cell matrix. To summarize: In the two code snippets above, we have performed the following calculation of the unwrapped vector \(\mathbf{v}\) for every bond (a, b) in parallel:

  > \(\mathbf{v} = \mathbf{x}_b - \mathbf{x}_a + \mathbf{H} \cdot (n_x, n_y, n_z)^{T}\),

  with \(\mathbf{H}\) denoting the simulation cell matrix and \((n_x, n_y, n_z)\) the bond’s PBC shift vector.

  Standard bond properties

  The following standard properties are defined for bonds:

  Property name | Python access | Data type | Component names
  --- | --- | --- | ---
  Bond Type | `bond_types` | int32 |
  Color | `colors` | float32 | R, G, B
  Length |  | float64 |
  Particle Identifiers |  | int64 | A, B
  Periodic Image | `pbc_vectors` | int32 | X, Y, Z
  Selection | `selection` | int8 |
  Topology | `topology` | int64 | 1, 2
  Transparency |  | float32 |
  Width |  | float32 |

  add_bond(a, b, type=None, pbcvec=None)

    Creates a new bond between two particles a and b, both parameters being indices into the particles list.

    Parameters:

      - a (int) – Index of first particle connected by the new bond. Particle indices start at 0.

      - b (int) – Index of second particle connected by the new bond.

      - type (int | None) – Optional type ID to be assigned to the new bond. This value will be stored to the `bond_types` array.

      - pbcvec (tuple[int, int, int] | None) – Three integers specifying the bond’s crossings of periodic cell boundaries. The information will be stored in the `pbc_vectors` array.

    Returns:

      The 0-based index of the newly created bond, which is `(Bonds.count-1)`.

    Return type:

      int

    The method does not check if there already is an existing bond connecting the same pair of particles.

    The method does not check if the particle indices a and b do exist. Thus, it is your responsibility to ensure that both indices are in the range 0 to `(Particles.count-1)`.

    In case the `SimulationCell` has periodic boundary conditions enabled, and the two particles connected by the bond are located in different periodic images, make sure you provide the pbcvec argument. It is required so that OVITO does not draw the bond as a direct line from particle a to particle b but as a line passing through the periodic cell faces. You can use the `Particles.delta_vector()` function to compute pbcvec or use the `pbc_shift` vector returned by the `CutoffNeighborFinder` utility.

  property bond_types: Property | None

    The `Property` data array for the `Bond Type` standard bond property; or `None` if that property is undefined.

  property colors: Property | None

    The `Property` data array for the `Color` standard bond property; or `None` if that property is undefined.

  property pbc_vectors: Property | None

    The `Property` data array for the `Periodic Image` standard bond property; or `None` if that property is undefined.

  property selection: Property | None

    The `Property` data array for the `Selection` standard bond property; or `None` if that property is undefined.

  property topology: Property | None

    The `Property` data array for the `Topology` standard bond property; or `None` if that property is undefined.

class ovito.data.BondsEnumerator(bonds: Bonds)

  Utility class that permits efficient iteration over the bonds connected to specific particles.

  The constructor takes a `Bonds` object as input. From the generally unordered list of bonds, the `BondsEnumerator` will build a lookup table for quick enumeration of bonds of particular particles.

  All bonds connected to a specific particle can be subsequently visited using the `bonds_of_particle()` method.

  Warning: Do not modify the underlying `Bonds` object while the `BondsEnumerator` is in use. Adding or deleting bonds would render the internal lookup table of the `BondsEnumerator` invalid.

  Usage example

      from ovito.io import import_file
      from ovito.data import BondsEnumerator
      from ovito.modifiers import ComputePropertyModifier

      # Load a dataset containing atoms and bonds.
      pipeline = import_file('input/bonds.data.gz', atom_style='bond')

      # For demonstration purposes, let's define a compute modifier that calculates the length
      # of each bond, storing the results in a new bond property named 'Length'.
      pipeline.modifiers.append(ComputePropertyModifier(operate_on='bonds', output_property='Length', expressions=['BondLength']))

      # Obtain pipeline results.
      data = pipeline.compute()
      positions = data.particles.positions  # array with atomic positions
      bond_topology = data.particles.bonds.topology  # array with bond topology
      bond_lengths = data.particles.bonds['Length']     # array with bond lengths

      # Create bonds enumerator object.
      bonds_enum = BondsEnumerator(data.particles.bonds)

      # Loop over atoms.
      for particle_index in range(data.particles.count):
          # Loop over bonds of current atom.
          for bond_index in bonds_enum.bonds_of_particle(particle_index):
              # Obtain the indices of the two particles connected by the bond:
              a = bond_topology[bond_index, 0]
              b = bond_topology[bond_index, 1]

              # Bond directions can be arbitrary (a->b or b->a):
              assert(a == particle_index or b == particle_index)

              # Obtain the length of the bond from the 'Length' bond property:
              length = bond_lengths[bond_index]

              print("Bond from atom %i to atom %i has length %f" % (a, b, length))

  bonds_of_particle(index: int) → Iterator[int]

    Returns an iterator yielding the indices of the bonds connected to the given particle. The indices can be used to index into the `Property` arrays of the `Bonds` object.

class ovito.data.CutoffNeighborFinder(cutoff, data_collection)

  A utility class that computes particle neighbor lists.

  This class lets you iterate over all neighbors of a particle that are located within a specified spherical cutoff. You can use it to build neighbor lists or perform computations that require neighbor vector information.

  The constructor takes a positive cutoff radius and a `DataCollection` providing the input particles and the `SimulationCell` (needed for periodic systems).

  Once the `CutoffNeighborFinder` has been constructed, you can call its `find()` method to iterate over the neighbors of a particle, for example:

      from ovito.io import import_file
      from ovito.data import CutoffNeighborFinder

      # Load input simulation file.
      pipeline = import_file("input/simulation.dump")
      data = pipeline.compute()

      # Initialize neighbor finder object:
      cutoff = 3.5
      finder = CutoffNeighborFinder(cutoff, data)

      # Prefetch the property array containing the particle type information:
      ptypes = data.particles.particle_types

      # Loop over all particles:
      for index in range(data.particles.count):
          print("Neighbors of particle %i:" % index)

          # Iterate over the neighbors of the current particle:
          for neigh in finder.find(index):
              print(neigh.index, neigh.distance, neigh.delta, neigh.pbc_shift)

              # The index can be used to access properties of the current neighbor, e.g.
              type_of_neighbor = ptypes[neigh.index]

  Note: If you want to determine the N nearest neighbors of a particle, use the `NearestNeighborFinder` class instead.

  Parameters:

    - cutoff (float)

    - data_collection (DataCollection)

  find(index)

    Returns an iterator over all neighbors of the given particle.

    Parameters:

      index (int) – The zero-based index of the central particle whose neighbors should be enumerated.

    Returns:

      A Python iterator that visits all neighbors of the central particle within the cutoff distance. For each neighbor the iterator returns an object with the following property fields:

      > - index: The zero-based global index of the current neighbor particle.

      > - distance: The distance of the current neighbor from the central particle.

      > - distance_squared: The squared neighbor distance.

      > - delta: The three-dimensional vector connecting the central particle with the current neighbor (taking into account periodicity).

      > - pbc_shift: The periodic shift vector, which specifies how often each periodic boundary of the simulation cell is crossed when going from the central particle to the current neighbor.

    Return type:

      Iterator

    The index value returned by the iterator can be used to look up properties of the neighbor particle, as demonstrated in the example above.

    Note that all periodic images of particles within the cutoff radius are visited. Thus, the same particle index may appear multiple times in the neighbor list of the central particle. In fact, the central particle may be among its own neighbors in a small periodic simulation cell. However, the computed vector (`delta`) and PBC shift (`pbc_shift`) will be unique for each visited image of the neighbor particle.

  find_all(indices=None, sort_by=None)

    This is a vectorized version of the `find()` method, computing the neighbor lists and neighbor vectors of several particles in a single operation. Thus, this method can help you avoid a slow, nested Python loop in your code and it will make use of all available processor cores. You can request the neighbor lists for the whole system in one go, or just for a specific subset of particles given by indices.

    The method produces a uniform array of neighbor list entries. Each entry comprises a pair of indices, i.e. the central particle and one of its neighboring particles within the cutoff distance, and the corresponding spatial neighbor vector in 3d Cartesian coordinates. For best performance, the method returns all neighbors of all particles as one large array, which is unsorted by default (sort_by = `None`). That means the neighbors of central particles will not form contiguous blocks in the output array; entries belonging to different central particles may rather appear in intermingled order!

    Set sort_by to `'index'` to request grouping the entries in the output array based on the central particle index. That means each particle’s neighbor list will be output as a contiguous block. All blocks are stored back-to-back in the output array in ascending order of the central particle index or, if parameter indices was specified, in that order. The ordering of neighbor entries within each block will still be arbitrary though. To change this, set sort_by to `'distance'`, which additionally sorts the neighbors of each particle by increasing distance.

    The method returns two NumPy arrays:

    `neigh_idx` : Array of shape (M, 2) containing pairs of indices of neighboring particles, with M equal to the total number of neighbors in the system. Note that the array will contain symmetric entries (a, b) and (b, a) if neighbor list computation was requested for both particles a and b and they are within reach of each other.

    `neigh_vec` : Array of shape (M, 3) containing the xyz components of the Cartesian neighbor vectors (“delta”), which connect the M particle pairs stored in `neigh_idx`.

    Parameters:

      - indices (Optional[ArrayLike]) – List of zero-based indices of central particles for which the neighbor lists should be computed. If left unspecified, neighbor lists will be computed for every particle in the system.

      - sort_by (Optional[Literal['index', 'distance']]) – One of “index” or “distance”. Requests ordering of the output arrays based on central particle index and, optionally, neighbor distance. If left unspecified, neighbor list entries will be returned in arbitrary order.

    Returns:

      `(neigh_idx, neigh_vec)`

    Return type:

      tuple[NDArray[int64], NDArray[float32]]

    Tip

    Sorting of neighbor lists will incur an additional runtime cost and should only be requested if necessary. In any case, however, this vectorized method will be much faster than an equivalent Python for-loop invoking the `find()` method for each individual particle.

    Attention

    The same index pair (a, b) may appear multiple times in the list `neigh_idx` if the `SimulationCell` uses periodic boundary conditions and its size is smaller than twice the neighbor cutoff radius. Note that, in such a case, the corresponding neighbor vectors in `neigh_vec` will still be unique, because they are computed for each periodic image of the neighbor b.

    Added in version 3.8.1.

  find_at(coords)

    Returns an iterator over all particles located within the spherical range of the given center position. In contrast to `find()` this method can search for neighbors around arbitrary spatial locations, which don’t have to coincide with any physical particle position.

    Parameters:

      coords (ArrayLike) – A (x,y,z) coordinate triplet specifying the center location around which to search for particles.

    Returns:

      A Python iterator enumerating all particles within the cutoff distance. For each neighbor the iterator returns an object with the following properties:

      > - index: The zero-based global index of the current neighbor particle.

      > - distance: The distance of the current particle from the center position.

      > - distance_squared: The squared distance.

      > - delta: The three-dimensional vector from the center to the current neighbor (taking into account periodicity).

      > - pbc_shift: The periodic shift vector, which specifies how often each periodic boundary of the simulation cell is crossed when going from the center point to the current neighbor.

    Return type:

      Iterator

    The index value returned by the iterator can be used to look up properties of the neighbor particle, as demonstrated in the example above.

    Note that all periodic images of particles within the cutoff radius are visited. Thus, the same particle index may appear multiple times in the neighbor list. However, the computed vector (`delta`) and image offset (`pbc_shift`) will be unique for each visited image of a neighbor particle.

  neighbor_distances(index: int) → NDArray[float64]

    Returns the list of distances between some central particle and all its neighbors within the cutoff range.

    Parameters:

      index – The 0-based index of the central particle whose neighbors should be enumerated.

    Returns:

      NumPy array containing the radial distances to all neighbor particles within the cutoff range (in arbitrary order).

    This method is equivalent to the following code, but performance is typically a lot better:

        def neighbor_distances(index):
            distances = []
            for neigh in finder.find(index):
                distances.append(neigh.distance)
            return numpy.asarray(distances)

  neighbor_vectors(index: int) → NDArray[float64]

    Returns the list of vectors from some central particle to all its neighbors within the cutoff range.

    Parameters:

      index – The 0-based index of the central particle whose neighbors should be enumerated.

    Returns:

      Two-dimensional NumPy array containing the vectors to all neighbor particles within the cutoff range (in arbitrary order).

    The method is equivalent to the following code, but performance is typically a lot better:

        def neighbor_vectors(index):
            vecs = []
            for neigh in finder.find(index):
                vecs.append(neigh.delta)
            return numpy.asarray(vecs)

class ovito.data.DataCollection

  Base: `ovito.data.DataObject`

  A `DataCollection` is a container class that holds together individual data objects, each representing different fragments of a dataset. For example, a dataset loaded from a simulation data file may consist of particles, simulation cell information, and additional auxiliary data such as the current time step number of the snapshots, etc. All this information is contained in one `DataCollection`, which exposes the individual pieces of information as sub-objects, for example, via the `DataCollection.particles`, `DataCollection.cell`, and `DataCollection.attributes` fields.

  Data collections are the elementary entities that get processed within a data `Pipeline`. Each modifier receives a data collection from the preceding modifier, alters it in some way, and passes it on to the next modifier. The output data collection of the last modifier in the pipeline is returned by the `Pipeline.compute()` method.

  A data collection essentially consists of a bunch of `DataObjects`, which are all stored in the `DataCollection.objects` list. Typically, you don’t access the data objects list directly but rather use one of the special accessor fields provided by the `DataCollection` class, which give more convenient access to data objects of a particular kind. For example, the `DataCollection.surfaces` dictionary provides key-based access to all the `SurfaceMesh` instances currently in the data collection.

  apply(modifier, frame=None)

    This method applies a `Modifier` function to the data stored in this collection to modify it in place.

    Parameters:

      - modifier (Modifier) – The `Modifier` instance that should alter the contents of this data collection in place.

      - frame (int | None) – Optional animation frame number to be passed to the modifier function, which may use it for time-dependent modifications.

    The method allows modifying a data collection with one of OVITO’s modifiers directly without the need to build up a complete `Pipeline` first. In contrast to a data pipeline, the `apply()` method executes the modifier function immediately and alters the data in place. In other words, the original data in this `DataCollection` gets replaced by the output produced by the invoked modifier function. It is possible to first create a copy of the original data using the `clone()` method if needed. The following code example demonstrates how to use `apply()` to successively modify a dataset:

        from ovito.io import import_file
        from ovito.modifiers import *

        data = import_file("input/simulation.dump").compute()
        data.apply(RadialDistributionFunctionModifier(cutoff=2.9))
        data.apply(ExpressionSelectionModifier(expression="Coordination<9"))
        data.apply(DeleteSelectedModifier())

    Note that it is typically possible to achieve the same result by first populating a `Pipeline` with the modifiers and then calling its `compute()` method at the very end:

        pipeline = import_file("input/simulation.dump")
        pipeline.modifiers.append(RadialDistributionFunctionModifier(cutoff=2.9))
        pipeline.modifiers.append(ExpressionSelectionModifier(expression="Coordination<9"))
        pipeline.modifiers.append(DeleteSelectedModifier())
        data = pipeline.compute()

    An important use case of the `apply()` method is in the implementation of a user-defined modifier function, making it possible to invoke other modifiers as sub-routines:

        # A user-defined modifier function that calls the built-in ColorCodingModifier
        # as a sub-routine to assign a color to each atom based on some property
        # created within the function itself:
        def modify(frame: int, data: DataCollection):
            data.particles_.create_property('idx', data=numpy.arange(data.particles.count))
            data.apply(ColorCodingModifier(property='idx'), frame)

        # Set up a data pipeline that uses the user-defined modifier function:
        pipeline = import_file("input/simulation.dump")
        pipeline.modifiers.append(modify)
        data = pipeline.compute()

  property attributes: MutableMapping[str, Any]

    This field contains a dictionary view with all the global attributes currently associated with this data collection. Global attributes are key-value pairs that represent small tokens of information, typically simple value types such as `int`, `float` or `str`. Every attribute has a unique identifier such as `'Timestep'` or `'ConstructSurfaceMesh.surface_area'`. This identifier serves as lookup key in the `attributes` dictionary. Identifiers starting with `'.'` are hidden in the GUI. Attributes are dynamically generated by modifiers in a data pipeline or come from the data source. For example, if the input simulation file contains timestep information, the timestep number is made available by the `FileSource` as the `'Timestep'` attribute. It can be retrieved from pipeline’s output data collection:

        >>> pipeline = import_file('snapshot_140000.dump')
        >>> pipeline.compute().attributes['Timestep']
        140000

    Some modifiers report their calculation results by adding new attributes to the data collection. See each modifier’s reference documentation for the list of attributes it generates. For example, the number of clusters identified by the `ClusterAnalysisModifier` is available in the pipeline output as an attribute named `ClusterAnalysis.cluster_count`:

        pipeline.modifiers.append(ClusterAnalysisModifier(cutoff = 3.1))
        data = pipeline.compute()
        nclusters = data.attributes["ClusterAnalysis.cluster_count"]

    The `ovito.io.export_file()` function can be used to output dynamically computed attributes to a text file, possibly as functions of time:

        export_file(pipeline, "data.txt", "txt/attr",
            columns = ["Timestep", "ClusterAnalysis.cluster_count"],
            multiple_frames = True)

    If you are writing your own modifier function, you let it add new attributes to a data collection. In the following example, the `CommonNeighborAnalysisModifier` first inserted into the pipeline generates the `'CommonNeighborAnalysis.counts.FCC'` attribute to report the number of atoms that have an FCC-like coordination. To compute an atomic fraction from that, we need to divide the count by the total number of atoms in the system. To this end, we append a user-defined modifier function to the pipeline, which computes the fraction and outputs the value as a new attribute named `'fcc_fraction'`.

        pipeline.modifiers.append(CommonNeighborAnalysisModifier())

        def compute_fcc_fraction(frame, data):
            n_fcc = data.attributes['CommonNeighborAnalysis.counts.FCC']
            data.attributes['fcc_fraction'] = n_fcc / data.particles.count

        pipeline.modifiers.append(compute_fcc_fraction)
        print(pipeline.compute().attributes['fcc_fraction'])

  property cell: SimulationCell | None

    Returns the `SimulationCell` data object describing the cell vectors and periodic boundary condition flags. It may be `None`.

    Important

    The `SimulationCell` data object returned by this attribute may be marked as read-only, which means your attempts to modify the cell object will raise a Python error. This is typically the case if the data collection was produced by a pipeline and its objects are owned by the system.

    If you intend to modify the `SimulationCell` data object within this data collection, use the `cell_` attribute instead to explicitly request a mutable version of the cell object. See topic Announcing object modification for more information. Use `cell` for read access and `cell_` for write access, e.g.

        print(data.cell.volume)
        data.cell_.pbc = (True, True, False)

    To create a `SimulationCell` in a data collection that might not have a simulation cell yet, use the `create_cell()` method or simply assign a new instance of the `SimulationCell` class to the `cell` attribute.

  clone()

    Returns a shallow copy of this `DataCollection` containing the same data objects as the original.

    The method can be used to retain a copy of the original data before modifying a data collection in place, for example, using the `apply()` method:

        original = data.clone()
        data.apply(ExpressionSelectionModifier(expression="Position.Z < 0"))
        data.apply(DeleteSelectedModifier())
        print("Number of atoms before:", original.particles.count)
        print("Number of atoms after:", data.particles.count)

    Note that the `clone()` method performs an inexpensive shallow copy, meaning that the newly created collection still shares the data objects with the original collection.

    Keep in mind that data objects shared by two or more data collections are implicitly protected against modifications to avoid unexpected side effects. Thus, in order to subsequently modify the objects in either the original or the copy of the data collection, you have to use the underscore notation or the `DataObject.make_mutable()` method to make a deep copy of the particular data object(s) you want to modify. For example:

        copy = data.clone()
        # Data objects are shared by original and copy:
        assert(copy.cell is data.cell)

        # In order to modify the SimulationCell in the dataset copy, we must request
        # a mutable version of the SimulationCell using the 'cell_' accessor:
        copy.cell_.pbc = (False, False, False)

        # As a result, the cell object in the second data collection has been replaced
        # with a deep copy and the two data collections no longer share the same
        # simulation cell object:
        assert(copy.cell is not data.cell)

    Tip

    The `clone()` method is equivalent to the standard Python function `copy.copy()` when applied to a `DataCollection`. In fact, most OVITO object types can be shallow-copied with Python’s `copy.copy()` function and deep-copied with the `copy.deepcopy()` function.

    Return type:

      DataCollection

  create_cell(matrix, pbc=(True, True, True), vis_params=None)

    This convenience method conditionally creates a new `SimulationCell` object and stores it in this data collection. If a simulation cell already existed in the collection (`cell` is not `None`), then that cell object is replaced with a modifiable copy if necessary and the matrix and PBC flags are set to the given values. The attached `SimulationCellVis` element is maintained in this case.

    Parameters:

      - matrix (ArrayLike) – A 3x4 array to initialize the cell matrix with. It specifies the three cell vectors and the origin.

      - pbc (tuple[bool, bool, bool]) – A tuple of three Booleans specifying the cell’s `pbc` flags.

      - vis_params (Mapping[str, Any] | None) – Optional dictionary to initialize attributes of the attached `SimulationCellVis` element (only used if the cell object is newly created by the method).

    Return type:

      SimulationCell

    The logic of this method is roughly equivalent to the following code:

        def create_cell(data: DataCollection, matrix, pbc, vis_params=None) -> SimulationCell:
            if data.cell is None:
                data.cell = SimulationCell(pbc=pbc)
                data.cell[...] = matrix
                data.cell.vis.line_width = <...> # Some value that scales with the cell's size
                if vis_params:
                    for name, value in vis_params.items(): setattr(data.cell.vis, name, value)
            else:
                data.cell_[...] = matrix
                data.cell_.pbc = pbc
            return data.cell_

    See also

    Example M5: Shrink-wrap simulation box

    Added in version 3.7.4.

  create_particles(*, vis_params=None, **params)

    This convenience method conditionally creates a new `Particles` container object and stores it in this data collection. If the data collection already contains an existing particles object (`particles` is not `None`), then that particles object is replaced with a modifiable copy if necessary. The associated `ParticlesVis` element is preserved.

    Parameters:

      - params (Any) – Key-value pairs passed to the method as keyword arguments are used to set attributes of the `Particles` object (even if the particles object already existed).

      - vis_params (Mapping[str, Any] | None) – Optional dictionary to initialize attributes of the attached `ParticlesVis` element (only used if the particles object is newly created by the method).

    Return type:

      Particles

    The logic of this method is roughly equivalent to the following code:

        def create_particles(data: DataCollection, vis_params=None, **params) -> Particles:
            if data.particles is None:
                data.particles = Particles()
                if vis_params:
                    for name, value in vis_params.items(): setattr(data.particles.vis, name, value)
            for name, value in params.items(): setattr(data.particles_, name, value)
            return data.particles_

    Usage example:

        coords = [(-0.06,  1.83,  0.81), # xyz coordinates of the 3 particle system to create
                  ( 1.79, -0.88, -0.11),
                  (-1.73, -0.77, -0.61)]
        particles = data.create_particles(count=len(coords), vis_params={'radius': 1.4})
        particles.create_property('Position', data=coords)

    Added in version 3.7.4.

  property dislocations: DislocationNetwork | None

    Returns the `DislocationNetwork` data object; or `None` if there is no object of this type in the collection. Typically, the `DislocationNetwork` is created by a pipeline containing the `DislocationAnalysisModifier`.

  get(ref: Ref, require: bool = True, path: bool = False) → DataObject | None

    Resolves a `DataObject.Ref` reference by retrieving the referenced data object from this `DataCollection`.

    Parameters:

      - ref – The reference to the data object to be retrieved.

      - require – If `True`, the method raises a KeyError if the referenced object does not exist in the data collection. If `False`, the method returns `None` in the not-found case.

      - path – If `True`, the method returns a list of the data objects in the nested object hierarchy leading to the referenced object from the root of the `DataCollection`.

    Returns:

      The referenced `DataObject`, or `None` if require=False and the data object could not be found or if ref is a null reference.

    An “underscore version” of this method is available, which should be used whenever you intend to modify the returned data object. `get_()` implicitly calls `make_mutable()` to ensure the data object can be modified without unexpected side effects.

    Added in version 3.11.0.

  property grids: Mapping[str, VoxelGrid]

    Returns a dictionary view providing key-based access to all `VoxelGrids` in this data collection. Each `VoxelGrid` has a unique `identifier` key, which allows you to look it up in this dictionary. To find out which voxel grids exist in the data collection and what their identifiers are, use

        print(data.grids)

    Then retrieve the desired `VoxelGrid` from the collection using its identifier key, e.g.

        charge_density_grid = data.grids['charge-density']
        print(charge_density_grid.shape)

    The view provides the convenience method `grids.create()`, which inserts a newly created `VoxelGrid` into the data collection. The method expects the unique `identifier` of the new grid as first argument. All other keyword arguments are forwarded to the constructor to initialize the member fields of the `VoxelGrid` class:

        grid = data.grids.create(
            identifier="grid",
            title="Field",
            shape=(10,10,10),
            domain=data.cell)

    If there is already an existing grid with the same `identifier` in the collection, the `create()` method modifies and returns that existing grid instead of creating another one.

  property lines: Mapping[str, Lines]

    A dictionary view providing key-based access to all `Lines` objects in this data collection. Each `Lines` object has a unique `identifier` key, which can be used to look it up in the dictionary. You can use

        print(data.lines)

    to see which identifiers exist. Then retrieve the desired `Lines` object from the collection using its identifier key, e.g.

        lines = data.lines["trajectories"]
        print(lines["Position"])

    The `Lines` object with the identifier `"trajectories"`, for example, is the one that gets created by the `GenerateTrajectoryLinesModifier`.

    If you would like to create a new `Lines` object, in a user-defined modifier for instance, the dictionary view provides the method `lines.create()`, which creates a new `Lines` and adds it to the data collection. The method expects the unique `identifier` of the new lines object as first argument. All other keyword arguments are forwarded to the class constructor to initialize the member fields of the `Lines` object:

        lines = data.lines.create(identifier="mylines")

    If there is already an existing `Lines` object with the same `identifier` in the collection, the `create()` method returns that object instead of creating another one and makes sure it can be safely modified.

  property objects: MutableSequence[DataObject]

    List of all top-level `DataObjects` in this data collection. You can add or remove data objects from this list as needed.

    Typically, however, you don’t need to work with this list directly, because the `DataCollection` class provides several convenience accessor attributes for the different flavors of data objects in OVITO. For example, `DataCollection.particles` returns the `Particles` object (by looking it up in the `objects` list for you). Dictionary-like views such as `DataCollection.tables` and `DataCollection.surfaces` provide key-based access to particular kinds of data objects in the collection.

    To add new objects to the data collection, you can append them to the `objects` list or, more conveniently, use creation functions such as `create_particles()`, `create_cell()`, or `tables.create()`, which are provided by the `DataCollection` class.

  property particles: Particles | None

    Returns the `Particles` object, which manages all per-particle properties. It may be `None` if the data collection contains no particle model at all.

    Important

    The `Particles` data object returned by this attribute may be marked as read-only, which means attempts to modify its contents will raise a Python error. This is typically the case if the data collection was produced by a pipeline and all data objects are owned by the system.

    If you intend to modify the contents of the `Particles` object in some way, use the `particles_` attribute instead to explicitly request a mutable version of the particles object. See topic Announcing object modification for more information. Use `particles` for read access and `particles_` for write access, e.g.

        print(data.particles.positions[0])
        data.particles_.positions_[0] += (0.0, 0.0, 2.0)

    To create a new `Particles` object in a data collection that might not have particles yet, use the `create_particles()` method or simply assign a new instance of the `Particles` class to the `particles` attribute.

  property surfaces: Mapping[str, SurfaceMesh]

    Returns a dictionary view providing key-based access to all `SurfaceMesh` objects in this data collection. Each `SurfaceMesh` has a unique `identifier` key, which can be used to look it up in the dictionary. See the documentation of the modifier producing the surface mesh to find out what the right key is, or use

        print(data.surfaces)

    to see which identifier keys exist. Then retrieve the desired `SurfaceMesh` object from the collection using its identifier key, e.g.

        surface = data.surfaces['surface']
        print(surface.vertices['Position'])

    The view provides the convenience method `surfaces.create()`, which inserts a newly created `SurfaceMesh` into the data collection. The method expects the unique `identifier` of the new surface mesh as first argument. All other keyword arguments are forwarded to the constructor to initialize the member fields of the `SurfaceMesh` class:

        mesh = data.surfaces.create(
            identifier="surface",
            title="A surface mesh",
            domain=data.cell)

    If there is already an existing mesh with the same `identifier` in the collection, the `create()` method modifies and returns that existing mesh instead of creating another one.

  property tables: Mapping[str, DataTable]

    A dictionary view of all `DataTable` objects in this data collection. Each `DataTable` has a unique `identifier` key, which allows it to be looked up in this dictionary. Use

        print(data.tables)

    to find out which table identifiers are present in the data collection. Then use the identifier to retrieve the desired `DataTable` from the dictionary, e.g.

        rdf = data.tables['coordination-rdf']
        print(rdf.xy())

    The view provides the convenience method `tables.create()`, which inserts a newly created `DataTable` into the data collection. The method expects the unique `identifier` of the new data table as first argument. All other keyword arguments are forwarded to the constructor to initialize the member fields of the `DataTable` class:

        # Code example showing how to compute a histogram of the particles' x-coordinates within some interval.
        x_interval = (0.0, 100.0)
        x_coords = data.particles.positions[:,0]
        histogram = numpy.histogram(x_coords, bins=50, range=x_interval)[0]

        # Output the histogram as a new DataTable, which makes it appear in OVITO's data inspector panel:
        table = data.tables.create(
            identifier='binning',
            title='Binned particle counts',
            plot_mode=DataTable.PlotMode.Histogram,
            interval=x_interval,
            axis_label_x='Position X',
            count=len(histogram))
        table.y = table.create_property('Particle count', data=histogram)

    If there is already an existing table with the same `identifier` in the collection, the `create()` method modifies and returns that existing table instead of creating another one.

  property triangle_meshes: Mapping[str, TriangleMesh]

    This is a dictionary view providing key-based access to all `TriangleMesh` objects currently stored in this data collection. Each `TriangleMesh` has a unique `identifier` key, which can be used to look it up in the dictionary.

  property vectors: Mapping[str, Vectors]

    A dictionary view providing key-based access to all `Vectors` objects in this data collection. Each `Vectors` object has a unique `identifier` key, which can be used to look it up in the dictionary. You can use

        print(data.vectors)

    to see which identifiers exist. Then retrieve the desired `Vectors` object from the collection using its identifier key, e.g.

        vectors = data.vectors["vectors"]
        print(vectors["Position"])
        print(vectors["Direction"])

    If you would like to create a new `Vectors` object, in a user-defined modifier for instance, the dictionary view provides the method `vectors.create()`, which creates a new `Vectors` object and adds it to the data collection. The method expects the unique `identifier` of the new vectors object as first argument. All other keyword arguments are forwarded to the class constructor to initialize the member fields of the `Vectors` object:

        vectors = data.vectors.create(identifier="myVectors")

    If there is already an existing `Vectors` object with the same `identifier` in the collection, the `create()` method returns that object instead of creating another one and makes sure it can be safely modified.

class ovito.data.DataObject

  Abstract base class for all data object types in OVITO.

  A `DataObject` represents a fragment of data processed in or by a data pipeline. See the `ovito.data` module for a list of different concrete data object types in OVITO. Data objects are typically contained in a `DataCollection`, which represents a whole data set. Furthermore, data objects can be nested into a hierarchy. For example, the `Bonds` data object is part of the parent `Particles` data object.

  Data objects by themselves are non-visual objects. Visualizing the information stored in a data object in images is the responsibility of so-called visual elements. A data object may be associated with a `DataVis` element by assigning it to the data object’s `vis` field. Each type of visual element exposes a set of parameters that allow you to configure the appearance of the data visualization in rendered images and animations.

  See also

  Data model

  Visual elements

  class Ref(cls: type[DataObject] | None = None, path: str = '')

    This data structure describes a reference to some `DataObject` to be retrieved from a `DataCollection`. In other words, the `Ref` class does not hold an actual data object but all the information needed to locate it in the output of a `Pipeline`.

    Parameters:

      - cls – The class type of the object being referenced.

      - path – The `identifier` of the object being referenced.

    Given a `Ref` and some `DataCollection`, you can look up the actual data object with the `DataCollection.get()` method:

        ref = DataObject.Ref(VoxelGrid, 'density')
        data = pipeline.compute()
        voxel_grid = data.get(ref)
        assert voxel_grid is data.grids['density']

    A `Ref` instance is what the `ovito.traits.DataObjectReference` parameter trait uses to let the user select a data object from a data collection.

    Examples for valid `Ref` definitions:

        DataObject.Ref()                              # Null reference
        DataObject.Ref(Particles)                     # References the Particles object
        DataObject.Ref(Bonds)                         # References the Bonds object
        DataObject.Ref(DataTable, 'coordination-rdf') # References the DataTable 'coordination-rdf'
        DataObject.Ref(PropertyContainer, 'isosurface/vertices') # References the vertices of a SurfaceMesh
        DataObject.Ref(AttributeDataObject, 'ClusterAnalysis.cluster_count') # References a global attribute

    Added in version 3.11.0.

    property cls: type[DataObject] | None

      The concrete Python class type of the referenced data object, e.g. `Particles` or `DataTable`.

    property path: str

      The unique `identifier` of the referenced data object. This identifier is used by the `get()` method to locate the object in a data collection. If the referenced object is nested in a hierarchy of data objects, the path contains multiple identifiers separated by slashes, e.g. `'particles/bonds/Bond Types/1'`. If only a single instance of the object type specified by `cls` exists in the data collection, the path can be omitted. This is the case, for example, for the `Particles` and `Bonds` objects.

  property identifier: str

    The unique identifier string of the data object.

    This identifier serves as a lookup key in object dictionaries, such as the `DataCollection.tables` collection. Generally, the identifier also serves as a way to reference the object within the `DataCollection`, for example, when specifying which data object a modifier should operate on.

    The identifier string must not contain slashes (‘/’) or colons (‘:’).

    Data objects generated by modifiers typically receive an automatically assigned identifier, as described in the documentation of the respective modifier. When implementing a custom modifier function, it is your responsibility to assign meaningful identifiers to any new data objects your function creates. This ensures that subsequent modifiers can correctly reference and look up these objects.

  make_mutable(subobj: DataObject) → DataObject

    Ensures exclusive ownership of the given sub-object by performing a copy-on-write operation if necessary.

    This method checks whether subobj, a child of the calling `DataObject`, is shared with any other parent object. If subobj is referenced by multiple parent objects, a copy is created to ensure that modifications do not affect other owners. However, if subobj is exclusively owned by this `DataObject`, no copy is made, and the original instance is returned.

    By ensuring exclusive ownership before modification, this method prevents unintended side effects caused by modifying a shared object. The returned object is guaranteed to be safe for modification without affecting any other references.

    See Announcing object modification for a discussion of object ownership and common use cases for this method.

    Parameters:

      subobj – An existing sub-object of this parent data object, for which exclusive ownership is requested.

    Returns:

      A copy of subobj if it was shared with another parent; otherwise, the original object.

  property vis: DataVis | None

    The `DataVis` element currently associated with this data object. This object is responsible for visually rendering the stored data. If set to `None`, the data object remains non-visual and does not appear in rendered images or viewports. Additionally, note that the same `DataVis` element may be assigned to multiple data objects to synchronize their visual appearance.

    See the `ovito.vis` module for a list of visual element types.

class ovito.data.DataTable

  Base: `ovito.data.PropertyContainer`

  This data object type in OVITO represents a series of data points and is primarily used for histogram plots and other 2d graphs. More generally, however, it can store tabulated data consisting of an arbitrary number of columns of numeric values.

  When used for 2d plots, a data table consists of an array of y-values and, optionally, an array of corresponding x-values, one value pair for each data point. These arrays are regular `Property` objects managed by the data table (a sub-class of `PropertyContainer`).

  If no `x` data array has been set, the x-coordinates of the data points are implicitly determined by the table’s `interval`, which specifies a range along the x-axis over which the data points are evenly distributed. This is used, for example, for histograms with equisized bins, which don’t require explicit x-coordinates.

  Data tables generated by modifiers such as `RadialDistributionFunctionModifier` and `HistogramModifier` are accessible via the `DataCollection.tables` dictionary. You can retrieve them based on their unique `identifier`:

      >>> print(data.tables)  # Print list of available data tables
      {'coordination-rdf': DataTable(), 'clusters': DataTable()}

      >>> rdf = data.tables['coordination-rdf']  # Look up tabulated RDF produced by a RadialDistributionFunctionModifier

  Exporting the values in a data table to a simple text file is possible using the `export_file()` function (use file format `txt/table`). You can either export a single `DataTable` or, as in the following code example, write a series of text files to export all the tables generated by a `Pipeline` for a simulation trajectory in one go. The `key` parameter selects which table from the `DataCollection.tables` dict is to be exported based on its unique `identifier`:

      export_file(pipeline, 'output/rdf.*.txt', 'txt/table', key='coordination-rdf', multiple_frames=True)

  To programmatically create a new data table in Python, you should use the `data.tables.create()` method, for example when implementing a custom modifier function that should output its results as a data plot. The following code examples demonstrate how to add a new `DataTable` to the data collection and fill it with values.

  To create a simple x-y scatter point plot:

      # Create a DataTable object and specify its plot type and a human-readable title:
      table = data.tables.create(identifier='myplot', plot_mode=DataTable.PlotMode.Scatter, title='My Scatter Plot')
      # Set the x- and y-coordinates of the data points:
      table.x = table.create_property('X coordinates', data=numpy.linspace(0.0, 10.0, 50))
      table.y = table.create_property('Y coordinates', data=numpy.cos(table.x))

  Note how the `create_property()` method is being used here to create two `Property` objects storing the coordinates of the data points. These property objects are then set as `x` and `y` arrays of the `DataTable`. This is necessary because a data table is a general `PropertyContainer`, which can store an arbitrary number of data columns. We have to tell the table which of these properties should be used as x- and y-coordinates for plotting.

  A multi-line plot is obtained by using a vectorial property for the `y` array of the `DataTable`:

      table = data.tables.create(identifier='plot', plot_mode=DataTable.PlotMode.Line, title='Trig functions')
      table.x = table.create_property('Parameter x', data=numpy.linspace(0.0, 14.0, 100))
      # Use the x-coords to compute two y-coords per data point: y(x) = (cos(x), sin(x))
      y1y2 = numpy.stack((numpy.cos(table.x), numpy.sin(table.x)), axis=1)
      table.y = table.create_property('f(x)', data=y1y2, components=['cos(x)', 'sin(x)'])

  To generate a bar chart, the table’s `x` property must be filled with numeric IDs 0,1,2,3,… denoting the individual bars. Each bar is then given a text label by adding an `ElementType` to the `Property.types` list using `Property.add_type_id()`:

      table = data.tables.create(identifier='chart', plot_mode=DataTable.PlotMode.BarChart, title='My Bar Chart')
      table.x = table.create_property('Structure Type', data=[0, 1, 2, 3])
      table.x.add_type_id(0, table, name='Other')
      table.x.add_type_id(1, table, name='FCC')
      table.x.add_type_id(2, table, name='HCP')
      table.x.add_type_id(3, table, name='BCC')
      table.y = table.create_property('Count', data=[65, 97, 10, 75])

  For histogram plots, one can specify the complete range of values covered by the histogram by setting the table’s `interval` property. The bin counts must be stored in the table’s `y` property. The number of elements in the `y` property array, together with the `interval`, determine the number of histogram bins and their uniform widths:

      table = data.tables.create(identifier='histogram', plot_mode=DataTable.PlotMode.Histogram, title='My Histogram')
      table.y = table.create_property('Counts', data=[65, 97, 10, 75])
      table.interval = (0.0, 2.0)   # Four histogram bins of width 0.5 each.
      table.axis_label_x = 'Values' # Set the x-axis label of the plot.

  If you are going to access or export the data table after it was inserted into the `DataCollection`, refer to it using its unique `identifier` given at construction time, as shown in the following example:

      def modify(frame: int, data: DataCollection):
          table = data.tables.create(identifier='trig-func', title='My Plot', plot_mode=DataTable.PlotMode.Line)
          table.x = table.create_property('X coords', data=numpy.linspace(0.0, 10.0, 50))
          table.y = table.create_property('Y coords', data=numpy.cos(frame * table.x))

      pipeline.modifiers.append(modify)
      export_file(pipeline, 'output/data.*.txt', 'txt/table', key='trig-func', multiple_frames=True)

  property axis_label_x: str

    The text label of the x-axis. This string is only used for a data plot if the `x` property of the data table is `None` and the x-coordinates of the data points are implicitly defined by the table’s `interval` property. Otherwise the `name` of the `x` property is used as axis label.

    Default:

      `''`

  property interval: tuple[float, float]

    A pair of float values specifying the x-axis interval covered by the data points in this table. This interval is only used by the table if the data points do not possess explicit x-coordinates (i.e. if the table’s `x` property is `None`). In the absence of explicit x-coordinates, the interval specifies the range of equispaced x-coordinates implicitly generated by the data table.

    Implicit x-coordinates are typically used in data tables representing histograms, which consist of equally-sized bins covering a certain value range along the x-axis. The bin size is then given by the interval width divided by the number of data points (see `PropertyContainer.count` property). The implicit x-coordinates of data points are placed in the centers of the bins. You can call the table’s `xy()` method to let it explicitly calculate the x-coordinates from the value interval for every data point.

    Default:

      `(0.0, 0.0)`

  property plot_mode

    The type of graphical plot for rendering the data in this `DataTable`. Must be one of the following predefined constants:

    > - `DataTable.PlotMode.NoPlot`

    > - `DataTable.PlotMode.Line`

    > - `DataTable.PlotMode.Histogram`

    > - `DataTable.PlotMode.BarChart`

    > - `DataTable.PlotMode.Scatter`

    Default:

      `DataTable.PlotMode.Line`

  property x: Property | None

    The `Property` containing the x-coordinates of the data points (for the purpose of plotting). The data points may not have explicit x-coordinates, so this property may be `None` for a data table. In such a case, the x-coordinates of the data points are implicitly determined by the table’s `interval`.

    Default:

      `None`

  xy()

    This convenience method returns a two-dimensional NumPy array containing both the x- and the y-coordinates of the data points in this data table. If the table has no explicit `x` coordinate property set, this method automatically computes equispaced x-coordinates from the `interval`.

    Return type:

      ndarray

  property y: Property | None

    The `Property` containing the y-coordinates of the data points (for the purpose of plotting). This may be a vector property having more than one component per data point, in which case this data table represents a family of data plots.

    Default:

      `None`

class ovito.data.DelaunayTessellation(points: ArrayLike, cell: SimulationCell | None = None, ghost_layer_size: float = 0.0)

  Added in version 3.13.0.

  This class computes the 3D triangulation of the given set of points in space. The Delaunay triangulation is a partitioning of the convex hull of the input points into tetrahedra, such that no point lies inside the circumsphere of any tetrahedron.

  The input points are specified as a NumPy array of shape (N, 3), where N is the number of points. An optional `SimulationCell` with periodic boundary conditions can be provided to build a periodic tessellation. In this case a positive ghost_layer_size must be specified, which defines the thickness of the ghost layer around the simulation cell where periodic images of the input points are created.

  Caution

  This class is still under development and may change in future releases. It is merely a wrapper around the corresponding C++ class from the OVITO source code. The Python API is not yet stable and the behavior may change without notice. Documentation is also incomplete. Please use with caution and contact the developers if you have questions or intend to use this facility in your own code.

  adjacent_facet(cell1: int, cell2: int) → int | None

    Returns the local index of the facet in cell1 that leads from cell1 to cell2.

    Parameters:

      - cell1 – The first cell.

      - cell2 – The second cell.

    Returns:

      The local index of the facet of cell1 that is shared by cell2; or `None` if the two cells don’t share any facet.

  alpha_test(cell: int, alpha: float) → bool | None

    Returns whether the specified cell passes the alpha test.

    Parameters:

      - cell – The index of the cell.

      - alpha – The alpha value to test.

    Returns:

      `True` if the cell passes the alpha test, `False` if not. `None` if the cell is a degenerate sliver element, for which an alpha value cannot be computed.

  cell_adjacent(cell: int, local_facet: int) → int

    Returns the index of the adjacent cell for the specified cell and local facet.

    Parameters:

      - cell – The index of the cell.

      - local_facet – The local facet index (0-3).

    Returns:

      The adjacent cell.

  property cell_count: int

    Returns the total number of tetrahedra in the tessellation, including ghost cells and infinite cells.

  static cell_facet_vertices(cell_facet_index: int) → tuple[int, int, int]

    Returns the cell-local indices of the three vertices of the specified triangular facet.

    Parameters:

      cell_facet_index – The index of a cell facet (0-3).

    Returns:

      The three cell-local vertex indices, all in the range 0-3.

  cell_primary_index(cell: int) → int | None

    Returns the index of the given Delaunay cell in the contiguous list of primary cells. Returns `None` if the cell is a ghost or infinite cell.

    Parameters:

      cell – The cell to be queried.

    Returns:

      The cell’s index in the contiguous list of primary cells; or `None` if the cell is a ghost or infinite cell.

  cell_vertex(cell: int, local_index: int) → int

    Returns the index of the vertex at the given local index in the specified cell.

    Parameters:

      - cell – The index of the cell.

      - local_index – The local index of the vertex (0-3).

    Returns:

      The (global) index of the vertex.

  incident_facets(cell: int, i: int, j: int) → list[tuple[int, int]]

    Returns the list of facets incident to the specified Delaunay edge.

    Parameters:

      - cell – The index of the cell.

      - i – The cell-local index of the first vertex of the edge.

      - j – The cell-local index of the second vertex of the edge.

    Returns:

      A list of tuples, each containing the index of the adjacent cell and the local facet index.

  input_point_index(vertex: int) → int

    Returns the index of the input point corresponding to the specified Delaunay vertex. This is the index into the original list of input points passed to the constructor. Several Delaunay vertices may correspond to the same input point if they are periodic images of each other, in which case this function returns the same index for all of them.

    Parameters:

      vertex – The index of the Delaunay vertex; or `None` if the vertex does not correspond to any physical input point.

    Returns:

      The index into the original list of input points passed to the constructor.

  is_finite_cell(cell: int) → bool

    Returns whether the given tessellation cell connects four physical vertices. Returns false if one of the four vertices is the infinite vertex.

    Parameters:

      cell – The index of the cell to check.

    Returns:

      `True` if the cell is finite, `False` otherwise.

  is_ghost_cell(cell: int) → bool

    Returns whether the given tessellation cell is a ghost cell.

    Parameters:

      cell – The index of the cell to check.

    Returns:

      `True` if the cell is a ghost cell or an infinite cell, `False` if it is a primary cell.

  is_ghost_vertex(vertex: int) → bool

    Returns whether the given vertex is a ghost vertex.

    Parameters:

      vertex – The index of the vertex to check.

    Returns:

      `True` if the vertex is a ghost vertex, `False` otherwise.

  is_primary_cell(cell: int) → bool

    Returns whether the given tessellation cell is a primary cell.

    Parameters:

      cell – The index of the cell to check.

    Returns:

      `True` if the cell is a primary cell, `False` if it is either a ghost or an infinite cell.

  local_vertex_index(cell: int, vertex: int) → int

    Returns the local index of the specified vertex in the given cell.

    Parameters:

      - cell – The index of the cell.

      - vertex – The global index of the vertex to look up. Must not be the infinite vertex.

    Returns:

      The local index of the vertex in the cell; or -1 if the vertex is not part of the given cell.

  mirror_facet(cell: int, local_facet: int) → tuple[int, int]

    Returns the adjacent cell and the local facet index that are opposite to the specified input facet.

    Parameters:

      - cell – The index of the cell.

      - local_facet – The local facet index (0-3).

    Returns:

      A tuple containing the index of the adjacent cell and the local facet index within that cell.

  property points: ndarray

    Returns the coordinates of the vertices in the tessellation as a NumPy array. This includes ad-hoc generated ghost vertices and helper points.

    Returns:

      A NumPy array of shape (N, 3) containing the coordinates of the vertices.

    Note

    The vertex coordinates are not exactly equal to the input point coordinates. They are slightly perturbed to make the Delaunay triangulation more robust against singular input data.

  property primary_cell_count: int

    Returns the number of finite tetrahedra in the tessellation, only including those belonging to the primary image of the periodic simulation box.

  property simulation_cell: SimulationCell | None

    The input simulation cell (if any).

  property vertex_count: int

    Returns the number of Delaunay vertices in the tessellation, including ghost vertices.

class ovito.data.DislocationNetwork

  Base: `ovito.data.DataObject`

  A network of dislocation lines extracted from a crystal model by the `DislocationAnalysisModifier`. The modifier stores the dislocation network in a pipeline’s output data collection, from where it can be retrieved via the `DataCollection.dislocations` field:

      data = pipeline.compute()
      network = data.dislocations

  The visual appearance of the dislocation lines in rendered images and videos is controlled by the associated `DislocationVis` element. You can access it as `vis` attribute of the `DataObject` base class:

      network.vis.line_width = 1.5
      network.vis.coloring_mode = DislocationVis.ColoringMode.ByBurgersVector

  The `lines` list gives you access to the list of individual dislocations, which are all represented by instances of the `DislocationNetwork.Line` class. Furthermore, you can use the `find_nodes()` method to obtain a list of nodes at which dislocation lines are connected. These connections are represented by `DislocationNetwork.Connector` objects.

  Important

  Keep in mind that the list of dislocations is not ordered. In particular, the order in which the DXA modifier discovers each dislocation line in the crystal will change arbitrarily from one simulation frame to the next. Generally, there is no safe way to track individual dislocation lines through time, because dislocations (unlike atoms) don’t possess a unique identity and are not conserved – they can nucleate, annihilate, or undergo other reactions in between trajectory frames.

  Code example

  Complete script example for loading a molecular dynamics simulation, performing the DXA on a single snapshot, printing the list of extracted dislocation lines, and exporting the dislocation network to disk:

      from ovito.io import import_file, export_file
      from ovito.modifiers import DislocationAnalysisModifier
      from ovito.data import DislocationNetwork

      import ovito
      ovito.enable_logging()

      pipeline = import_file("input/simulation.dump")

      # Extract dislocation lines from a crystal with diamond structure:
      modifier = DislocationAnalysisModifier()
      modifier.input_crystal_structure = DislocationAnalysisModifier.Lattice.CubicDiamond
      pipeline.modifiers.append(modifier)
      data = pipeline.compute()

      total_line_length = data.attributes['DislocationAnalysis.total_line_length']
      cell_volume = data.attributes['DislocationAnalysis.cell_volume']
      print("Dislocation density: %f" % (total_line_length / cell_volume))

      # Print list of dislocation lines:
      print("Found %i dislocation lines" % len(data.dislocations.lines))
      for line in data.dislocations.lines:
          print("Dislocation %i: length=%f, Burgers vector=%s" % (line.id, line.length, line.true_burgers_vector))
          print(line.points)

      # Export dislocation lines to a CA file:
      export_file(pipeline, "output/dislocations.ca", "ca")

      # Or export dislocations to a ParaView VTK file:
      export_file(pipeline, "output/dislocations.vtk", "vtk/disloc")

  File import and export

  Dislocation networks can be exported as a set of polylines to the legacy VTK file format using the `ovito.io.export_file()` function (specify the “vtk/disloc” format). During export to this file format, which does not support periodic boundary conditions, lines that cross a periodic domain boundary get split (i.e., wrapped around) at the simulation box boundaries.

  OVITO’s native format for storing dislocation networks on disk is the CA file format, a simple text-based format that supports periodic boundary conditions. This format can be written by the `export_file()` function (”ca” format) and read by the `import_file()` function. It stores the dislocation lines, their connectivity, as well as the “defect mesh” produced by the `DislocationAnalysisModifier`.

  class Connector

    A dislocation `Line` has two end point `connectors` and is described by a sequence of spatial `points`.

    A connector object represents one of the two end points of each `Line` in the network. In other words, every `Line` has exactly two unique `Connector` objects belonging to the line. This pair is accessible via the `Line.connectors` attribute. Since dislocations always have a direction (their line sense, with respect to which their Burgers vector is defined), one connector is located at the “head” (forward) and one at the “tail” (backward) end of the directed line.

    Three dislocation arms meet at a dislocation node (junction). The node is formed by a circular linked-list of connectors.

    A dislocation network node (junction) is formed by several connectors located at the same point in space, as illustrated in the figure to the right. This node structure consists of three interlinked connectors belonging to the three dislocation arms meeting in the node. Dislocation arms can be either inbound or outbound.

    Network nodes may consist of one, two, three or more connectors:

    1. A single connector, only interlinked with itself, represents a dangling line end. They occur when a dislocation terminates in another extended crystal defect, such as a grain boundary or free surface.

    2. A 2-node, consisting of two interlinked connectors, is part of a dislocation loop or infinite periodic dislocation line. They occur when a dislocation line is closed on itself, i.e, its head and tail are connected.

    3. A node with three or more connectors represents a physical dislocation junction, where three or more arms with non-zero Burgers vector meet.

    The connectors belonging to the same network node are interlinked with each other in the form of a circular linked list. The `Connector.next_arm` field leads to the next connector in the circular list. The last connector of the node points back to the first connector of the node. This way, all connectors can be visited by starting from any connector of the node and following the `Connector.next_arm` field until the starting connector is reached again. For a 1-node (a dangling line end), the `Connector.next_arm` field points to itself.

    The `Connector.arms` method yields a list of all connectors belonging to the same local node as this connector (including the connector itself). The `Connector.arm_count` property counts the number of connectors in the local node. The `Connector.line` field points to the `Line` object that the connector belongs to.

    The `DislocationNetwork.find_nodes()` method can be used to generate a list of `Connector` objects, one for each node in the network. It is useful if you want to iterate over all unique nodes in the network.

    Added in version 3.10.2.

    property arm_count: int

      The number of arms meeting at the node formed by this connector and others, including the connector itself.

    arms() → list[Connector]

      This method builds a list of `Connector` objects representing the arms connected to the node. Each connector object links to a different dislocation line incident to the network node.

    property is_head: bool

      True if the connector is located at the head of its dislocation line, i.e., `self` is `self.line.connectors[1]`. Then the connected `Line` is inbound on the node.

    property is_tail: bool

      True if the connector is located at the tail of its dislocation line, i.e., `self` is `self.line.connectors[0]`. Then the connected `Line` is outbound from the node.

    property line: Line

      The dislocation `Line` this connector belongs to.

    property next_arm: Connector

      The `Connector` belonging to the next dislocation line incident to the node.

    property position: ArrayLike[float64]

      The Cartesian coordinates of the connector in the global simulation coordinate system. This corresponds to the start or end point of the dislocation, i.e., either `self.line.points[0]` or `self.line.points[-1]`.

      Note

      The positions of the connectors in the same network node are typically identical, but they will differ if their dislocation lines belong to different periodic images of the simulation cell. In this case, the positions of the connectors are shifted by a periodicity vector of the simulation domain.

  class Line

    Describes a single continuous dislocation line that is part of a `DislocationNetwork`.

    A dislocation line is a curve in 3d space, approximated by a sequence of `points` connected by linear line segments. You can query its total curve `length` or compute some location on the line from a linear path coordinate t using the method `point_along_line()`. The line is terminated by two `connectors` at its two end points, which represent the connectivity of the dislocation network.

    A dislocation line is embedded in some crystallite (a region with uniform lattice orientation), which is identified by the numerical `cluster_id`. All dislocation lines belonging to the same crystallite share the same lattice coordinate system in which their true Burgers vectors are expressed. A line’s `true_burgers_vector` is given in Bravais lattice units.

    Each crystallite has a particular mean orientation within the global simulation coordinate system and a mean lattice parameter and elastic strain. Applying these mean crystal properties to the `true_burgers_vector` yields the line’s `spatial_burgers_vector`, which is expressed in the global coordinate system shared by all dislocations of the entire `DislocationNetwork`. The `spatial_burgers_vector` is given in simulation coordinate units (typically Angstroms).

    The `is_loop` property flag indicates that the two end points of the dislocation line form a 2-junction. This property does not necessarily mean that the dislocation forms an actual circular loop. In simulations using periodic boundary conditions, a straight dislocation can also connect to itself through the periodic cell boundaries and form an infinite periodic line. This situation is indicated by the `is_infinite_line` property, which implies that the `is_loop` property is also true.

    All fields of this class are read-only. To modify a dislocation line, you can use the `DislocationNetwork.set_line()` method.

    Changed in version 3.10.2: Renamed this class from `DislocationSegment` to `DislocationNetwork.Line`.

    property cluster_id: int

      The numeric identifier of the crystal cluster containing this dislocation line. A crystal cluster is the technical term for a contiguous group of atoms forming a spatial region with uniform lattice orientation, i.e., a crystallite or grain.

      The `true_burgers_vector` of the dislocation is expressed in the local coordinate system of the crystal cluster. The `spatial_burgers_vector` of the dislocation is computed by transforming the true Burgers vector with the mean elastic deformation gradient tensor of the crystal cluster.

    property connectors: tuple[Connector, Connector]

      A tuple of two `Connector` objects representing the two end points of the dislocation line. The first connector is located at the start of the line (its tail), the second connector at the end of the line (its head).

      Added in version 3.10.2.

    property custom_color: tuple[float, float, float]

      The RGB color value to be used for visualizing this particular dislocation line, overriding the default coloring scheme imposed by the `DislocationVis.coloring_mode` setting. The custom color is only used if its RGB components are non-negative (i.e. in the range 0-1); otherwise the line will be rendered using the computed color depending on the line’s Burgers vector.

      Default:

        `(-1.0, -1.0, -1.0)`

    property id: int

      The unique numerical identifier of this dislocation line within the `DislocationNetwork`. This is simply the zero-based index of the line in the `DislocationNetwork.lines` list.

      Important: This identifier is derived from the arbitrary storage order of the lines in the network and cannot be used to identify the same dislocation in another simulation snapshot.

    property is_infinite_line: bool

      Indicates that this dislocation is an infinite line passing through a periodic simulation box boundary. A dislocation is considered infinite if it is a closed loop but its start and end do not coincide (because they are located in different periodic images).

    property is_loop: bool

      Indicates whether this line forms a loop, i.e., its end is connected to its start point. Note that an infinite dislocation line passing through a periodic simulation cell boundary is also considered a logical loop (see `is_infinite_line` property).

    property length: float

      Computes the length of this dislocation line in simulation units of length, integrating the piecewise linear segments it is made of.

    point_along_line(t: float) → NDArray[float64]

      Returns the Cartesian coordinates of a point on the dislocation line. The location to be calculated must be specified in the form of a fractional position t along the continuous dislocation line.

      Parameters:

        t – Normalized path coordinate in the range [0,1]

      Returns:

        The xyz coordinates of the requested point on the dislocation line.

      Added in version 3.10.0.

    property points: NDArray[float64]

      The sequence of spatial points that define the curved shape of this dislocation (in simulation coordinates). This is a N x 3 Numpy array, with N>2 being the number of points along the line.

      For true dislocation loops, the first and the last point in the list coincide exactly. For infinite lines, the first and the last point coincide modulo a periodicity vector of the simulation domain.

      The point sequence always forms a continuous line, which may lead outside the primary `SimulationCell` if periodic boundary conditions (PBCs) are used, i.e., only the start of the dislocation is always inside the primary simulation cell but its end point may not. Thus, the line is stored in unwrapped form. A wrapping happens ad-hoc during visualization, when the `DislocationVis` element renders the dislocation network or if the network is exported to a file format, e.g. VTK, which does not support PBCs.

    property spatial_burgers_vector: NDArray[float64]

      The Burgers vector of the segment, expressed in the global coordinate system of the simulation. This vector is calculated by transforming the true Burgers vector from the local lattice coordinate system to the global simulation coordinate system using the average orientation matrix of the crystal cluster the dislocation segment is embedded in.

    property true_burgers_vector: NDArray[float32]

      The Burgers vector of the dislocation expressed in the local coordinate system of the crystal the dislocation is located in. The true Burgers vectors of two dislocation lines may only be added if both belong to the same `cluster_id`.

  find_nodes() → list[Connector]

    Returns a list of all unique dislocation nodes in the network, each represented by a `Connector`.

    For a detailed description of what a “node” is, see the `Connector` class. The list returned by this method contains one (arbitrary) `Connector` from each network node, in no particular order. Each of these connectors serves as access into a node and can be used to visit the other connectors (dislocation arms) in the same node via `Connector.arms`:

        network = data.dislocations

        for node in network.find_nodes():
            print(node.arm_count, node.position)
            for arm in node.arms():
                print(arm.line.true_burgers_vector)

    Added in version 3.10.2.

  property lines: Sequence[Line]

    The list of dislocation lines in this dislocation network. This list-like object contains `Line` objects in arbitrary order and is read-only.

  set_line(index: int, true_burgers_vector: ArrayLike | None = None, cluster_id: int | None = None, points: ArrayLike | None = None, custom_color: ArrayLike | None = None)

    This method can be used to manipulate certain aspects of a `Line` in the network. Fields for which no new value is specified will keep their current values.

    Parameters:

      - index – The zero-based index of the dislocation line to modify in the `lines` array.

      - true_burgers_vector – The new lattice-space Burgers vector (`true_burgers_vector`).

      - cluster_id – The numeric ID of the crystallite cluster the dislocation line is embedded in (`cluster_id`).

      - points – An \((N, 3)\) NumPy array of Cartesian coordinates containing the dislocation’s vertices (`points`).

      - custom_color – RGB color to be used for rendering the line instead of the automatically determined color (`custom_color`).

    Example of a user-defined modifier function that manipulates the dislocation line data:

        import numpy as np

        def modify(frame: int, data: DataCollection):

            # Flip Burgers vector and line sense of each dislocation:
            for index, line in enumerate(data.dislocations.lines):
                data.dislocations_.set_line(index,
                    true_burgers_vector = np.negative(line.true_burgers_vector),
                    points = np.flipud(line.points))

            # Highlight all 1/6[121] dislocations by giving them a red color:
            for index, line in enumerate(data.dislocations.lines):
                if np.allclose(line.true_burgers_vector, (1/6, 2/6, 1/6)):
                    data.dislocations_.set_line(index, custom_color=(1, 0, 0))

class ovito.data.ElementType

  Base: `ovito.data.DataObject`

  This class describes a single “type”, for example a particle or bond type, that is part of a typed property array.

  The `ElementType` class is the generic base class used for all type descriptors in OVITO. It stores general attributes such as a type’s unique numeric `id`, its human-readable `name`, and its display `color`. Note that, for certain typed properties, OVITO uses more specific sub-classes such as `ParticleType` and `BondType`, which can store additional attributes such as `radius` and `mass`.

  The `ElementType` instances associated with a typed property are found in the `Property.types` list.

  You can use the `Property.type_by_id()` and `Property.type_by_name()` methods to look up a certain `ElementType` based on a numeric identifier or name string.

  property color: tuple[float, float, float]

    The color used when rendering elements of this type. This is a RGB tuple with components in the range 0.0 – 1.0.

    Default:

      `(1.0, 1.0, 1.0)`

  property enabled: bool

    Controls whether this type is currently active or inactive. This flag currently has a meaning only in the context of atomic structure identification. Some analysis modifiers manage a list of the structure types they can identify (e.g. FCC, BCC, etc.). The identification of individual structure types can be turned on or off by the user by changing their `enabled` flag. See `StructureIdentificationModifier.structures` for further information.

    Default:

      `True`

  property id: int

    The unique numeric identifier of the type (typically some positive `int`). The identifier is and must be unique among all element types in the `types` list of a typed `Property`. Thus, if you create a new element type, make sure you give it a unique id before inserting it into the `types` list of a typed property.

    Default:

      `0`

  property name: str

    The name of this type, e.g. the chemical element symbol of an atom type. This string may be empty, in which case its numeric `id` is the only way of referring to this type.

    Default:

      `''`

class ovito.data.Lines

  Base: `ovito.data.PropertyContainer`

  Added in version 3.10.0.

  The `Lines` class represents one or more 3D polylines. You can create an instance of this class in a `DataCollection` using the `GenerateTrajectoryLinesModifier` or the `DataCollection.lines.create()` method.

  You can retrieve existing `Lines` objects from a pipeline’s output through the `DataCollection.lines` dictionary view. Each `Lines` object has a unique `identifier` name that serves as a lookup key.

  `Lines` objects are always associated with `LinesVis` element, which controls the visual appearance of the lines in rendered images. You can access the visual element through the `vis` attribute provided by the `DataObject` base class. The `LinesVis` element provides the capability to visualize a local quantity defined at each line vertex using pseudo-color mapping.

  The `Lines` container uses the following standard properties with predefined names and data layouts. Additional per-vertex properties may be added using the `create_property()` method of the base class.

  Property name | Python access | Data type | Component names
  --- | --- | --- | ---
  Color | `colors` | float32 | R, G, B
  Position | `positions` | float64 | X, Y, Z
  Section | `sections` | int64 |
  Selection | `selection` | int8 |
  Time | `time_stamps` | int32 |

  Data model

  The `Lines` data object type is `PropertyContainer`, which means it consist of a set of uniform property arrays. The standard property Position stores the vertex coordinates. When rendering a `Lines` object, consecutive vertices get connected by linear line segments to form a polyline (which is also called a line “section”). To denote the end of a contiguous polyline and the start of a new one, the property Section must be filled with section identifiers, which mark consecutive sequences of vertices, each forming a separate polyline. Section identifiers are arbitrary integer numbers that stay the same within a polyline but change from one polyline to the next:

  Example: Definition of three polylines of length 2, 3, and 2, respectively.
  Vertex | Position | Section
  --- | --- | ---
  0 | \((x_0, y_0, z_0)\) | 0
  1 | \((x_1, y_1, z_1)\) | 0
  2 | \((x_2, y_2, z_2)\) | 1
  3 | \((x_3, y_3, z_3)\) | 1
  4 | \((x_4, y_4, z_4)\) | 1
  5 | \((x_5, y_5, z_5)\) | 2
  6 | \((x_6, y_6, z_6)\) | 2

  The `Lines` class provides the `create_line()` method to add new polylines to the container. It appends a list of vertex coordinates to the Position property and automatically assigns a new unique Section value to these vertices to define a new polyline.

  Note

  In a `Lines` object created by the `GenerateTrajectoryLinesModifier`, the Section property reflects the unique identifiers of the particles that traced the individual trajectory lines.

  If the Time property is present, it stores the animation frame number at which each vertex should appear in a trajectory animation. This feature allows to animate the lines over time and is used for particle trajectory visualization. The gradual rendering of lines is only active if the `LinesVis.upto_current_time` option is enabled in the attached visual element.

  property colors: Property | None

    The `Property` data array for the Color standard (line property); or `None` if that property is undefined.

  create_line(positions)

    Adds a new section (a polyline) to an existing `Lines` container. The container’s vertex `count` will be incremented by the number of newly inserted points. The method copies positions into the `Position` property array after extending the array and gives the new polyline a unique `Section` property value.

    Parameters:

      positions (ArrayLike) – The xyz coordinates for the new lines section (N x 3 array). N must be at least 2.

    Returns:

      The unique section identifier that was assigned to the newly added polyline.

    Return type:

      int

  property positions: Property | None

    The `Property` array containing the XYZ coordinates of the line vertices (standard property Position). May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `positions_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

  property sections: Property | None

    The `Property` array with the section each line vertex belongs to (standard property Section). May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `sections_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

  property selection: Property | None

    The `Property` data array for the `Selection` standard line vertices property; or `None` if that property is undefined.

  property time_stamps: Property | None

    The `Property` array with the time stamps of the line vertices (standard property Time). May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `time_stamps_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

class ovito.data.NearestNeighborFinder(N, data_collection)

  A utility class that finds the N nearest neighbors of a particle or around some other spatial query point.

  See also

  To find all neighbors within a spherical cutoff region around another particle, use the `CutoffNeighborFinder` instead.

  The class constructor takes the requested number of nearest neighbors, N, and a `DataCollection` containing the input particles and the optional simulation cell. N must be a positive integer not greater than 64, which is the maximum number of neighbors supported by this class.

  Note

  Keep in mind that, if the system contains only N particles or less, and if the simulation cell does not use periodic boundary conditions, then the search algorithm will return less than the requested number of nearest neighbors.

  Once the `NearestNeighborFinder` has been initialized, you can call its `find()` method to iterate over the sorted list of nearest neighbors of a given central particle:

      # Set up a neighbor finder for visiting the 12 closest neighbors of each particle.
      finder = NearestNeighborFinder(12, data)

      # Loop over all input particles:
      for index in range(data.particles.count):
          print("Nearest neighbors of particle %i:" % index)
          # Iterate over the neighbors of the current particle, starting with the closest:
          for neigh in finder.find(index):
              print(neigh.index, neigh.distance, neigh.delta)
              # The index can be used to access properties of the current neighbor, e.g.
              type_of_neighbor = data.particles.particle_types[neigh.index]

  In addition, the class provides the `find_at()` method, which determines the N nearest particles around some arbitrary spatial location:

      # Visit particles closest to some spatial point (x,y,z):
      xyz_coords = (0.0, 0.0, 0.0)
      for neigh in finder.find_at(xyz_coords):
          print(neigh.index, neigh.distance, neigh.delta)

  The corresponding `find_all()` and `find_all_at()` methods allow you to perform these queries efficiently for multiple particles or spatial locations at once.

  find(index)

    Returns an iterator that visits the N nearest neighbors of the given particle in order of ascending distance.

    Parameters:

      index (int) – The zero-based index of the central particle whose neighbors should be determined.

    Returns:

      A Python iterator that visits the N nearest neighbors of the central particle in order of ascending distance. For each neighbor being visited, the iterator returns an object having the following attributes:

      > - index: The global index of the current neighbor particle.

      > - distance: The distance of the current neighbor from the central particle.

      > - distance_squared: The squared neighbor distance.

      > - delta: The three-dimensional vector connecting the central particle with the current neighbor (correctly taking into account periodic boundary conditions).

    Return type:

      Iterator

    The index can be used to look up properties of the neighbor particle, as demonstrated in the first example code above.

    Note that several periodic images of the same particle may be visited if the periodic simulation cell is sufficiently small. Then the same particle index will appear more than once in the neighbor list. In fact, the central particle may be among its own neighbors in a sufficiently small periodic simulation cell. However, the computed neighbor vector (delta) will be unique for each image of a neighboring particle.

    The number of neighbors actually visited may be smaller than the requested number, N, if the system contains too few particles and is non-periodic.

    Note that the `find()` method will not find other particles located exactly at the same spatial position as the central particle for technical reasons. To find such particles too, which are positioned exactly on top of each other, use `find_at()` instead.

  find_all(indices=None)

    Finds the N nearest neighbors of each particle in the system or of the subset of particles specified by indices. This is the batch-processing version of `find()`, allowing you to efficiently compute the neighbor lists and neighbor vectors of several particles at once, without explicit for-loop and by making parallel use of all available processor cores.

    Parameters:

      indices (Optional[ArrayLike]) – List of zero-based particle indices for which the neighbor lists should be computed. If left unspecified, neighbor lists will be computed for every particle in the system.

    Returns:

      `(neigh_idx, neigh_vec)`

    Return type:

      tuple[NDArray[int64], NDArray[float64]]

    The method returns two arrays:

    `neigh_idx` : NumPy array of shape (M, N) storing the indices of neighbor particles, with M equal to len(indices) or, if indices is None, the total number of particles in the system. N refers to the number of nearest neighbors requested in the `NearestNeighborFinder` constructor. The computed indices in this array can be used to look up properties of neighbor particles in the global `Particles` object.

    `neigh_vec` : NumPy array of shape (M, N, 3) storing the xyz components of the three-dimensional neighbor vectors (“delta”), which connect the M central particles with their N respective nearest neighbors.

    Tip

    To compute all pair-wise distances in one go, i.e. the 2-norms of the neighbor vectors, you can do:

        distances = numpy.linalg.norm(neigh_vec, axis=2)   # Yields (M,N) array of neighbor distances

  find_all_at(coords)

    Finds the N nearest neighbors around each spatial point specified by coords. This is the batch-processing version of `find_at()`, allowing you to efficiently determine the closest neighbors around several spatial locations at once, without an explicit for-loop and by making parallel use of all available processor cores.

    Parameters:

      coords (ArrayLike) – NumPy array of shape (M, 3) containing the xyz coordinates of M query points at each of which the N nearest particles should be found.

    Returns:

      `(neigh_idx, neigh_vec)`

    Return type:

      tuple[NDArray[int64], NDArray[float64]]

    The method returns two NumPy arrays:

    `neigh_idx` : NumPy array of shape (M, N) storing the indices of nearest particles, with M equal to len(coords). N refers to the number of nearest neighbors requested in the `NearestNeighborFinder` constructor. Each neighbor list is sorted by distance from the corresponding query point.

    `neigh_vec` : NumPy array of shape (M, N, 3) storing the xyz components of the three-dimensional neighbor vectors (“delta”), which connect the M query points with their N respective nearest neighbors.

    If there is a particle located exactly at a query location, it will be among the returned neighbors for that point. This is in contrast to the `find_all()` function, which skips the central particles at the query locations.

    The number of returned neighbors may be smaller than the requested number, N, if the system contains fewer than N particles and is non-periodic. In this case, the corresponding columns of `neigh_idx` will be filled up with -1.

    Added in version 3.11.0.

  find_at(coords)

    Returns an iterator that visits the N nearest particles around a spatial point given by coords in order of ascending distance. Unlike the `find()` method, which queries the nearest neighbors of a physical particle, `find_at()` allows searching for nearby particles at arbitrary locations in space.

    Parameters:

      coords (ArrayLike) – A coordinate triplet (x,y,z) specifying the spatial location where the N nearest particles should be queried.

    Returns:

      A Python iterator that visits the N nearest neighbors in order of ascending distance. For each visited particle the iterator returns an object with the following attributes:

      > - index: The index of the current particle (starting at 0).

      > - distance: The distance of the current neighbor from the query location.

      > - distance_squared: The squared distance to the query location.

      > - delta: The three-dimensional vector from the query point to the current particle (correctly taking into account periodic boundary conditions).

    Return type:

      Iterator

    If there is a particle located exactly at the query location coords, it will be among the returned neighbors. This is in contrast to the `find()` function, which skips the central particle itself.

    The number of neighbors actually visited may be smaller than the requested number, N, if the system contains too few particles and is non-periodic.

class ovito.data.ParticleType

  Base: `ovito.data.ElementType`

  This data object describes one particle or atom type. In atomistic simulations, each chemical element is typically represented by an instance of the `ParticleType` class. The attributes of this class control how the particles of that type get visualized in terms of e.g. color, particle radius, shape, etc.

  The `ParticleType` class inherits several general attribute fields from its base class `ElementType`, e.g. the `color`, `name` and `id` fields. It adds specific fields for particles: `radius` and `shape`. Furthermore, the class has additional fields controlling the visual appearance of particles with user-defined shapes.

  The `ParticleType` instances all live in the `Property.types` list of the `'Particle Type'` standard `Property` array, which is accessible as `Particles.particle_types`. The association of particles with particle types is established through the unique type IDs. The following code shows how to first list all unique particle types defined for a structure and then print each particle’s type ID by iterating over the data array:

      # Access the property with the name 'Particle Type':
      type_property = data.particles.particle_types

      # Print list of particle types (their numeric IDs and names)
      for t in type_property.types:
          print(f'ID {t.id} -> {t.name}')

      # Print the numeric type ID of each particle:
      for tid in type_property[...]:
          print(tid)

  A common task is to look up the `ParticleType` that corresponds to a given numeric type ID. For this, the `Property` class provides the `type_by_id()` method:

      # Look up the particle type with unique ID 2:
      t = type_property.type_by_id(2)
      print(t.name, t.color, t.radius)

      # Iterate over all particles and print their type's name:
      for tid in type_property[...]:
          print(type_property.type_by_id(tid).name)

  Another common operation is to look up a particle type by name, for example the type representing a certain chemical element. For this type of look-up the `type_by_name()` method is available, which assumes that types have unique `names`:

      print(type_property.type_by_name('Si').id)   # Print numeric ID of type 'Si'

  property backface_culling: bool

    Activates back-face culling for the user-defined particle shape mesh to speed up rendering. If turned on, polygonal sides of the shape mesh facing away from the viewer will not be rendered. You can turn this option off if the particle’s shape is not closed and two-sided rendering is required. This option only has an effect if a user-defined shape has been assigned to the particle type using the `load_shape()` method.

    Default:

      `True`

  property highlight_edges: bool

    Activates the highlighting of the polygonal edges of the user-defined particle shape during rendering. This option only has an effect if a user-defined shape has been assigned to the particle type using the `load_shape()` method.

    Default:

      `False`

  load_defaults()

    Given the type’s chemical `name`, which must have been set before invoking this method, initializes the type’s `color`, `radius`, `vdw_radius` and `mass` fields with default values from OVITO’s internal database of chemical elements.

    See also

    `Property.add_type_name()`

  load_shape(filepath: str)

    Assigns a user-defined shape to the particle type. Particles of this type will subsequently be rendered using the polyhedral `mesh` loaded from the given file. The method will automatically detect the format of the geometry file and supports standard file formats such as OBJ, STL and VTK that contain triangle meshes, see this table.

    The shape loaded from the geometry file will be scaled with the `radius` value set for this particle type or the per-particle value stored in the `Radius` particle property if present. The shape of each particle will be rendered such that its origin is located at the coordinates of the particle (`Position` property).

    The following example script demonstrates how to load a user-defined shape for the first particle type (index 0) loaded from a LAMMPS dump file, which can be accessed through the `Property.types` list of the `Particle Type` particle property.

        pipeline = import_file("input/simulation.dump")
        pipeline.add_to_scene()

        types = pipeline.source.data.particles_.particle_types_
        types.type_by_id_(1).load_shape("input/tetrahedron.vtk")
        types.type_by_id_(1).highlight_edges = True

  property mass: float

    The mass of this particle type.

    Default:

      `0.0`

  property mesh: TriangleMesh | None

    The `TriangleMesh` object to be used as custom shape for rendering particles of this type. You can either programmatically create a `TriangleMesh` from a list of vertices and faces and assign it to this field, or let the `load_shape()` method read the shape mesh from a separate geometry file. Also some file readers (e.g. GSD and Aspherix) may generate the shape mesh automatically based on information found in the simulation file.

    The `ParticlesVis` element, which is responsible for visualizing a particle system, will render an instance of the mesh at each particle site, uniformly scaled by the particle’s `radius`, translated by the coordinates taken from the `Position` particle property, and rotated by the quaternion transformation taken from the `Orientation` particle property.

    Note: This mesh will be ignored by the `ParticlesVis` element unless the type’s `shape` is set to `ParticlesVis.Shape.Mesh`.

    Default:

      `None`

    Added in version 3.8.0.

  property radius: float

    This attribute controls the display radius of all particles of this type.

    When set to zero, particles of this type will be rendered using the standard size specified by the `ParticlesVis.radius` parameter. Furthermore, precedence is given to any per-particle sizes assigned to the `Radius` particle property if that property has been defined.

    Default:

      `0.0`

    The following example script demonstrates how to set the display radii of two particle types loaded from a simulation file, which can be accessed through the `Property.types` list of the `Particle Type` particle property.

        pipeline = import_file("input/simulation.dump")
        pipeline.add_to_scene()

        def setup_particle_types(frame, data):
            types = data.particles_.particle_types_
            types.type_by_id_(1).name = "Cu"
            types.type_by_id_(1).radius = 1.35
            types.type_by_id_(2).name = "Zr"
            types.type_by_id_(2).radius = 1.55
        pipeline.modifiers.append(setup_particle_types)

  property shape: ParticlesVis.Shape

    Selects the geometric shape used when rendering particles of this type. Supported modes are:

    > - `ParticlesVis.Shape.Unspecified` (default)

    > - `ParticlesVis.Shape.Sphere`

    > - `ParticlesVis.Shape.Box`

    > - `ParticlesVis.Shape.Circle`

    > - `ParticlesVis.Shape.Square`

    > - `ParticlesVis.Shape.Cylinder`

    > - `ParticlesVis.Shape.Spherocylinder`

    > - `ParticlesVis.Shape.Mesh`

    By default, the standard particle shape that is set in the `ParticlesVis` visual element is used to render particles of this type. Parameter values other than `Unspecified` allow you to control the rendering shape on a per-type basis. Mode `Sphere` includes ellipsoid and superquadric particle shapes, which are enabled by the presence of the `Aspherical Shape` and `Superquadric Roundness` particle properties.

    The `load_shape()` method lets you specify a user-defined `mesh` geometry for this particle type. Calling this method automatically switches the shape parameter to mode `Mesh`.

    Setting the shapes of particle types permanently, i.e., for all frames of a loaded simulation trajectory, typically requires a user-defined modifier function. This function is inserted into the `Pipeline` to make the necessary changes to the `ParticleType` objects associated with the `Property` named `Particle Type`:

        from ovito.io import import_file
        from ovito.vis import *

        # Load a simulation file containing numeric particle types 1, 2, 3, ...
        pipeline = import_file("input/nylon.data")
        pipeline.add_to_scene()

        # Set the default particle shape in the ParticlesVis visual element,
        # which will be used by all particle types for which we do not specify a different shape below.
        pipeline.compute().particles.vis.shape = ParticlesVis.Shape.Box
        pipeline.compute().particles.vis.radius = 1.0

        # A user-defined modifier function that configures the shapes of particle types 1 and 2:
        def setup_particle_types(frame, data):
            # Write access to property 'Particle Type':
            types = data.particles_.particle_types_
            # Write access to numeric ParticleTypes, which are sub-objects of the Property object:
            types.type_by_id_(1).radius = 0.5
            types.type_by_id_(1).shape = ParticlesVis.Shape.Cylinder
            types.type_by_id_(2).radius = 1.2
            types.type_by_id_(2).shape = ParticlesVis.Shape.Sphere
        pipeline.modifiers.append(setup_particle_types)

        # Render a picture of the 3d scene:
        vp = Viewport(camera_dir = (-2,1,-1))
        vp.zoom_all()
        vp.render_image(filename='output/particles.png', size=(320,240), renderer=TachyonRenderer())

  property use_mesh_color: bool

    Use the intrinsic mesh color(s) instead of the particle color when rendering particles of this type. This option only has an effect if a user-defined shape `mesh` has been assigned to this particle type, e.g., by calling the `load_shape()` method.

    Default:

      `False`

  property vdw_radius: float

    The van der Waals radius of the particle type. This value is used by the `CreateBondsModifier` to decide which pairs of particles are close enough to be connected by a bond. In contrast to the `radius` parameter, the van der Waals radius does not affect the visual appearance of the particles of this type.

    Default:

      `0.0`

class ovito.data.Particles

  Base: `ovito.data.PropertyContainer`

  This object stores a system of particles and their properties. Additional things which are typically associated with molecular systems, e.g. `bonds`, `angles`, etc. are stored in corresponding sub-objects.

  A `Particles` object is usually part of a `DataCollection` where it can be found via the `DataCollection.particles` property.

  The total number of particles is specified by the `count` attribute, which the `Particles` class inherits from its `PropertyContainer` base class.

  Particles are usually associated with a set of properties, e.g. position, type, velocity. Each of the properties is represented by a separate `Property` data object, which is basically an array of numeric values, one for each particle in the system. A particle property is identified by its unique name and can be looked up via the dictionary interface of the `PropertyContainer` base class. OVITO predefines a set of standard properties, which have a fixed data layout, meaning, and role:

  Standard property name | Data type | Component names
  --- | --- | ---
  Angular Momentum | float64 | X, Y, Z
  Angular Velocity | float64 | X, Y, Z
  Aspherical Shape | float32 | X, Y, Z
  Centrosymmetry | float64 |
  Charge | float64 |
  Cluster | int64 |
  Color | float32 | R, G, B
  Coordination | int32 |
  Deformation Gradient | float64 | XX, YX, ZX, XY, YY, ZY, XZ, YZ, ZZ
  Dipole Magnitude | float64 |
  Dipole Orientation | float64 | X, Y, Z
  Displacement Magnitude | float64 |
  Displacement | float64 | X, Y, Z
  DNA Strand | int32 |
  Elastic Deformation Gradient | float64 | XX, YX, ZX, XY, YY, ZY, XZ, YZ, ZZ
  Elastic Strain | float64 | XX, YY, ZZ, XY, XZ, YZ
  Force | float64 | X, Y, Z
  Kinetic Energy | float64 |
  Mass | float64 |
  Molecule Identifier | int64 |
  Molecule Type | int32 |
  Nucleobase | int32 |
  Nucleotide Axis | float64 | X, Y, Z
  Nucleotide Normal | float64 | X, Y, Z
  Orientation | float32 | X, Y, Z, W
  Particle Identifier | int64 |
  Particle Type | int32 |
  Periodic Image | int32 | X, Y, Z
  Position | float64 | X, Y, Z
  Potential Energy | float64 |
  Radius | float32 |
  Rotation | float64 | X, Y, Z, W
  Selection | int8 |
  Spin | float64 |
  Strain Tensor | float64 | XX, YY, ZZ, XY, XZ, YZ
  Stress Tensor | float64 | XX, YY, ZZ, XY, XZ, YZ
  Stretch Tensor | float64 | XX, YY, ZZ, XY, XZ, YZ
  Structure Type | int32 |
  Superquadric Roundness | float32 | Phi, Theta
  Torque | float64 | X, Y, Z
  Total Energy | float64 |
  Transparency | float32 |
  Vector Color | float32 | R, G, B
  Vector Transparency | float32 |
  Velocity Magnitude | float64 |
  Velocity | float64 | X, Y, Z

  For some of the most important properties, this container class provides quick access getters such as `positions`, `identifiers`, or `particle_types` to look them up:

      coords = data.particles.positions

  User-defined particle properties having non-standard names, and standard properties for which no quick access getter exists, can be looked up by literal name:

      mol_ids = data.particles['Molecule Identifier']

  For more information on how to add or modify particle properties, please see the `PropertyContainer` and `Property` classes.

  add_particle(position)

    Adds a new particle to the model. The particle `count` will be incremented by one. The method assigns position to the `Position` property of the new particle. The values of all other properties are initialized to zero.

    Parameters:

      position (ArrayLike) – The xyz coordinates for the new particle.

    Returns:

      The 0-based index of the newly created particle, which is `(Particles.count-1)`.

    Return type:

      int

  property angles: PropertyContainer | None

    A `PropertyContainer` storing the list of angles defined for the molecular model (may be `None`).

  property bonds: Bonds | None

    The `Bonds` data object storing the list of bonds and their properties (may be `None`).

  property colors: Property | None

    The `Property` data array for the `Color` standard particle property; or `None` if that property is undefined.

  create_bonds(*, vis_params=None, **params)

    This convenience method conditionally creates and associates a `Bonds` object with this `Particles` parent object. If there is already an existing bonds object (`bonds` is not `None`), then that bonds object is replaced with a modifiable copy if necessary. The attached `BondsVis` element is preserved.

    Parameters:

      - params (Any) – Key-value pairs passed to the method as keyword arguments are used to set attributes of the `Bonds` object (even if the bonds object already existed).

      - vis_params (Mapping[str, Any] | None) – Optional dictionary to initialize attributes of the attached `BondsVis` element (only used if the bonds object is newly created by the method).

    Return type:

      Bonds

    The logic of this method is roughly equivalent to the following code:

        def create_bonds(particles: Particles, vis_params=None, **params) -> Bonds:
            if particles.bonds is None:
                particles.bonds = Bonds()
                if vis_params:
                    for name, value in vis_params.items(): setattr(particles.bonds.vis, name, value)
            for name, value in params.items(): setattr(particles.bonds_, name, value)
            return particles.bonds_

    Usage example:

        pairs = [(0, 1), (1, 2), (2, 0)] # Pairs of particle indices to connect by bonds
        bonds = data.particles_.create_bonds(count=len(pairs), vis_params={'width': 0.6})
        bonds.create_property('Topology', data=pairs)

    Added in version 3.7.4.

  delta_vector(a, b, cell, return_pbcvec=False)

    Computes the vector connecting two particles a and b in a periodic simulation cell by applying the minimum image convention.

    This is a convenience wrapper for the `SimulationCell.delta_vector()` method, which computes the vector between two arbitrary spatial locations \(r_a\) and \(r_b\) taking into account periodic boundary conditions. The version of the method described here takes two particle indices a and b as input, computing the shortest vector \({\Delta} = (r_b - r_a)\) between them using the minimum image convention. Please see the `SimulationCell.delta_vector()` method for further information.

    Parameters:

      - a (int | Sequence[int]) – Zero-based index of the first input particle. This may also be an array of particle indices.

      - b (int | Sequence[int]) – Zero-based index of the second input particle. This may also be an array of particle indices with the same length as a.

      - cell (SimulationCell) – The periodic domain. Typically, `DataCollection.cell` is used as argument here.

      - return_pbcvec (bool) – If true, lets the method also return the vector \(n\), which specifies how often the computed particle-to-particle vector crosses the cell’s face.

    Returns:

      The delta vector and, optionally, the vector \(n\).

    Return type:

      ndarray | tuple[ndarray, ndarray]

  property dihedrals: PropertyContainer | None

    A `PropertyContainer` storing the list of dihedrals defined for the molecular model (may be `None`).

  property forces: Property | None

    The `Property` data array for the `Force` standard particle property; or `None` if that property is undefined.

  property identifiers: Property | None

    Returns a `Property` data array containing the values of the `Particle Identifier` standard particle property; or `None` if that particle property does not exist.

    The property array stores the numerical IDs that are typically used by simulation codes to uniquely identify individual particles.

    Note

    A particle identifier is an arbitrary and unique 64-bit integer value permanently associated with a particle. In contrast, the particle’s index is implicitly given by the particle’s current position within the particles list.

    If you delete some of the particles from the system, using the `DeleteSelectedModifier` or the `delete_elements()` method for example, the indices of the remaining particles get typically shifted but their unique IDs stay the same.

    Some of OVITO’s simulation file readers provide the option to sort the list of particles by ID during import to obtain a stable ordering. Generally, however, the storage order of particles is arbitrary and can vary between frames of a trajectory. The `remap_indices()` method can be useful in this situation.

    Note

    The value of `identifiers` may be `None`, which means particles don’t have any identifiers. Many operations in OVITO then assume that the ordering and total count of particles are constant throughout the entire simulation trajectory and the identities are implicitly given by the particles’ indices.

    Given some list of zero-based particle indices, determining the corresponding unique identifiers requires just a simple NumPy indexing expression:

        query_indices = [0, 7, 3, 2] # <-- zero-based particle indices for which we want to look up IDs
        ids = data.particles.identifiers[query_indices]
        assert len(ids) == len(query_indices)

    The reverse lookup, i.e., finding the indices at which particles with certain IDs are stored in the list, requires some more work. That’s because particles may be stored in arbitrary order, i.e., the sequence of unique IDs is generally not sorted nor contiguous. A rather slow approach is to `search` through the entire array of IDs to locate the one we are looking for:

        query_id = 37 # <-- a unique particle ID we are looking for
        index = numpy.argwhere(data.particles.identifiers == query_id)[0,0]
        assert data.particles.identifiers[index] == query_id

    We can speed things up with some extra effort, which pays off when there is a need to look up several particle IDs. To this end, we first `sort` the list of IDs, then perform a more efficient `sorted search`, and finally map the found indices back to the original particle ordering:

        query_ids = [2, 37, 8] # <-- some unique particle IDs we want to look up all at once
        ordering = numpy.argsort(data.particles.identifiers)
        indices = ordering[numpy.searchsorted(data.particles.identifiers, query_ids, sorter=ordering)]
        assert numpy.array_equal(data.particles.identifiers[indices], query_ids)

    The above `assert` statements are for illustration purposes only.

  property impropers: PropertyContainer | None

    A `PropertyContainer` storing the list of impropers defined for the molecular model (may be `None`).

  property masses: Property | None

    The `Property` data array for the `Mass` standard particle property; or `None` if that property is undefined.

  property orientations: Property | None

    The `Property` data array for the `Orientation` standard particle property; or `None` if that property is undefined.

  property particle_types: Property | None

    The `Property` data array for the `Particle Type` standard particle property; or `None` if that property is undefined.

  property positions: Property | None

    Returns the `Property` data array storing the particle coordinates, i.e. the values of the `Position` standard particle property. Accessing this field is equivalent to a name-based lookup in the `PropertyContainer`:

        assert data.particles.positions is (data.particles['Position'] if 'Position' in data.particles else None)

    Under special circumstances the `Position` particle property might not be defined (yet). Then the value is `None`.

    Note

    The returned `Property` will likely be write-protected. If you intend to modify (some of) the particle coordinates in the property array, request a modifiable version of the array by using the underscore notation:

        data.particles_.positions_[:] = new_coordinates

    Alternatively, you can use the `create_property()` method to newly create or overwrite the entire property:

        data.particles_.create_property('Position', data=new_coordinates)

  remap_indices(particles: Particles, indices: Sequence[int] = None) → ndarray | slice

    In case the storage order of atoms or particles changes during the course of a simulation, this method can determine the mapping of particles from one snapshot of the trajectory to another. It uses the unique `identifiers` of the particles to do that.

    Given two data collections A and B containing the same set of particles but in different order, `remap_indices()` determines for each particle in B the zero-based index at which the same particle is found in A. For instance:

        >>> A = pipeline.compute(frame=0)
        >>> B = pipeline.compute(frame=1)
        >>> A.particles.identifiers[...]
        [8 101  5 30 99]
        >>> B.particles.identifiers[...]
        [5 101 30 99  8]
        >>> A.particles.remap_indices(B.particles)
        [2 1 3 4 0]

    The index mapping generated by `remap_indices()` allows you to retrieve property values of particles in A in the same order in which they appear in B, making it easy to perform computations involving property values at different trajectory timesteps, e.g.:

        mapping = A.particles.remap_indices(B.particles)
        displacements = B.particles.positions - A.particles.positions[mapping]

    `remap_indices()` compares the unique `identifiers` stored in the `Particle Identifier` property arrays of both snapshots to compute the index permutation map. If this property is not defined, which may be the case if the imported trajectory file did not contain atom IDs, the `remap_indices()` method simply assumes that both snapshots use the same constant storage order and returns the identity mapping - as a Python `slice` object for optimal performance when being used for NumPy indexing. A slice object is also returned in case the ordering of particle IDs turns out to be the same in both snapshots and no remapping is necessary.

    Note

    An error will be raised if particles with duplicate IDs occur in snapshot A - but it is okay if B contains duplicate IDs. Furthermore, it is not an error if A contains additional particles that are not present in B - as long as all particles from B are found in A.

    The default behavior of the method is to look up all particles of B in A. But the index mapping can also be established just for a subset of particles from B by supplying the optional parameter indices. The method expects an array of zero-based indices specifying which particles from snapshot B should be looked up in snapshot A. The returned mapping will have the same length as indices. Example:

        # The numeric ID of atom type 'H':
        hydrogen_type = B.particles.particle_types.type_by_name('H').id
        # Determine the indices of all H atoms in data collection B:
        hydrogen_indices = numpy.flatnonzero(B.particles.particle_types == hydrogen_type)

        # Determine the corresponding indices of the same atoms in data collection A:
        mapping = A.particles.remap_indices(B.particles, hydrogen_indices)

        # In snapshot A the same particles are all H atoms too:
        assert numpy.all(A.particles.particle_types[mapping] == hydrogen_type)

    Added in version 3.7.5.

  property selection: Property | None

    The `Property` data array for the `Selection` standard particle property; or `None` if that property is undefined.

  property structure_types: Property | None

    The `Property` data array for the `Structure Type` standard particle property; or `None` if that property is undefined.

  property velocities: Property | None

    The `Property` data array for the `Velocity` standard particle property; or `None` if that property is undefined.

class ovito.data.Property

  Base: `ovito.data.DataObject`

  A storage array for the values of one uniform property of particles, bonds, voxel grid cells, etc. For example, the “Position” property of particles is represented by one `Property` object storing the xyz coordinates of all the particles.

  `Property` objects are always managed by a specific sub-type of the `PropertyContainer` class, for example `Particles`, `Bonds`, `VoxelGrid`, or `DataTable`. These container classes allow to add and remove properties to the data elements they represent. The properties within the `PropertyContainer` are accessed by name. Here, for example, the particle property holding the particle coordinates:

      positions = data.particles['Position']

  This `Property` object behaves almost like a regular NumPy array. For example, you can access the value for the i-th element using array indexing:

      print('XYZ coordinates of first particle:', positions[0])
      print('z-coordinate of sixth particle:', positions[5,2])
      print(positions.shape)   # --> (data.particles.count, 3)

  Since the “Position” standard property has three components, this `Property` object is an array of shape (N,3). Properties can be either vectorial or scalar, and they can hold uniform data types `float64`, `float32`, `int8`, `int32` or `int64`.

  If you want to set or modify the values stored in a property array, make sure you are working with a modifiable version of the `Property` object by employing the underscore notation, e.g.:

      modifiable_positions = data.particles_['Position_']
      modifiable_positions[0] += (2.0, 0.0, 0.5)

  Typed properties

  In OVITO, the standard particle property “Particle Type” contains the types of particles encoded as integer values, e.g.:

      >>> data = pipeline.compute()
      >>> type_property = data.particles['Particle Type']
      >>> print(type_property[...])
      [2 1 3 ..., 2 1 2]

  The property array stores numeric type identifiers denoting each particle’s chemical type (e.g. 1=Cu, 2=Ni, 3=Fe, etc.). The mapping of unique numeric IDs to human-readable type names is found in the `types` list, which is attached to the `Property` array, making it a so-called typed property. This list contains one `ParticleType` descriptor per unique numerical type, specifying its human-readable `name` as well as other attributes such as display `color`, `radius` and `mass`:

      >>> for t in type_property.types:
      ...     print(t.id, t.name, t.color, t.radius)
      ...
      1 Cu [0.188 0.313 0.972] 0.74
      2 Ni [0.564 0.564 0.564] 0.77
      3 Fe [1 0.050 0.050] 0.74

  Numeric type IDs typically start at 1 and form a consecutive sequence as in the example above. But they don’t have to. The descriptors may be listed in any order and their numeric IDs may be arbitrary integers. Thus, in general, it is not valid to directly use a numeric type ID as an index into the `types` list. Instead, the `type_by_id()` method should be used to look up the `ParticleType` descriptor for a given numeric ID:

      >>> for i,t in enumerate(type_property): # loop over the type IDs of particles
      ...     print(f"Atom {i} is of type {type_property.type_by_id(t).name}")
      ...
      Atom 0 is of type Ni
      Atom 1 is of type Cu
      Atom 2 is of type Fe
      Atom 3 is of type Cu

  Similarly, a `type_by_name()` method exists that allows you to look up a `ParticleType` from the `types` list by name. For example, to count the number of Fe atoms in a system, we first need to determine the numeric ID of the type “Fe” and then count the number of occurrences of the value in the `Property` array:

      >>> Fe_type_id = type_property.type_by_name('Fe').id  # Determine numeric ID of the 'Fe' type.
      >>> numpy.count_nonzero(type_property == Fe_type_id)  # Count particles having that type ID.
      957

  Note that the data model supports multiple type classifications per particle. For example, while the “Particle Type” standard particle property, stores the chemical types of atoms (e.g. C, H, Fe, …), the “Structure Type” property stores the structural lattice types computed for each atom (e.g. FCC, BCC, …). In other words, multiple typed properties can co-exist to define several orthogonal classifications, and each typed property maintains its separate list of type descriptors in the associated `types` list.

  New types can be added to a typed property either using `add_type_id()` or `add_type_name()`. Use the former method if it is important that the new type gets a particular numeric ID (which must not collide with existing types in the `types` list). Use the latter method if you don’t care about the numeric ID and let the method automatically assign a unique ID to the new type.

  See also

  Typed properties

  add_type_id(id: int, container: PropertyContainer, name: str = '') → ElementType | ParticleType | BondType

    Creates a new numeric `ElementType` with the given numeric id and an optional human-readable name and adds it to this property’s `types` list. If the list already contains an existing element type with the same numeric id, that existing type will be returned (without updating its name).

    Additionally, you must specify the `PropertyContainer` containing this property object as second parameter, because it determines the kind of `ElementType` to create. For example, when calling `add_type_id()` on the property “Particle Type” of a `Particles` container, this method will create a new `ParticleType` object – a specific sub-class of the more general `ElementType` class. Furthermore, if name matches one of the standard type names predefined for that particle property, e.g., a chemical symbol in case of the “Particle Type” property, the type’s display color, radius, and mass will be pre-configured (as if `load_defaults()` was called).

        type_property = data.particles_.create_property("Particle Type")
        type_1 = type_property.add_type_id(1, data.particles, name="A")
        type_2 = type_property.add_type_id(2, data.particles, name="B")

        # Configure visual appearance of the two ParticleTypes
        type_1.radius = 0.9; type_1.color = (1.0, 0.0, 0.0)
        type_2.radius = 1.2; type_2.color = (0.0, 0.0, 1.0)

        # Randomly assign types "A" (1) or "B" (2) to the particles
        type_property[...] = numpy.random.randint(low=1, high=1+2, size=data.particles.count)

    See also

    `add_type_name()`

    Added in version 3.9.0.

  add_type_name(name: str, container: PropertyContainer) → ElementType | ParticleType | BondType

    Creates a new `ElementType` with the given human-readable `name` and adds it to this property’s `types` list. A unique numeric `id` will be automatically assigned to the type (starting at 1). If the list already contains an existing element type of the same name, that existing type will be returned.

    Additionally, you must specify the `PropertyContainer` containing this property object as second parameter, because it determines the kind of `ElementType` to create. For example, when calling `add_type_name()` on the property “Particle Type” of a `Particles` container, this method will create a new `ParticleType` object – a specific sub-class of the more general `ElementType` class. Furthermore, if name matches one of the standard type names predefined for that particle property, e.g., a chemical symbol in case of the “Particle Type” property, the type’s display color, radius, and mass will be pre-configured (as if `load_defaults()` was called).

        type_property = data.particles_.create_property("Particle Type")
        type_Au = type_property.add_type_name("Au", data.particles)
        type_Ag = type_property.add_type_name("Ag", data.particles)

        # Randomly assign types "Au" or "Ag" to the particles
        type_property[...] = numpy.random.choice([type_Au.id, type_Ag.id], size=data.particles.count)

    See also

    - `add_type_id()`

    - Example FR1: Custom file reader loading particle properties and the simulation cell

    Added in version 3.9.0.

  property component_count: int

    The number of vector components if this is a vector property; or 1 if this is a scalar property.

    This attribute is read-only. For predefined standard properties, OVITO automatically determines the vector component count. For user-defined properties you can specify the component count during creation with the `PropertyContainer.create_property()` method.

  property component_names: Sequence[str]

    The list of component names if this is a vectorial property. For example, the `Position` particle property has three components: `['X', 'Y', 'Z']`.

    The number of elements in this list must always be equal to `component_count` or zero, in which case the property components are referenced by numeric index (1, 2, 3, …).

    This list is read-only. For predefined standard properties, OVITO automatically initializes the component names. For user-defined properties you may specify the component names during creation of the property with the `PropertyContainer.create_property()` method.

  property name: str

    The name of the property – a non-empty string.

    The name may contain spaces, digits, or special characters, but no dots, because `.` is used by OVITO as a delimiter for vector `component_names`.

  remove_type_id(id: int)

    Removes the numeric `ElementType` with the given numeric id from this property’s `types` list. If the list does not contain an element type with the specified id, this method raises a `KeyError`.

    Added in version 3.15.0.

  type_by_id(id: int, require: bool = True) → ElementType | ParticleType | BondType | None

    Looks up a `ElementType` from this property’s `types` list based on its unique numeric ID. Depending on the parameter require, raises a `KeyError` or returns `None` if no type with the numeric ID exists.

    Usage example:

        # Iterate over the numeric per-particle types stored in the 'Structure Type'
        # particle property array and print the corresponding human-readable type names:
        for index, type_id in enumerate(data.particles.structure_types):
            print("Atom {} is a {} atom".format(
                index, data.particles.structure_types.type_by_id(type_id).name))

    An “underscore version” of the method is available, which should be used whenever you intend to modify the returned type object. `type_by_id_()` implicitly calls `make_mutable()` on the `ElementType` to make sure it can be changed without unexpected side effects:

        # Give some names to the numeric atom types from a LAMMPS simulation:
        data.particles_.particle_types_.type_by_id_(1).name = 'C'
        data.particles_.particle_types_.type_by_id_(2).name = 'H'

  type_by_name(name: str, require: bool = True) → ElementType | ParticleType | BondType | None

    Looks up an `ElementType` from this property’s `types` list based on its `name`. If multiple types exist with the same name, the first one in the list is returned. Depending on the parameter require, raises a `KeyError` or returns `None` if there isn’t a type with that name.

    Usage example:

        # Look up the numeric ID of atom type Si and count how many times it appears in the 'Particle Type' array
        id_Si = data.particles.particle_types.type_by_name('Si').id
        Si_atom_count = numpy.count_nonzero(data.particles.particle_types == id_Si)

    An “underscore version” of the method is available, which should be used whenever you intend to modify the returned type object. `type_by_name_()` implicitly calls `make_mutable()` on the `ElementType` to make sure it can be changed without unexpected side effects:

        # Rename a structure type created by the PTM modifier:
        data.particles_.structure_types_.type_by_name_('Hexagonal diamond').name = 'Wurtzite'

  property types: MutableSequence[ElementType]

    The list of `ElementType` descriptors associated with this property if it is a typed property.

    A typed property, such as the “Particle Type” property for particles, stores each particle’s type information, for example its chemical type, in the form of a numeric type ID in a uniform data array. The `types` list represents a look-up table containing a descriptor for each unique numeric type, which maps the numeric ID to a corresponding human-readable type name, a chemical symbol for example.

    The `types` list consists of instances of the `ElementType` class or one of its sub-classes, describing the individual types. For each unique type, `ElementType.id` specifies the numeric identifier and `ElementType.name` the human-readable name. Furthermore, `ElementType.color` specifies the color used for rendering elements of this type.

    Some typed properties in OVITO use a sub-class of `ElementType` to associate additional information with each unique type. For example, the “Particle Type” property for `Particles` uses `ParticleType` descriptors. This descriptor class defines additional fields such as `ParticleType.radius` and `ParticleType.mass` for each type.

    Note

    The type descriptors are stored in arbitrary order in the `types` list. Therefore, you should never use a numeric type ID as a direct index into this list to look up the corresponding type descriptor. Instead, use the `type_by_id()` method to retrieve the `ElementType` corresponding to a given numeric type ID.

    If you want to manipulate the descriptors in the `types` list one by one, you should iterate over the “underscore” version of the list, `types_`, to automatically make all the type descriptors mutable. This shortcut implicitly invokes `make_mutable()` on each `ElementType`, making sure it can be modified without unexpected side effects:

        # Get a mutable reference to the "Particle Type" property array.
        type_property = data.particles_.particle_types_

        # Iterate over all defined ParticleType descriptors and modify their radius.
        for t in type_property.types_:
            t.radius *= 0.5

    See also

    - Type descriptor lookup: `type_by_id()`, `type_by_name()`

    - Adding new types: `add_type_id()`, `add_type_name()`

    - Variants of type descriptors: `ElementType`, `ParticleType`, `BondType`

class ovito.data.PropertyContainer

  Base: `ovito.data.DataObject`

  A dictionary-like object storing a set of `Property` objects.

  It implements the `collections.abc.Mapping` interface. That means it can be used like a standard read-only Python `dict` object to access the properties by name, e.g.:

      data = pipeline.compute()

      positions = data.particles['Position']
      has_selection = 'Selection' in data.particles
      name_list = data.particles.keys()

  New properties are typically added to a container with a call to `create_property()` as described here. To remove an existing property from a container, you can use Python’s `del` statement:

      del data.particles_['Selection']

  OVITO has several concrete implementations of the abstract `PropertyContainer` interface:

  > - `Particles`

  > - `Bonds`

  > - `VoxelGrid`

  > - `DataTable`

  > - `Lines`

  > - `Vectors`

  > - `SurfaceMesh.vertices`

  > - `SurfaceMesh.faces`

  > - `SurfaceMesh.regions`

  append(new_row, strict=True)

    Appends a new row of data to the end of the `PropertyContainer` by incrementing the `count` by one. The data of the new element is provided as a dictionary of key-value pairs, where the keys are the property names in the container and the values are the corresponding property values. If the container type does not support appending elements, a `RuntimeError` is raised.

    Parameters:

      - new_row (Mapping[str, Number | Sequence[Number]]) – A dictionary mapping property names to their values for the new row.

      - strict (bool) – If set to `True` (default), a strict checking of the keys in new_row is performed.

    Returns:

      The zero-based index of the newly added row.

    Return type:

      int

    When the strict parameter is set to `True` (default), the dictionary keys must match the container’s property names exactly. In other words, you have to specify a value for every existing property in the container (and only those properties). If any keys are missing or extra, a `KeyError` is raised.

    When strict is set to `False`:

    > - Missing keys are ignored, and the corresponding property values are initialized to 0.

    > - For extra keys, new properties are added to the container and initialized to 0 for all existing elements.

    > - The dtype and number of vector components of new properties are inferred from the provided values.

    Example usage of the `append()` method:

        print(sorted(data.particles.keys()))
        # >>> ['Force', 'Particle Identifier', 'Particle Type', 'Position', 'peatom']
        print(data.particles.count)
        # >>> 7071
        data.particles_.append({"Force": (1.2, -1.2, 3.1),
                                "Particle Identifier": 7072,
                                "Particle Type": 2,
                                "Position": (31.2, 33.0, 29.8),
                                "peatom": -4.32})
        print(data.particles.count)
        # -> 7072
        data.particles_.append({"Charge": -0.33, "Gradient 2D": (1.3, 1.2)}, strict=False)
        print(sorted(data.particles.keys()))
        # >>> ['Charge', 'Force', 'Gradient 2D', 'Particle Identifier', 'Particle Type', 'Position', 'peatom']

  property count: int

    The number of data elements in this container, e.g. the number of particles. This value is always equal to the lengths of all `Property` arrays managed by this container.

  create_property(name, dtype=None, components=None, data=None)

    Adds a new property with the given name to the container and optionally initializes its element-wise values with data. If a property with the given name already exists in the container, that existing property is returned (after replacing its contents with data if provided).

    Parameters:

      - name (str) – Name of the property to create.

      - data (ArrayLike | None) – Optional array with initial values for the new property. The size of the array must match the element `count` of the container and the shape must be consistent with the number of components of the property to be created.

      - dtype (DTypeLike | None) – Data type of the user-defined property. Must be either `int`, `float`, `numpy.int8`, `numpy.int32`, `numpy.int64`, `numpy.float32`, or `numpy.float64`.

      - components (int | Sequence[str] | None) – Number of vector components of the user-defined property (1 if not specified) or a list of strings specifying the property’s `component_names`.

    Returns:

      The new `Property` object.

    Return type:

      Property

    You can create standard and user-defined properties in a container. A standard property with a prescribed data layout is automatically created if name matches one of the predefined names for the container type:

    > - `Particles`: List of standard particle properties

    > - `Bonds`: List of standard bond properties

    > - `SurfaceMesh.vertices`: List of standard mesh vertex properties

    > - `SurfaceMesh.faces`: List of standard mesh face properties

    > - `SurfaceMesh.regions`: List of standard mesh region properties

    > - `Vectors`: List of standard vector properties

    > - `Lines`: List of standard line properties

    The length of the provided data array must match the number of elements in the container, which is given by `PropertyContainer.count`. If the property to be created is a vectorial property (having \(M>1\) components), the initial data array should be of shape \((N,M)\) if provided:

        colors = numpy.random.random_sample(size=(data.particles.count, 3))
        data.particles_.create_property('Color', data=colors)

    In general, however, data may be any value that is broadcastable to the array dimensions of the standard property (e.g. a uniform value).

    If you don’t specify the function argument data, OVITO will automatically initialize the property elements with sensible default values (0 in most cases). Subsequently, you can set the property values for all or some of the elements:

        prop = data.particles_.create_property('Color')
        prop[...] = numpy.random.random_sample(size=prop.shape)

    To create a user-defined property, specify a non-standard property name:

        values = numpy.arange(0, data.particles.count, dtype=int)
        data.particles_.create_property('My Integer Property', data=values)

    In this case, the data type and the number of vector components of the new property are inferred from the provided data array. Specifying a one-dimensional array creates a scalar property whereas a two-dimensional array creates a vectorial property.

    If a property of the same name already exists in the container, it gets replaced with a modifiable copy if necessary. Its contents get overwritten with the data array while maintaining all other attributes of the existing property, e.g. its `types` list.

    When creating a user-defined property, the dtype and components parameters may also be specified explicitly if you are going to fill in the property values in a second step:

        prop = data.particles_.create_property('My Vector Property', dtype=float, components=3)
        prop[...] = numpy.random.random_sample(size = prop.shape)

    If desired, the components of the user-defined vector property can be given names, e.g. `components=('X', 'Y', 'Z')`.

    Note: If you’re creating new empty `PropertyContainer`, its initial element `count` is 0. In this state, and only then, the `create_property()` method allows you to initialize the count while adding the very first property by providing a data array of the desired length:

        # Creating an empty Particles container to begin with:
        particles = Particles()

        # Create 10 particles with random xyz coordinates:
        xyz = numpy.random.random_sample(size=(10,3))
        particles.create_property('Position', data=xyz)

        assert particles.count == len(xyz)

    All subsequently added properties must have a matching length.

  delete_elements(mask)

    Deletes a subset of the elements from this container. The elements to be deleted must be specified in terms of a 1-dimensional mask array having the same length as the container (see `count`). The method will delete those elements whose corresponding mask value is non-zero, i.e., the `i`-th element will be deleted if `mask[i]!=0`.

    For example, to delete all currently selected particles, i.e., the subset of particles whose `Selection` property is non-zero, one would simply write:

        data.particles_.delete_elements(data.particles['Selection'])

    The effect of this statement is the same as for applying the `DeleteSelectedModifier` to the particles list.

    Parameters:

      mask (ArrayLike)

  delete_indices(indices)

    Deletes a subset of the elements from this container. The elements to be deleted must be specified in terms of a sequence of indices, all in the range 0 to `count`-1. The method accepts any type of iterable object, including sequence types, arrays, and generators.

    For example, to delete every other particle, one could use Python’s `range` function to generate all even indices up to the length of the particle container:

        data.particles_.delete_indices(range(0, data.particles.count, 2))

    Parameters:

      indices (Iterable[int])

  get(name: str, require: bool = False) → Property | None

    Retrieves a property array from this container.

    Parameters:

      - name – The name of the property to retrieve.

      - require – If `True`, the method raises a KeyError in case the property does not exist in the container. If `False`, the method returns `None` in the not-found case.

    Returns:

      The requested `Property`, or `None` if require=False and the property is not present in the container.

    Added in version 3.11.0.

  property title: str

    The title of the data object under which it appears in the user interface of OVITO.

class ovito.data.SimulationCell

  Base: `ovito.data.DataObject`

  This object stores the geometric shape and boundary conditions of the simulation box. Typically there is exactly one `SimulationCell` object in a `DataCollection`, which is accessible through the `cell` field:

      data = pipeline.compute()
      print(data.cell[...])   # Use [...] to cast SimulationCell object to a NumPy array

  The cell matrix

  The geometry of the simulation cell is encoded as a 3x4 matrix \(\mathbf{M}\). The first three columns \(\mathbf{a}\), \(\mathbf{b}\), \(\mathbf{c}\) of the matrix are the vectors spanning the three-dimensional parallelepiped in Cartesian space. The fourth column specifies the Cartesian coordinates of the cell’s origin \(\mathbf{o}\) within the global simulation coordinate system:

  \[\begin{split}\mathbf{M} = \begin{pmatrix} a_x & b_x & c_x & o_x \\ a_y & b_y & c_y & o_y \\ a_z & b_z & c_z & o_z \\ \end{pmatrix}\end{split}\]

  The cell matrix is represented by a two-dimensional NumPy array of shape (3,4) using row-major storage order:

      a = data.cell[:,0]
      b = data.cell[:,1]
      c = data.cell[:,2]
      o = data.cell[:,3]

  The `is2D` flag of the simulation cell indicates whether the system is two-dimensional. The cell matrix of a 2d system also has the 3x4 shape, but the cell vector \(\mathbf{c}\) and the last row of the cell matrix are ignored by many computations in OVITO if the system is marked as 2d.

  Periodic boundary conditions

  The `pbc` field stores a tuple of three Boolean flags that indicate for each cell vector whether the system is periodic in that direction or not. OVITO uses that information in various computations. If the system is two-dimensional, the value of the third pbc flag is ignored.

  Modifying the simulation cell

  When you modify the entries of the cell matrix, make sure you use the underscore notation to request a modifiable version of the `SimulationCell` object:

      # Make cell twice as large along the Y direction by scaling the second cell vector:
      data.cell_[:,1] *= 2.0

  Reset the simulation cell to an orthogonal box \((L_x, L_y, L_z)\) centered at the origin:

      lx = 20.0; ly = 10.0; lz = 8.0
      data.cell_[:,0] = (lx, 0, 0)
      data.cell_[:,1] = (0, ly, 0)
      data.cell_[:,2] = (0, 0, lz)
      data.cell_[:,3] = numpy.dot((-0.5, -0.5, -0.5), data.cell[:3,:3])
      data.cell_.pbc = (True, True, True)

  Conversion between Cartesian and reduced coordinates

  Given a point in 3d space, \(\mathbf{p}=(x, y, z)\), expressed in coordinates of the Cartesian simulation system, you can compute the corresponding reduced cell coordinates by extending the point to a quadruplet \((x, y, z, 1)\) and multiplying it with the `inverse` cell matrix \(\mathbf{M}^*\):

      p_cartesian = (x, y, z)
      p_reduced   = cell.inverse @ numpy.append(p_cartesian, 1.0)  # @-operator is shorthand for numpy.matmul()

  This effectively performs an affine transformation. The reverse transformation back to Cartesian coordinates in the global simulation system works in the same way. The following operation converts a 3d point from reduced cell coordinates to simulation coordinates:

      p_reduced   = (xs, ys, zs)
      p_cartesian = cell @ numpy.append(p_reduced, 1.0)  # @-operator is shorthand for numpy.matmul()

  Transforming vectors (as opposed to points) between Cartesian and reduced cell coordinates works somewhat differently, because vectors are not affected by the translation of the simulation cell, i.e., when the cell’s origin does not coincide with the origin of the global simulation coordinate system. A vector \(\mathbf{v}=(x, y, z)\) should thus be amended with a zero, \((x, y, z, 0)\), before applying the 3x4 transformation matrix to ignore the translational component:

      v_cartesian     = (vx, vy, vz)
      v_reduced       = cell.inverse @ numpy.append(v_cartesian, 0.0)
      v_cartesian_out = cell @ numpy.append(v_reduced, 0.0)
      assert numpy.allclose(v_cartesian_out, v_cartesian)

  The operations described above transform individual 3d points or vectors. In case you have to transform an entire array of points or vectors, for example the list of atomic positions, it is most efficient to apply the transformation to all elements of the array at once. Here is how you can do the affine transformation back and forth between Cartesian and reduced coordinates for an array:

      cartesian_positions     = data.particles.positions
      reduced_positions       = (cell.inverse[0:3,0:3] @ cartesian_positions.T).T + cell.inverse[0:3,3]
      cartesian_positions_out = (cell[0:3,0:3] @ reduced_positions.T).T + cell[0:3,3]
      assert numpy.allclose(cartesian_positions_out, cartesian_positions)

  When transforming an array of vectors, leave out the translation term and perform just the linear transformation (3x3 matrix-vector multiplication).

  Visual representation

  Each `SimulationCell` object has an attached `SimulationCellVis` element, which controls the visual appearance of the wireframe box in rendered images. It can be accessed via the `vis` attribute inherited from the `DataObject` base class:

      data = pipeline.compute()
      # Change display color of simulation cell to red:
      data.cell.vis.rendering_color = (1.0, 0.0, 0.0)
      # Or turn off the display of the cell completely:
      data.cell.vis.enabled = False

  delta_vector(ra, rb, return_pbcvec=False)

    Computes the vector connecting two points \(r_a\) and \(r_b\) in a periodic simulation cell by applying the minimum image convention.

    The method starts by computing the 3d vector \({\Delta} = r_b - r_a\) for two points \(r_a\) and \(r_b\), which may be located in different images of the periodic simulation cell. The minimum image convention is then applied to obtain the new vector \({\Delta'} = r_b' - r_a\), where the original point \(r_b\) has been replaced by the periodic image \(r_b'\) that is closest to \(r_a\), making the vector \({\Delta'}\) as short as possible (in reduced coordinate space). \(r_b'\) is obtained by translating \(r_b\) an integer number of times along each of the three cell directions: \(r_b' = r_b - H*n\), with \(H\) being the 3x3 cell matrix and \(n\) being a vector of three integers that are chosen by the method such that \(r_b'\) is as close to \(r_a\) as possible.

    Note that the periodic image convention is applied only along those cell directions for which periodic boundary conditions are enabled (see `pbc` property). For other directions no shifting is performed, i.e., the corresponding components of \(n = (n_x,n_y,n_z)\) will always be zero.

    The method is able to compute the results for either an individual pair of input points or for two arrays of input points. In the latter case, i.e. if the input parameters ra and rb are both 2-D arrays of shape Nx3, the method returns a 2-D array containing N output vectors. This allows applying the minimum image convention to a large number of point pairs in one function call.

    The option return_pbcvec lets the method return the vector \(n\) introduced above as an additional output. The components of this vector specify the number of times the image point \(r_b'\) needs to be shifted along each of the three cell directions in order to bring it onto the original input point \(r_b\). In other words, it specifies the number of times the computed vector \({\Delta} = r_b - r_a\) crosses a periodic boundary of the cell (either in positive or negative direction). For example, the PBC shift vector \(n = (1,0,-2)\) would indicate that, in order to get from input point \(r_a\) to input point \(r_b\), one has to cross the cell boundaries once in the positive x-direction and twice in the negative z-direction. If return_pbcvec is true, the method returns the tuple (\({\Delta'}\), \(n\)); otherwise it returns just \({\Delta'}\). Note that the vector \(n\) computed by this method can be used, for instance, to correctly initialize the `Bonds.pbc_vectors` property for newly created bonds that cross a periodic cell boundary.

    Parameters:

      - ra (ArrayLike) – The Cartesian xyz coordinates of the first input point(s). Either a 1-D array of length 3 or a 2-D array of shape (N,3).

      - rb (ArrayLike) – The Cartesian xyz coordinates of the second input point(s). Must have the same shape as ra.

      - return_pbcvec (bool) – If true, also returns the vector \(n\), which specifies how often the vector \((r_b' - r_a)\) crosses the periodic cell boundaries.

    Returns:

      The vector \({\Delta'}\) and, optionally, the vector \(n\).

    Return type:

      ndarray | tuple[ndarray, ndarray]

    Note that there exists also a convenience method `Particles.delta_vector()`, which should be used in situations where \(r_a\) and \(r_b\) are the coordinates of two particles in the simulation cell.

  property inverse: ndarray

    Read-only property returning the reciprocal cell matrix \(\mathbf{M}^*\) - an array of shape (3,4):

    \[\mathbf{M}^* = \begin{bmatrix} \mathbf{a}^* & \mathbf{b}^* & \mathbf{c}^* & \mathbf{o}^* \end{bmatrix}\]

    with the real-space cell volume \(V = (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c}\) and reciprocal cell vectors given by

    \[\mathbf{a}^* = \frac{\mathbf{b} \times \mathbf{c}}{V} \qquad \mathbf{b}^* = \frac{\mathbf{c} \times \mathbf{a}}{V} \qquad \mathbf{c}^* = \frac{\mathbf{a} \times \mathbf{b}}{V} \qquad \mathbf{o}^* = -\begin{pmatrix} \mathbf{a}^* \; \mathbf{b}^* \; \mathbf{c}^* \end{pmatrix} \mathbf{o} \mathrm{.}\]
  property is2D: bool

    Specifies whether the system is two-dimensional (instead of three-dimensional). For two-dimensional systems, the third `pbc` flag and the cell vector \(\mathbf{c}\) are typically ignored.

    Default:

      `False`

  property pbc: tuple[bool, bool, bool]

    A tuple of three Boolean flags specifying whether periodic boundary conditions are enabled along the cell’s three spatial directions.

    Default:

      `(False, False, False)`

  property volume: float

    Read-only property computing the volume of the three-dimensional simulation cell. The returned value is equal to the absolute determinant of the 3x3 submatrix formed by the three cell vectors, i.e. the scalar triple product \(V=|(\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c}|\):

        assert cell.volume == abs(numpy.linalg.det(cell[0:3,0:3]))

  property volume2D: float

    Read-only property computing the area of the two-dimensional simulation cell (see `is2D`). The returned value is equal to the magnitude of the cross-product of the first two cell vectors, i.e. \(V_{\mathrm{2d}} = |\mathbf{a} \times \mathbf{b}|\):

        assert cell.volume2D == numpy.linalg.norm(numpy.cross(cell[:,0], cell[:,1]))

  wrap_point(pos: ArrayLike) → ArrayLike

    Maps a point into the primary image of the periodic simulation cell.

    This function returns the coordinates of pos wrapped into the primary simulation cell image. pos must be a 3-D Cartesian point or an array of such points, which will be processed all at once by the method. Points that are already inside the simulation cell are returned as-is. The wrapping only takes place along those simulation cell directions which have the `pbc` flag set.

    To find the shortest distance or vector between two points while accounting for periodic boundary conditions, use the `delta_vector()` method instead.

    Parameters:

      pos – The Cartesian xyz coordinates of the input point(s). This can be either a 1-D array of length 3, or a 2-D array of shape (N, 3).

    Returns:

      The wrapped coordinates - returned as an array with the same shape as the input

class ovito.data.SurfaceMesh

  Base: `ovito.data.DataObject`

  This data object type represents a surface in three-dimensional space, i.e., a two-dimensional manifold that is usually closed and orientable. The underlying representation of the surface is a discrete mesh made of vertices, edges, and planar faces. See the user manual page on surface meshes for more information on this data object type.

  Surface meshes are typically produced by modifiers such as `ConstructSurfaceModifier`, `CreateIsosurfaceModifier`, `CoordinationPolyhedraModifier` or `VoronoiAnalysisModifier`.

  Each surface mesh has a unique `identifier` by which it can be looked up in the `DataCollection.surfaces` dictionary:

      # Apply a CreateIsosurfaceModifier to a VoxelGrid to create a SurfaceMesh:
      pipeline.modifiers.append(CreateIsosurfaceModifier(operate_on='voxels:charge-density', property='Charge Density', isolevel=0.05))
      data = pipeline.compute()

      # The SurfaceMesh created by the modifier has the identifier 'isosurface':
      surface = data.surfaces['isosurface']

  Vertices, halfedges, and faces

  A surface mesh is made of a set of vertices, a set of directed halfedges each connecting two vertices, and a set of faces, each formed by a circular sequence of halfedges. The connectivity information, i.e., which vertices are connected by halfedges and which halfedges form the faces, is stored in the `topology` sub-object of the `SurfaceMesh`. See the `SurfaceMeshTopology` class for more information.

  Vertices and faces of the surface mesh can be associated with arbitrary property values, similar to how particles can have arbitrary properties assigned to them in OVITO. These properties are managed by the `vertices` and `faces` `PropertyContainer` sub-objects of the surface mesh. The vertices of the mesh are always associated with the property named `Position`, which stores the three-dimensional coordinates of each vertex, similar to the `Position` property of particles in OVITO.

      vertex_coords = surface.vertices['Position']

  The `SurfaceMeshVis` element, which is responsible for rendering the surface mesh, provides the option to visualize local vertex and face property values using a color mapping scheme.

      surface.vis.color_mapping_mode = SurfaceMeshVis.ColorMappingMode.Vertex
      surface.vis.color_mapping_property = 'Position.Z'
      surface.vis.color_mapping_interval = (min(vertex_coords[:,2]), max(vertex_coords[:,2]))

  If you want to modify property values of the mesh, keep in mind that you have to use underscore notation, for example:

      data.surfaces['isosurface_'].vertices_['Position_'] += (xoffset, yoffset, zoffset)

  Periodic simulation domains

  A surface mesh may be embedded in a periodic domain, i.e. in a simulation cell with periodic boundary conditions. That means edges and faces of the surface mesh can connect vertices on opposite sides of the simulation box and will wrap around correctly. OVITO takes care of computing the intersections of such a periodic surface with the box boundaries and automatically produces a non-periodic representation of the mesh when it comes to displaying the surface. If needed, you can explicitly request a non-periodic version of the mesh, which was clipped at the periodic box boundaries, by calling the `to_triangle_mesh()` method from a script.

  The spatial domain of the surface mesh is the `SimulationCell` object stored in its `SurfaceMesh.domain` field. Note that this attached `SimulationCell` may, in some situations, not be identical with the global simulation `cell` set for the `DataCollection`.

  Spatial regions

  If it is a closed, orientable manifold, the surface mesh subdivides three-dimensional space into separate spatial regions. For example, if the surface mesh was constructed by the `ConstructSurfaceModifier` from a set of input particles, then the volume enclosed by the surface is the “filled” interior region and the exterior space is the “empty” region containing no particles.

  In general, the `SurfaceMesh` class manages a variable list of `regions`, each being identified by a numeric, zero-based index. The `locate_point()` method allows you to determine which spatial region some point in space belongs to.

  A surface mesh may be degenerate, which means it contains no vertices and faces. In such a case there is only one spatial region filling the entire space. For example, when there exist no input particles, the `ConstructSurfaceModifier` is unable to construct a regular surface mesh and the “empty” region fills the entire simulation cell. Conversely, if the periodic simulation cell is completely filled with particles, the “filled” region covers the entire periodic simulation domain and the resulting surface mesh consists of no vertices or faces, i.e., it is also degenerate. To discriminate between the two situations, the `SurfaceMesh` class has a `space_filling_region` field, which specifies the spatial region that fills the entire space in cases where the mesh is degenerate.

  File export

  A surface mesh may be exported to a geometry file in the form of a triangle mesh using OVITO’s `export_file()` function. To this end, a non-periodic version is produced by truncating triangles at the domain boundaries and generating “cap polygons” filling the holes that occur at the intersection of the surface with periodic domain boundaries. The following example code writes a VTK geometry file (`vtk/trimesh` export format):

      from ovito.io import import_file, export_file
      from ovito.data import SurfaceMesh
      from ovito.modifiers import ConstructSurfaceModifier

      # Load a particle set and construct the surface mesh:
      pipeline = import_file("input/simulation.dump")
      pipeline.modifiers.append(ConstructSurfaceModifier(radius = 2.8))
      mesh = pipeline.compute().surfaces['surface']

      # Export the mesh to a VTK file for visualization with ParaView.
      export_file(mesh, 'output/surface_mesh.vtk', 'vtk/trimesh')

  Clipping planes

  A set of clipping planes can be assigned to a `SurfaceMesh` to clip away parts of the mesh for visualization purposes. This may be useful to e.g. cut a hole into a closed surface allowing you to look inside the enclosed volume. The `SurfaceMesh` object manages a list of clipping planes, which is accessible through the `get_clipping_planes()` and `set_clipping_planes()` methods. Note that the cut operations are non-destructive and get performed only on the transient, non-periodic version of the mesh generated during image rendering or when exporting the mesh to a file. The original surface mesh is not affected. The `SliceModifier`, when applied to a `SurfaceMesh`, performs the slice by simply adding a corresponding clipping plane to the `SurfaceMesh`. The actual truncation of the mesh happens later on, during the final visualization step, when a non-periodic version is computed.

  connect_opposite_halfedges() → bool

    Links together pairs of halfedges in the mesh to form a two-dimensional manifold made of connected faces. For each halfedge \(a \to b\) the method tries to find the corresponding reverse halfedge \(b \to a\), which bounds the adjacent face. The two halfedges are then linked together to form a pair. The method returns `True` to indicate that all halfedges of the mesh have been successfully associated with a corresponding opposite halfedge. In this case, the mesh is said to be closed, i.e., its faces form a contiguous manifold.

    Important

    For this method to work, the faces of the mesh must have been created all with the same winding order. That means their vertices must consistently be ordered counter-clockwise when viewed from the outside of the closed surface manifold (the front side). Only then do the halfedges of adjacent faces run in opposite directions and can be successfully paired by this method.

    See also

    `SurfaceMeshTopology.is_closed`, `SurfaceMeshTopology.opposite_edge()`, `SurfaceMeshTopology.has_opposite_edge()`

    Added in version 3.7.9.

  create_face(vertices: Sequence[int]) → int

    Adds a new face to the mesh. vertices must be a sequence of two or more zero-based indices into the mesh’s vertex list. The method creates a loop of halfedges connecting the given vertices to form a closed polygon. The zero-based index of the newly created face is returned.

    Tip

    If you intend to add several faces to the mesh, consider using `create_faces()` instead. It is potentially much faster than calling `create_face()` multiple times.

    Note

    Visible faces should be made of three or more vertices that form a convex polygon. Faces that represent a non-convex polygon will likely be rendered incorrectly by OVITO. Faces having only two edges, while technically valid, will not get rendered because they are degenerate.

    The vertex winding order used by OVITO is counter-clockwise on the front side of mesh faces. When constructing a closed mesh, make sure you always specify vertices in counter-clockwise order when viewed from the outside of enclosed region.

    Code example:

        # Add a new SurfaceMesh object to the DataCollection with unique object identifier 'quad'.
        # The simulation cell of the particle system is adopted also as domain of the SurfaceMesh.
        mesh = data.surfaces.create(identifier='quad', title='Quad', domain=data.cell)

        # Create 4 mesh vertices forming a quadrilateral.
        verts = [[0,0,0], [10,0,0], [10,10,0], [0,10,0]]
        mesh.create_vertices(verts)

        # Create a face connecting the 4 vertices.
        mesh.create_face([0,1,2,3])

        # Initialize the 'Color' property of the newly created face.
        mesh.faces.create_property('Color', data=[(1,0,0)])

    Added in version 3.7.9.

  create_faces(vertex_lists: Sequence[Sequence[int]] | ArrayLike[int]) → int

    Adds several new polygonal faces to the mesh.

    Parameters:

      vertex_lists – A sequence of sequences, one for each face to be created, which specify the vertex indices to be connected by the new mesh faces. May also be a two-dimensional array.

    Returns:

      Index of the first newly created face.

    vertex_lists may be list of tuples for example. The following call creates a 3-sided and a 4-sided polygonal face:

        mesh.create_faces([(0,1,2), (3,4,5,6)])

    For best performance, pass a two-dimensional NumPy array to create multiple faces which all have the same number of vertices:

        # Nx3 array [[0,1,2], [3,4,5], [6,7,8], ...] for connecting 3N vertices with triangle faces.
        triangle_list = numpy.arange(mesh.vertices.count).reshape((mesh.vertices.count//3, 3))
        mesh.create_faces(triangle_list)

    A third option is to specify the faces as one linear array, in which each face’s vertex list is prefixed with the number of vertices. For example, to create a 3-sided face 0-1-2 and a 4-sided face 3-4-5-6, one would write:

        mesh.create_faces(numpy.asarray([3,0,1,2,  4,3,4,5,6]))

    Note that the data must be provided as a NumPy array in this case, not a Python list.

    The `create_faces()` method has two effects: It increments the mesh’s `topology.face_count` and it extends the arrays in the mesh’s `faces` property container, which stores all per-face properties. The method raises an error if any of the specified vertex indices does not exist in the mesh. That means you should first call `create_vertices()` to add vertices to the mesh before creating faces referencing these vertices.

    Note

    Visible faces should be made of three or more vertices forming convex polygons. Faces that represent non-convex polygons will likely be rendered incorrectly by OVITO. Faces having only two edges, while technically valid, will not get rendered because they are degenerate.

    The vertex winding order used by OVITO is counter-clockwise on the front side of mesh faces. When constructing a closed mesh, make sure you always specify vertices in counter-clockwise order when viewed from the outside of enclosed region.

    Usage example:

        # Add a new SurfaceMesh object to the DataCollection with unique object identifier 'tetrahedron'.
        # The simulation cell of the particle system is adopted also as domain of the SurfaceMesh.
        mesh = data.surfaces.create(identifier='tetrahedron', title='Tetrahedron', domain=data.cell)

        # Create 4 mesh vertices.
        verts = [[0,0,0], [10,0,0], [0,10,0], [0,0,10]]
        mesh.create_vertices(verts)

        # Create 4 triangular faces forming a tetrahedron.
        mesh.create_faces([[0,1,2], [0,2,3], [0,3,1], [1,3,2]])

        # Initialize the 'Color' property of the newly created faces with RGB values.
        mesh.faces.create_property('Color', data=[(1,0,0), (1,1,0), (0,0,1), (0,1,0)])

        # Make it a "closed" mesh, connecting the four faces to form a surface manifold.
        mesh.connect_opposite_halfedges()

    Added in version 3.7.9.

  create_vertices(coords: Sequence[Sequence[float]] | ArrayLike[float]) → int

    Adds a set of new vertices to the mesh. coords must be an \(n \times 3\) array specifying the xyz coordinates of the \(n\) vertices to create. The coordinates will be copied into the `Position` vertex property, which is managed by the `vertices` property container. Furthermore, the `vertex_count` value of the mesh’s `topology` will be incremented by \(n\).

    Initially, the new vertices will not be associated with any faces. Use `create_face()` or `create_faces()` to create faces connecting the vertices.

    Added in version 3.7.9.

  property domain: SimulationCell | None

    The `SimulationCell` describing the (possibly periodic) domain which this surface mesh is embedded in. Note that this cell generally is independent of and may be different from the `cell` found in the `DataCollection`.

  property faces: PropertyContainer

    The `PropertyContainer` storing the per-face properties of the mesh.

    In general, an arbitrary set of uniquely named properties may be associated with the faces of a surface mesh. OVITO defines the following standard face properties, which have a well-defined meaning and prescribed data layout:

    Standard property name | Data type | Component names
    --- | --- | ---
    Color | float32 | R, G, B
    Region | int32 |
    Selection | int8 |

    The property `Color` can be set to give each face of the surface mesh an individual color. It overrides the uniform coloring otherwise controlled by the `SurfaceMeshVis` element.

    The property `Region` links each face with the volumetric region of the `SurfaceMesh` that it bounds (see description above). The values of this property are zero-based indices into the `regions` list of the mesh.

    The property `Selection` controls the selection state of each individual mesh face. This property is set by modifiers that create selections, such as `ExpressionSelectionModifier`, and is used by modifiers that operate on the subset of currently selected faces, such as `AssignColorModifier`. All faces whose `Selection` property has a non-zero value are part of the current selection set.

  get_clipping_planes() → NDArray[float64]

    Returns an \(N \times 4\) array containing the definitions of the N clipping planes attached to this `SurfaceMesh`.

    Each plane is defined by its unit normal vector and a signed displacement magnitude, which determines the plane’s distance from the coordinate origin along the normal, giving four numbers per plane in total. Those parts of the surface mesh which are on the positive side of the plane (in the direction the normal vector) will be cut away during rendering.

    Note that the returned Numpy array is a copy of the internal data stored by the `SurfaceMesh`.

  get_face_vertices(flat: bool = False) → NDArray[int32] | list[list[int]]

    Returns an array with the vertex indices of all mesh faces. The parameter flat controls how the face vertices get returned by the function:

    > flat=False: If all \(n\) faces of the mesh have the same, uniform number of vertices, \(m\), for example, if they are all triangles, then a 2-d NumPy array of shape \((n, m)\) containing the zero-based vertex indices is returned. Otherwise, a list of lists is returned, in which nested lists may have different lengths.

    > flat=True: Returns a 1-d array with the vertex lists of all mesh faces stored back to back. A face’s vertex list is preceded by the number of vertices of that face. Then the actual vertex indices of the face follow. Then the number of vertices of the next face follows, and so on.

    Added in version 3.7.9.

  locate_point(pos: ArrayLike, eps: float = 1e-6, return_distances: bool = False) → int | None | tuple[int, float] | None | ArrayLike | tuple[ArrayLike, ArrayLike]

    Determines which spatial region of the mesh contains the given point in 3-d space. Optionally the distance to the mesh can be returned.

    The function returns the numeric ID of the region pos is located in. Note that region ID -1 is typically reserved for the empty exterior region, which, if it exists, is the one not containing any atoms or particles. Whether non-negative indices refer to only filled (interior) regions or also empty regions depends on the algorithm that created the surface mesh and its spatial regions.

    The parameter eps is a numerical precision threshold to detect if the query point is positioned exactly on the surface boundary, i.e. on the manifold separating two spatial regions. This condition is indicated by the special return value `None`. Set eps to 0.0 to disable the point-on-boundary test. Then the method will never return `None` as a result, but the determination of the spatial region will become numerically unstable if the query point is positioned right on a boundary surface.

    return_distances can be set to compute not only the containing region(s), but also the distance(s) from each input point to the closest point on the surface mesh.

    Parameters:

      - pos – The Cartesian xyz coordinates of the query point(s). Either a 1-D array of length 3 or a 2-D array of shape (N,3).

      - eps (float) – Numerical precision threshold for point-on-boundary test

      - return_distances (bool) – Request the computation of mesh-to-pos distances

    Returns:

      - If pos is a 1-D array: The numeric ID of the spatial region containing pos; or `None` if pos is exactly on the dividing boundary between two regions.

        If return_distances is set, a tuple containing the computed region and the distance from pos to the mesh is returned. Both are `None` if pos is located right on a region boundary.

      - If pos is a 2-D array: A `numpy.ma.MaskedArray` containing the numeric ID of the spatial region for each entry in pos is returned. Entries corresponding to positions exactly on the dividing boundary between two regions are masked. Internally, the masked values are set to the smallest valid integer, however, these values must not be used. The returned array is of shape (N,).

        When return_distances is requested, a second masked array of the same shape is returned. This array contains the distance from each pos to the nearest location on the mesh. Masked values are set to 0.0.

  property regions: PropertyContainer

    The `PropertyContainer` storing the properties of the spatial regions of the mesh.

    In general, an arbitrary set of uniquely named properties may be associated with the regions of a surface mesh. OVITO defines the following standard region properties, which have a well-defined meaning and prescribed data layout:

    Standard property name | Data type | Component names
    --- | --- | ---
    Color | float32 | R, G, B
    Filled | int8 |
    Selection | int8 |
    Surface Area | float64 |
    Volume | float64 |

    The property `Color` can be set to give the faces bounding each of the volumetric regions a different color. It overrides the uniform mesh coloring otherwise controlled by the `SurfaceMeshVis` element.

    The property `Filled` is a flag indicating for each region whether it is an interior region, e.g. inside a solid, or an empty exterior region, e.g. outside the solid bounded by the surface. This property is created by the `ConstructSurfaceModifier`. The same is true for the per-region properties `Surface Area` and `Volume`.

  set_clipping_planes(planes: ArrayLike)

    Sets the clipping planes of this `SurfaceMesh`. The array planes must follow the same format as the one returned by `get_clipping_planes()`.

  property space_filling_region: int

    Indicates the index of the spatial region that fills the entire domain in case the surface is degenerate, i.e. the mesh has zero faces. The invalid index -1 is typically associated with the empty (exterior) region.

  to_triangle_mesh() → tuple[TriangleMesh, TriangleMesh | None, NDArray[uint64]]

    Converts the surface into a non-periodic `TriangleMesh`.

    Returns:

      (trimesh, caps, facemap)

    - trimesh: A `TriangleMesh` representing the surface geometry after clipping it at the periodic boundaries of the `domain` and any attached clipping planes (see `get_clipping_planes()`).

    - caps: A `TriangleMesh` containing the cap polygons generated at intersections of the periodic surface mesh with boundaries of the simulation `domain`. Will be `None` if the surface mesh has no attached `domain`, the domain is degenerate, or the surface mesh does not represent a closed manifold.

    - facemap: A NumPy array of indices into the face list of this `SurfaceMesh`, one for each triangular face of the `TriangleMesh` trimesh. This map lets you look up for each face of the output mesh what the corresponding face of the input surface mesh is.

    Added in version 3.7.5.

  property topology: SurfaceMeshTopology

    A `SurfaceMeshTopology` object storing the face connectivity of the mesh.

  property vertices: PropertyContainer

    The `PropertyContainer` storing all per-vertex properties of the mesh, including the vertex coordinates.

    In general, an arbitrary set of uniquely named properties may be associated with the vertices of a surface mesh. OVITO defines the following standard vertex properties, which have a well-defined meaning and prescribed data layout:

    Standard property name | Data type | Component names
    --- | --- | ---
    Color | float32 | R, G, B
    Position | float64 | X, Y, Z
    Selection | int8 |

    The property `Position` is always present and stores the Cartesian vertex coordinates.

    The property `Color` can be set to give each vertex of the surface mesh an individual color. It overrides the uniform coloring otherwise controlled by the `SurfaceMeshVis` element. Vertex colors get interpolated across the mesh faces during rendering.

    The property `Selection` controls the selection state of each individual mesh vertex. This property is set by modifiers that create selections, such as `ExpressionSelectionModifier`, and is used by modifiers that operate on the subset of currently selected vertices, such as `AssignColorModifier`. All vertices whose `Selection` property has a non-zero value are part of the current selection set.

class ovito.data.SurfaceMeshTopology

  Base: `ovito.data.DataObject`

  Added in version 3.7.6.

  This data structure holds the connectivity information of a `SurfaceMesh`. It is accessible through the `SurfaceMesh.topology` field. The surface mesh topology consists of vertices, faces and halfedges.

  All these topological entities of the mesh are identified by numeric indices ranging from 0 to (`vertex_count`-1), (`face_count`-1), and (`edge_count`-1), respectively. The vertices and faces of the mesh may be associated with auxiliary properties, which are stored separately from the topology in the `SurfaceMesh.vertices` and `SurfaceMesh.faces` property containers. In particular, the spatial coordinates of the mesh vertices are stored as `Position` property array in `SurfaceMesh.vertices`.

  A halfedge is a directed edge \(a \to b\) connecting two vertices \(a\) and \(b\) – depicted as a half-arrow in the figure. A face is implicitly defined by a circular sequence of halfedges that bound the face. Typically, halfedges come in pairs. The halfedge \(a \to b\) and its opposite halfedge, \(b \to a\), form a pair that links two neighboring faces together. Thus, halfedge pairs are essential for forming a connected, two-dimensional surface manifold. The surface is said to be closed, i.e., it has no open boundaries if all halfedges of the mesh are associated with corresponding opposite halfedges (see `is_closed`).

  For each vertex the topology object maintains a linked-list of directed halfedges leaving that vertex. It can be accessed through the `first_vertex_edge()` and `next_vertex_edge()` methods.

  For each face the topology object maintains a circular linked-list of directed halfedges bounding that face (in counter-clockwise winding order). It can be accessed through the `first_face_edge()` and `next_face_edge()`/`prev_face_edge()` methods.

  Tip

  All query methods of this class are vectorized, which means they are able to process an array of arguments in a single function call and will return a corresponding array of results. The advantage of this is that the loop over the elements in the argument array runs entirely on the C++ side, which is typically much faster than a for-loop in Python. For example, to generate a list with the first halfedge of every mesh face:

  >     # Version 1: vectorized function call (fast)
  >     edges = mesh.topology.first_face_edge(range(mesh.topology.face_count))

  >     # Version 2: explicit loop (slow)
  >     edges = [mesh.topology.first_face_edge(face) for face in range(mesh.topology.face_count)]

  adjacent_face(edge: int) → int

    Returns the face that is bounded by the halfedge edge.

  count_face_edges(face: int) → int

    Returns the number of halfedges that bound face. See the code example for `next_face_edge()` to learn how this method works.

  count_manifolds(edge: int) → int

    Given a halfedge, this method returns the number of surface manifolds that meet at the edge. This is useful to identify triple junctions in a grain boundary network, for example. For halfedges that are located at the boundary of an open surface mesh, the method returns 1. For halfedges that are part of a regular two-sided manifold, the method returns 2.

    See also

    `next_manifold_edge`

  count_vertex_edges(vertex: int) → int

    Returns the number of halfedges that leave vertex. See the code example for `next_vertex_edge()` to learn how this method works.

  property edge_count: int

    Total number of halfedges in the `SurfaceMesh`. This property is read-only. Halfedges are created automatically by `SurfaceMesh.create_face()` or `SurfaceMesh.create_faces()` when adding new faces to the mesh topology.

  property face_count: int

    Number of faces in the `SurfaceMesh`. This is always equal to the `count` of the `SurfaceMesh.faces` property container.

    This property is read-only. Use `SurfaceMesh.create_face()` or `SurfaceMesh.create_faces()` to add new faces to the mesh.

  find_edge(face: int, vertex1: int, vertex2: int) → int

    Given a face, finds the halfedge of that face which leads from vertex1 to vertex2. If no such halfedge exists, returns -1.

    This method can be used to quickly find the edge connecting two vertices of a face without the need to explicitly visit and check each edge bounding the face.

  first_edge_vertex(edge: int) → int

    Returns the vertex the given halfedge is leaving from. To retrieve the vertex the halfedge is leading to, call `second_edge_vertex()`.

  first_face_edge(face: int) → int

    Returns some halfedge bounding the given face. Given that first halfedge, all other halfedges bounding the same face can be visited using `next_face_edge()` or `prev_face_edge()`.

  first_face_vertex(face: int) → int

    Given a face, this method returns some vertex of that face. This is equivalent to retrieving the vertex to which the first halfedge of the face is connected to, i.e. `first_edge_vertex(first_face_edge(face))`.

  first_vertex_edge(vertex: int) → int

    Returns the head halfedge from the linked list of halfedges leaving vertex. Subsequent halfedges from the linked list can be retrieved with `next_vertex_edge()`. If no halfedges are connected to vertex, the method returns -1.

  has_opposite_edge(edge: int) → bool

    Returns whether the given halfedge edge is associated with a corresponding reverse halfedge bounding an adjacent face in the same manifold. This is equivalent to checking the return value of `opposite_edge()`, which returns -1 to indicate that edge does not have an opposite edge.

  has_opposite_face(face: int) → bool

    Returns whether face is part of a two-sided manifold. A face that is part of a two-sided manifold has a ‘partner’ face with opposite orientation, which can be retrieved through the `opposite_face()` method.

  property is_closed: bool

    This is a read-only property indicating whether the surface mesh is fully closed. In a closed mesh, all faces are connected to exactly one adjacent face along each of their halfedges. That means the mesh presents a two-dimensional surface manifold without borders. Furthermore, a closed mesh divides space into an “interior” and an “exterior” region.

    See also

    `SurfaceMesh.connect_opposite_halfedges()`, `SurfaceMeshVis.show_cap`

    Added in version 3.7.9.

  next_face_edge(edge: int) → int

    Given the halfedge edge bounding some face, this method returns the following halfedge when going around the face in forward direction (counter-clockwise - when looking at the front side of the face). All halfedges of the face form a circular sequence - without a particular beginning or end. You can loop over this circular sequence in forward or backward direction with the `next_face_edge()` and `prev_face_edge()` methods. Given some mesh face, you can obtain a first halfedge through the `first_face_edge()` method.

    The following code example shows how to visit all halfedges of a face in order. Since the halfedges form a circular linked list, we have to remember which edge we started from to terminate the loop once we reach the first edge again:

        def count_edges(mesh: SurfaceMesh, face: int) -> int:
            start_edge = mesh.topology.first_face_edge(face)
            count = 1
            edge = mesh.topology.next_face_edge(start_edge)
            while edge != start_edge:
                assert mesh.topology.adjacent_face(edge) == face
                count += 1
                edge = mesh.topology.next_face_edge(edge)
            return count

        # The function defined above is equivalent to SurfaceMeshTopology.count_face_edges():
        assert count_edges(mesh, 0) == mesh.topology.count_face_edges(0)

  next_manifold_edge(edge: int) → int

    Advanced method to visit all surface manifolds meeting at an edge (e.g. along a triple junction in a grain boundary network). Given a halfedge, this method returns the halfedge that is part of the next manifold and which connects the same two mesh vertices.

    The manifold information may only be available in certain types of surface meshes, such as those generated by the `ConstructSurfaceModifier` when the `identify_regions` option is turned on.

    See also

    `count_manifolds()`

  next_vertex_edge(edge: int) → int

    Returns another halfedge leaving from the same vertex as edge. Together with `first_vertex_edge()` this method allows you to iterate over all halfedges connected to some vertex. When the end of the vertex’ edge list has been reached, the method returns -1.

    The following example demonstrates how to visit all outgoing halfedges of some vertex and count them:

        def count_edges(mesh: SurfaceMesh, vertex: int) -> int:
            count = 0
            edge = mesh.topology.first_vertex_edge(vertex)
            while edge != -1:
                assert mesh.topology.first_edge_vertex(edge) == vertex
                count += 1
                edge = mesh.topology.next_vertex_edge(edge)
            return count

        # The function defined above is equivalent to SurfaceMeshTopology.count_vertex_edges():
        assert count_edges(mesh, 0) == mesh.topology.count_vertex_edges(0)

  opposite_edge(edge: int) → int

    Given the halfedge edge, returns the reverse halfedge that bounds an adjacent face. This opposite halfedge connects the same two vertices as edge but in reverse order. You can use this method to determine whether the face bounded by edge has a neighboring face that is part of the same manifold:

        def get_neighboring_face(mesh: SurfaceMesh, edge: int) -> int:
            opp_edge = mesh.topology.opposite_edge(edge)
            if opp_edge == -1: return -1
            assert mesh.topology.first_edge_vertex(edge) == mesh.topology.second_edge_vertex(opp_edge)
            assert mesh.topology.second_edge_vertex(edge) == mesh.topology.first_edge_vertex(opp_edge)
            return mesh.topology.adjacent_face(opp_edge)

    You may call the convenience method `has_opposite_edge()` to determine whether a halfedge is associated with a corresponding opposite halfedge. If the surface mesh does not form a closed manifold, the halfedges at the boundary of the manifold do not have opposite halfedges, because there are no adjacent faces where the surface terminates.

  opposite_face(face: int) → int

    Returns the face on the opposite side of the two-sided manifold, or -1 if the manifold is one-sided. The returned face shares the same vertices with face but in reverse order. Note that `opposite_face(opposite_face(face))==face`.

  prev_face_edge(edge: int) → int

    Given the halfedge edge bounding some face, this method returns the previous halfedge going around that face in backward direction (clockwise - when looking at the front side of the face). All halfedges of a face form a circular sequence - without a particular beginning or end. You can loop over this circular sequence in forward or backward direction with the `next_face_edge()` and `prev_face_edge()` methods.

  second_edge_vertex(edge: int) → int

    Returns the vertex the given halfedge is leading to. To retrieve the vertex the halfedge is leaving from, call `first_edge_vertex()`.

  property vertex_count: int

    Number of vertices in the `SurfaceMesh`. This is always equal to the `count` of the `SurfaceMesh.vertices` property container.

    This property is read-only. Use `SurfaceMesh.create_vertices()` to add new vertices to the mesh.

class ovito.data.TriangleMesh

  Base: `ovito.data.DataObject`

  This data object type stores a three-dimensional mesh made of vertices and triangular faces. Such a mesh can describe general polyhedral geometry to be visualized side by side with the particle simulation data.

  Typically, triangle meshes are imported from external geometry data files (e.g. STL, OBJ, VTK formats) using the `import_file()` function. See also the corresponding section of the OVITO user manual. All triangle meshes in a data collection are accessible through the `DataCollection.triangle_meshes` dictionary view.

  Note that the `SurfaceMesh` class is a second object type that can represent surface geometries, just like a `TriangleMesh`. In contrast to triangle meshes, surface meshes may be embedded in periodic simulation domains and are closed manifolds in most cases. Furthermore, surface meshes can store arbitrary per-vertex and per-face property values – something triangle meshes cannot do. A triangle mesh is a more low-level data structure, which can be sent directly to a GPU for rendering. A surface mesh, in contrast, is a more high-level data structure, which gets automatically converted to a triangle mesh for visualization.

  The visual appearance of the triangle mesh is controlled through the attached `TriangleMeshVis` element (see `DataObject.vis` field of base class).

  A triangle mesh consists of \(n_{\mathrm{v}}\) vertices and \(n_{\mathrm{f}}\) triangular faces. These counts are exposed by the class as attributes `vertex_count` and `face_count`. Each face connects three vertices of the mesh, and several faces may share a vertex. The faces are stored as triplets of zero-based indices into the vertex list.

  property face_count: int

    The number of triangular faces of the mesh, \(n_{\mathrm{f}}\).

    Default:

      0

  get_faces() → NDArray[int32]

    Returns the list of triangles of the mesh as a NumPy array of shape \((n_{\mathrm{f}}, 3)\). The array contains for each face three zero-based indices into the mesh’s vertex list as returned by `get_vertices()`. The returned face array holds a copy of the internal data managed by the `TriangleMesh`.

  get_vertices() → NDArray[float64]

    Returns the xyz coordinates of the vertices of the mesh as a NumPy array of shape \((n_{\mathrm{v}}, 3)\). The returned array holds a copy of the internal vertex data managed by the `TriangleMesh`.

  set_faces(vertex_indices: ArrayLike)

    Sets the faces of the mesh. vertex_indices must be an array-like object of shape \((n_{\mathrm{f}}, 3)\) containing one integer triplet per triangular face. Each integer is a zero-based index into the mesh’s vertex list. The `TriangleMesh` copies the data from the array into its internal storage. If necessary, the value of `face_count` is automatically adjusted to match the first dimension of the vertex_indices array.

  set_vertices(coordinates: ArrayLike)

    Sets the xyz coordinates of the vertices of the mesh. coordinates must be an array-like object of shape \((n_{\mathrm{v}}, 3)\). The `TriangleMesh` copies the data from the array into its internal storage. If necessary, the value of `vertex_count` is automatically adjusted to match the first dimension of the coordinates array.

  property vertex_count: int

    The number of vertices of the mesh, \(n_{\mathrm{v}}\).

    Default:

      0

class ovito.data.Vectors

  Base: `ovito.data.PropertyContainer`

  The `Vectors` class represents a set of 3D arrow glyphs rendered by a `VectorVis` visual element. You can add an instance of this class to a `DataCollection` using the `DataCollection.vectors.create()` method.

  You can retrieve existing `Vectors` objects from a pipeline’s output data collection through the `DataCollection.vectors` dictionary view. Each `Vectors` object has a unique `identifier` name that serves as a lookup key.

  `Vectors` objects are always associated with `VectorVis` element, which controls the visual appearance of the arrows in rendered images. You can access the visual element through the `vis` attribute provided by the `DataObject` base class. The `VectorVis` element provides the capability to visualize a scalar quantity associated with each vector using pseudo-color mapping.

  The `Vectors` container uses the following standard properties with predefined names and data layouts. Additional per-arrow properties may be added using the `create_property()` method of the base class.

  Property name | Python access | Data type | Component names
  --- | --- | --- | ---
  Color | `colors` | float32 | R, G, B
  Direction | `directions` | float64 | X, Y, Z
  Position | `positions` | float64 | X, Y, Z
  Selection | `selection` | int8 |
  Transparency | `transparencies` | float32 |

  Added in version 3.11.0.

  property colors: Property | None

    The `Property` data array for the `Color` standard vector property; or `None` if that property is undefined. Use `create_property()` to add the property to the container if necessary. Use `colors_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

  property directions: Property | None

    The `Property` array containing the XYZ components of the vectors (standard property Direction). May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `directions_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

  property positions: Property | None

    The `Property` array containing the XYZ coordinates of vectors’ base points (standard property Position). May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `positions_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

  property selection: Property | None

    The `Property` data array for the `Selection` standard vectors property; or `None` if that property is undefined.

  property transparencies: Property | None

    The `Property` array containing the transparency values (standard property Transparency) of the vectors. May be `None` if the property is not defined yet. Use `create_property()` to add the property to the container if necessary. Use `transparencies_` (with an underscore) to access an independent copy of the array, whose contents can be safely modified in place.

class ovito.data.VoxelGrid

  Base: `ovito.data.PropertyContainer`

  Cell-data grid

  A two- or three-dimensional structured grid. Each cell (voxel) of the uniform grid is of the same size and shape. The overall geometry of the grid, its `domain`, is specified by the attached `SimulationCell` object, which describes a three-dimensional parallelepiped or a two-dimensional parallelogram. See also the corresponding user manual page for more information on this object type.

  The `shape` property of the grid specifies the number of data points uniformly distributed along each cell vector of the domain. The size of individual voxels depends on the overall domain size as well as the number of data points in each spatial direction. See the `grid_type` property, which controls whether the data values of the uniform grid are associated with the voxel interiors or the vertices (grid line intersections).

  Point-data grid

  Each data point or voxel of the grid may be associated with one or more field values. The data of these voxel properties is stored in standard `Property` array objects, similar to particle or bond properties. Voxel properties can be accessed by name through the dictionary interface that the `VoxelGrid` class inherits from its `PropertyContainer` base class.

  Voxel grids can be loaded from input data files, e.g. a CHGCAR file containing the electron density computed by the VASP code, or they can be dynamically generated within OVITO. The `SpatialBinningModifier` lets you project the information associated with the unstructured particle set to a structured voxel grid.

  Given a voxel grid, the `CreateIsosurfaceModifier` can then generate a `SurfaceMesh` representing an isosurface for a field quantity defined on the voxel grid.

  Example

  The following code example demonstrates how to create a new `VoxelGrid` from scratch and initialize it with data from a NumPy array:

  >     # Starting with an empty DataCollection:
  >     data = DataCollection()

  >     # Create a new SimulationCell object defining the outer spatial dimensions
  >     # of the grid and the boundary conditions, and add it to the DataCollection:
  >     cell = data.create_cell(
  >         matrix=[[10,0,0,0],[0,10,0,0],[0,0,10,0]],
  >         pbc=(True, True, True)
  >     )

  >     # Generate a three-dimensional Numpy array containing the grid cell values.
  >     nx = 10; ny = 6; nz = 8
  >     field_data = numpy.random.random((nx, ny, nz))

  >     # Create the VoxelGrid object and give it a unique identifier by which it can be referred to later on.
  >     # Link the voxel grid to the SimulationCell object created above, which defines its spatial extensions.
  >     # Specify the shape of the grid, i.e. the number of cells in each spatial direction.
  >     # Finally, assign a VoxelGridVis visual element to the data object to make the grid visible in the scene.
  >     grid = data.grids.create(
  >         identifier="field",
  >         domain=cell,
  >         shape=(nx,ny,nz),
  >         grid_type=VoxelGrid.GridType.CellData,
  >         vis_params={ "enabled": True, "transparency": 0.6 }
  >     )

  >     # Add a new property to the voxel grid cells and initialize it with the data from the NumPy array.
  >     # Note that the data must be provided as linear (1-dim.) array with the following type of memory layout:
  >     # The first grid dimension (x) is the fasted changing index while the third grid dimension (z) is the
  >     # slowest varying index. In this example, this corresponds to the "Fortran" memory layout of Numpy.
  >     grid.create_property('Field Value', data=field_data.flatten(order='F'))

  >     # Instead of the flatten() method above, we could also make use of the method VoxelGrid.view()
  >     # to obtain a 3-dimensional view of the property array, which supports direct assignment of grid values.
  >     field_prop = grid.create_property('Field Value', dtype=field_data.dtype, components=1)
  >     grid.view(field_prop)[...] = field_data

  >     # For demonstration purposes, compute an isosurface on the basis of the VoxelGrid created above.
  >     data.apply(CreateIsosurfaceModifier(operate_on='voxels:field', property='Field Value', isolevel=0.7))

  The `VoxelGrid` container uses the following standard properties with predefined names and data layouts. Additional per-voxel properties may be added using the `create_property()` method of the base class.

  Property name | Python access | Data type | Component names
  --- | --- | --- | ---
  Color |  | float32 | R, G, B

  property domain: SimulationCell | None

    The `SimulationCell` describing the (possibly periodic) domain which this grid is embedded in. Note that this cell generally is independent of and may be different from the `cell` found in the `DataCollection`.

    Default:

      `None`

  property grid_type: VoxelGrid.GridType

    This attribute specifies whether the values stored by the grid object are associated with the voxel cell centers or the grid points (vertices). Possible values are:

    > - `VoxelGrid.GridType.CellData` (default)

    > - `VoxelGrid.GridType.PointData`

    A `CellData` grid represents a field where the sampling points are located in the centers of the voxel cells. This grid type is typically used for volumetric datasets, which represent some quantity within the discrete voxel cell volumes.

    A `PointData` grid represents a field where the sampling points are located at the intersections of the grid lines. Note that, for this grid type only, the type of boundary conditions of the grid’s `domain` affect the uniform spacing of the sampling points:

    4 x 4 point-data grid (left: non-periodic domain, right: periodic domain)

    Default:

      `VoxelGrid.GridType.CellData`

  property shape: tuple[int, int, int]

    A 3-tuple specifying the number of sampling points along each of the three cell vectors of the `domain`.

    For two-dimensional grids, for which the `is2D` property of the `domain` is set, the third entry in this `shape` tuple must be equal to 1.

    Assigning a new shape to the grid automatically resizes the one-dimensional data arrays stored by this `PropertyContainer` and updates its `PropertyContainer.count` property to match the product of the three dimensions, i.e. the total number of data points.

    Default:

      `(0, 0, 0)`

  view(key)

    Returns a shaped view of the given grid property, which reflects the 2- or 3-dimensional `shape` of the grid.

    Parameters:

      key (str | Property) – The name of the grid property to look up. May include the underscore suffix to make the property mutable. Alternatively, you can directly specify a `Property` object from this `VoxelGrid`.

    Returns:

      A NumPy view of the underlying property array.

    Return type:

      NDArray

    Because the `VoxelGrid` class internally uses linear `Property` arrays to store the voxel cell values, you normally would have to convert back and forth between the linear index space of the underlying property storage and the 2- or 3-dimensional grid space to access individual voxel cells.

    The `view()` helper method frees you from having to map grid coordinates to array indices because it gives you a shaped NumPy view of the underlying linear storage, which reflects the correct multi-dimensional shape of the grid. For 3-dimensional grids, the ordering of the view’s dimensions is \(x,y,z[,k]\), with \(k\) being an extra dimension that is only present if the accessed property is a vector field quantity. For 2-dimensional grids, the ordering of the view’s dimensions is \(x,y[,k]\).

    The returned view lets you conveniently access the values of individual grid cells based on multi-dimensional grid coordinates. Here, as an example, the scalar field property `c_ave` of a 3-dimensional voxel grid:

        nx, ny, nz = grid.shape
        field = grid.view('c_ave')
        for x in range(nx):
            for y in range(ny):
                for z in range(nz):
                    print(field[x,y,z])

    Added in version 3.9.0.