# `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 of 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` (a specialized `PropertyContainer` for bonds)

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

> - `DataTable` (a specialized `PropertyContainer` for tabulated data)

> - `TrajectoryLines` (a set of particle trajectory lines)

Data objects:

> - `Property` (holds per-data-element 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 element type definitions)

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

> - `BondType` (describes a single bond type)

> - `DislocationSegment` (a dislocation line in a `DislocationNetwork`)

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_list = data.particles.bonds.bond_types.types
      for bond_type in bond_type_list:
          print(bond_type.id, bond_type.name, bond_type.color)

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 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 attribute name | 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) – Optional type ID to be assigned to the new bond. This value will be stored to the `bond_types` array.

      - pbcvec (tuple) – Three integers specifying the bond’s crossings of periodic cell boundaries. The information will be stored in the `pbc_vectors` array.

    Returns:

      The index of the newly created bond, i.e. `(Bonds.count-1)`.

    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

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

  property colors

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

  property pbc_vectors

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

  property selection

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

  property topology

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

class ovito.data.BondsEnumerator(bonds: ovito.data.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: In case you rather 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.

    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 – 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 – 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 completely arbitrary order.

    Returns:

      `(neigh_idx, neigh_vec)`

    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.

    New 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 – 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.

    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)

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

    Parameters:

      index (int) – 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)

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

    Parameters:

      index (int) – 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 holding 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, the simulation cell information and additional auxiliary data such as the current timestep 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 through this 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 `surfaces` dictionary provides key-based access to all the `SurfaceMesh` instances currently in the data collection.

  You can programmatically add or remove data objects from a data collection by manipulating its `objects` list. For instance, to populate a new data collection instance that is initially empty with a new `SimulationCell` object:

      data = DataCollection()
      cell = SimulationCell()
      data.objects.append(cell)
      assert(data.cell is cell)

  apply(modifier, frame=None)

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

    Parameters:

      - modifier (ovito.pipeline.Modifier) – The modifier object that should alter the contents of this data collection in place.

      - frame (int) – 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(CoordinationAnalysisModifier(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(CoordinationAnalysisModifier(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

    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. 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

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

    The method may 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 will still share the data objects with the original collection. Data objects that are shared by two or more data collections are protected against modification by default to avoid unwanted side effects. Thus, in order to subsequently modify the data objects in either the original collection or its copy, you will have to use the underscore notation or the `DataObject.make_mutable()` method to explicitly request 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)

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

      - pbc – A tuple of three Booleans specifying the cell’s `pbc` flags.

      - vis_params (Mapping[str, Any]) – Optional dictionary to initialize attributes of the attached `SimulationCellVis` element (only used if the cell object is newly created by the method).

    Return type:

      ovito.data.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

    New 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 – 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]) – Optional dictionary to initialize attributes of the attached `ParticlesVis` element (only used if the particles object is newly created by the method).

    Return type:

      ovito.data.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)

    New in version 3.7.4.

  property dislocations

    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`.

  property grids

    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 objects

    Flat list of all top-level `DataObjects` currently 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 a particular class 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

    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

    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

    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 trajectories

    Returns the `TrajectoryLines` object, which holds the continuous particle trajectories traced by the `GenerateTrajectoryLinesModifier`. `None` is returned if the data collection does not contain a `TrajectoryLines` object.

  property triangle_meshes

    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.

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

  property identifier

    The unique identifier string of the data object. It serves as lookup key in object dictionaries, for example the `DataCollection.tables` collection, or as a target name in various places where a data object needs to be referenced by name, e.g. the `TimeAveragingModifier.operate_on` field.

    Data objects generated by modifiers in a pipeline typically have an automatically assigned identifier, as documented in the description of the respective modifier. When writing your own modifier function, you are responsible for giving new data objects created by your modifier function a meaningful identifier, so that subsequent modifiers in the pipeline can refer to these data objects.

  make_mutable(subobj)

    This helper method requests a deep copy of subobj, which must be a child `DataObject` of this parent `DataObject`. A copy will only be made in case the sub-object is currently referenced by at least one more parent object. If, however, the sub-object is exclusively owned by this `DataObject`, no copy is made and the original sub-object is returned as is. The returned object is safe to modify without unexpected side effects, because any shared ownership is converted to an exclusive ownership by the method.

    Please see the section Announcing object modification for a discussion of object ownership and typical use cases for this method.

    Parameters:

      subobj (DataObject) – A existing sub-object of this parent data object, for which exclusive ownership is requested.

    Returns:

      A copy of subobj if its ownership was previously shared with some other parent. Otherwise the original object is returned.

  property vis

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

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 `CoordinationAnalysisModifier` 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 CoordinationAnalysisModifier

  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 programatically 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

    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

    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

    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`.

  property y

    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.DislocationNetwork

  Base: `ovito.data.DataObject`

  This data object stores the network of dislocation lines extracted by a `DislocationAnalysisModifier`. You can access it through the `DataCollection.dislocations` field.

  The dislocation network is associated with a `DislocationVis` element controlling the visual appearance of the dislocation lines. It can be accessed through the `vis` attribute of the `DataObject` base class.

  Example:

      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 segments" % len(data.dislocations.segments))
      for segment in data.dislocations.segments:
          print("Segment %i: length=%f, Burgers vector=%s" % (segment.id, segment.length, segment.true_burgers_vector))
          print(segment.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 export

  A dislocation network can be written to a data file in the form of polylines using the `ovito.io.export_file()` function (select the `vtk/disloc` output format). During export, a non-periodic version is produced by clipping dislocation lines at the domain boundaries.

  property segments

    The list of dislocation segments in this dislocation network. This list-like object is read-only and contains `DislocationSegment` objects.

  set_segment(index, true_burgers_vector=None, cluster_id=None, points=None, custom_color=None)

    This method allows you to change the data fields of individual dislocation lines. Fields for which no new value is specified will keep their current values.

    Parameters:

      - index – The zero-based index of the dislocation line in the `segments` array to be modified.

      - true_burgers_vector – The lattice-space Burgers vector (`true_burgers_vector`) to be assigned to the dislocation line.

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

      - points – A N x 3 NumPy array with the Cartesian coordinates of the dislocation line vertices.

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

    Example of a user-defined modifier function manipulating 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, seg in enumerate(data.dislocations.segments):
                data.dislocations_.set_segment(index,
                    true_burgers_vector = np.negative(seg.true_burgers_vector),
                    points = np.flipud(seg.points))

            # Highlight all 1/6[121] dislocations in a red color:
            for index, seg in enumerate(data.dislocations.segments):
                if np.allclose(seg.true_burgers_vector, (1/6, 2/6, 1/6)):
                    data.dislocations_.set_segment(index, custom_color=(1, 0, 0))

class ovito.data.DislocationSegment

  A single dislocation line from a `DislocationNetwork`.

  The list of dislocation segments is returned by the `DislocationNetwork.segments` attribute.

  property cluster_id

    The numeric identifier of the crystal cluster of atoms containing this dislocation segment.

    The true Burgers vector of the segment is expressed in the local coordinate system of this crystal cluster.

  property custom_color

    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

    The unique identifier of this dislocation segment.

  property is_infinite_line

    This property indicates whether this segment is an infinite line passing through a periodic simulation box boundary. A segment is considered infinite if it is a closed loop and its start and end points do not coincide.

    See also the `is_loop` property.

  property is_loop

    This property indicates whether this segment forms a closed dislocation loop. Note that an infinite dislocation line passing through a periodic boundary is also considered a loop.

    See also the `is_infinite_line` property.

  property length

    Returns the length of this dislocation segment.

  property points

    The list of space points that define the shape of this dislocation segment. This is a N x 3 Numpy array, where N is the number of points along the segment. For closed loops, the first and the last point coincide.

  property spatial_burgers_vector

    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

    The Burgers vector of the segment, expressed in the local coordinate system of the crystal. Also known as the True Burgers vector.

class ovito.data.ElementType

  Base: `ovito.data.DataObject`

  This class represents a single type of data elements, for example a particular atom or bond type. It serves as common base class for the `ParticleType` and `BondType` classes, which represent these more specific types.

  Each type has a unique numeric `id`, which is used when looking up types given some numeric value in a typed `Property` array. An example for a typed property is the particle property `'Particle Type'`. The property object manages all its associated types in its `Property.types` list.

  The `Property.type_by_id()` and `Property.type_by_name()` methods allow looking up a certain `ElementType` based on its numeric identifier or name string.

  property color

    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

    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

    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

    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.NearestNeighborFinder(N, data_collection)

  A utility class that finds the N nearest neighbors of a particle.

  See also

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

  The 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 built-in maximum of neighbors supported by this class.

  Note

  Keep in mind that, if the system contains only N particles or less, and if the simulation does not use periodic boundary conditions, then the neighbor finder 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)

  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).

    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 use of all parallel processor cores.

    The method returns two NumPy 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.

    Parameters:

      indices – 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)`

    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_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 – 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).

    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 property fields of the 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 data 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 are all stored in the `Property` object with the name `'Particle Type'`, which also stores for each particle what its type is. The association between particles and particle types is established via a unique numeric type `id`. The following code shows how to iterate over all particle types in a dataset, which are listed in the `Property.types` field of the `particle_types` property:

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

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

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

  The order in which the particle types are stored in the `Property.types` list is arbitrary, and the unique numeric IDs of particle types have no specific meaning in general. A common operation is to find the `ParticleType` in the list corresponding to a given numeric ID. For this look up operation, the `Property` class provides the `type_by_id()` method:

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

      # Iterate over all particles and print their type's name:
      for tid in prop[...]:
          print(prop.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 kind of look up operation, the `type_by_name()` method may be used, which assumes that each type has a unique `name` (which may not always be true):

      # Print numeric ID of particle type 'Si':
      print(prop.type_by_name('Si').id)

  property backface_culling

    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

    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 :py:`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

    The mass of this particle type.

    Default:

      `0.0`

  property mesh

    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, uniformely 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`

    New in version 3.8.0.

  property radius

    This property controls the display radius of the 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

    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

    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 :py:`mesh` has been assigned to this particle type, e.g., by calling the `load_shape()` method.

    Default:

      `False`

  property vdw_radius

    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
  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 (array-like) – The xyz coordinates for the new particle.

    Returns:

      The index of the newly created particle, i.e. `(Particles.count-1)`.

  property angles

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

  property bonds

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

  property colors

    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 – 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]) – Optional dictionary to initialize attributes of the attached `BondsVis` element (only used if the bonds object is newly created by the method).

    Return type:

      ovito.data.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)

    New 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 – Zero-based index of the first input particle. This may also be an array of particle indices.

      - b – 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, also returns 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 \(n\).

  property dihedrals

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

  property forces

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

  property identifiers

    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 contigous. 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

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

  property masses

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

  property orientations

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

  property particle_types

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

  property positions

    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) → numpy.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)

    New in version 3.7.5.

  property selection

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

  property structure_types

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

  property velocities

    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 cordinates 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 is a property with 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

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

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

  Here, each number in the property array refers to one of the particle types (e.g. 1=Cu, 2=Ni, 3=Fe, etc.). The defined particle types, each one represented by an instance of the `ParticleType` auxiliary class, are stored in the `types` array of the `Property`. Each type has a unique `id`, a human-readable `name` and other attributes like `color` and `radius` that control the visual appearance of particles belonging to the type:

      >>> for type in tprop.types:
      ...     print(type.id, type.name, type.color, type.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

  IDs of types typically start at 1 and form a consecutive sequence as in the example above. Note, however, that the `types` list may store the `ParticleType` objects in an arbitrary order. Thus, in general, it is not valid to directly use a type ID as an index into the `types` array. Instead, the `type_by_id()` method should be used to look up the `ParticleType`:

      >>> for i,t in enumerate(tprop): # (loop over the type ID of each particle)
      ...     print('Atom', i, 'is of type', tprop.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 looks up a `ParticleType` by name. For example, to count the number of Fe atoms in a system:

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

  Note that OVITO supports multiple type classifications. For example, in addition to the “Particle Type” standard particle property, which stores the chemical types of atoms (e.g. C, H, Fe, …), the “Structure Type” property may hold the structural types computed for atoms (e.g. FCC, BCC, …) maintaining its own list of known structure types in the `types` array.

  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 preconfigured (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()`

    New 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 preconfigured (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

    New in version 3.9.0.

  property component_count

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

  property component_names

    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, …).

    For predefined standard properties, OVITO automatically initializes the components list.

  property name

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

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

  type_by_id(id, raise_error=True)

    Looks up and returns the `ElementType` with the given unique numeric ID in this property’s `types` list. Depending on raise_error, 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 exists, 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 the numeric atom types from a LAMMPS simulation some names:
        data.particles_.particle_types_.type_by_id_(1).name = 'C'
        data.particles_.particle_types_.type_by_id_(2).name = 'H'

  type_by_name(name, raise_error=True)

    Looks up and returns the `ElementType` with the given name in this property’s `types` list. If multiple types exists with the same name, the first type is returned. Depending on raise_error, 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 exists, 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

    The list of `ElementType` instances attached to this property.

    Note that the element types may be stored in arbitrary order in this list. Thus, it is not valid to use a numeric type ID as an index into this list.

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`

  > - `TrajectoryLines`

  > - `SurfaceMesh.vertices`

  > - `SurfaceMesh.faces`

  > - `SurfaceMesh.regions`

  property count

    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).

    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

    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 NumPy array. Specifying a one-dimensional array creates a scalar property whereas a two-dimensional array creates a vectorial property. Alternatively, the dtype and components parameters can be specified explicitly if you are going to set the property values at a later time:

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

    If the property to be created already exists in the container, it gets replaced with a modifiable copy if necessary. The values of the property get overwritten with data in this case.

    Note: If you’re creating new `PropertyContainer`, its element `count` is 0 initially. In this state 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:

        # 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 properties subsequently added to the container must have the same length.

    Parameters:

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

      - data – 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 – Data type of the user-defined property. Must be `int`, `float`, `numpy.int8`, `numpy.int32`, `numpy.int64`, `numpy.float32`, or `numpy.float64`.

      - components (int) – Number of vector components of the user-defined property (1 if not specified).

    Returns:

      The new `Property` object.

  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.

  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 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))

  property title

    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 away 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 – 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 – 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 \(n\).

    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

    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

    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

    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

    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

    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]))

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 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 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 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 to look inside the enclosed volume. The `SurfaceMesh` objects 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()`

    New in version 3.7.9.

  create_face(vertices: Sequence[int] | numpy.ndarray) → 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)])

    New in version 3.7.9.

  create_faces(vertex_lists: Sequence[Sequence[int]] | numpy.ndarray) → 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.

    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()

    New in version 3.7.9.

  create_vertices(coords: Sequence[Sequence[float]] | numpy.ndarray) → 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.

    New in version 3.7.9.

  property domain

    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

    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()

    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=False) → numpy.ndarray | 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.

    New in version 3.7.9.

  locate_point(pos, eps=1e-6)

    Determines which spatial region of the mesh contains the given point in 3-d space.

    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.

    Parameters:

      - pos (array-like) – The (x,y,z) coordinates of the query point

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

    Returns:

      The numeric ID of the spatial region containing pos; or `None` if pos is exactly on the dividing boundary between two regions

  property regions

    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)

    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

    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, numpy.ndarray]

    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.

    New in version 3.7.5.

  property topology

    A `SurfaceMeshTopology` object storing the face connectivity of the mesh.

  property vertices

    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`

  New 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
  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

    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

    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

    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`

    New 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
  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 a given vertex. Once the end of the linked 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

    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.TrajectoryLines

  Base: `ovito.data.PropertyContainer`

  Data object that stores the trajectory lines of a set of particles, which have been traced by the `GenerateTrajectoryLinesModifier`. It is typically part of a pipeline’s output data collection, from where it can be accessed via the `DataCollection.trajectories` field.

  A `TrajectoryLines` object has an associated `TrajectoryVis` element, which controls the visual appearance of the trajectory lines in rendered images. This visual element is accessible through the `vis` attribute of the base class.

  property particle_ids

    The `Property` data array storing the particle IDs of the line vertices.

  property positions

    The `Property` data array storing the XYZ coordinates of the line vertices.

  property time_stamps

    The `Property` data array storing the time stamps of the line vertices.

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 describing 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

    The number of triangular faces of the mesh, \(n_{\mathrm{f}}\).

    Default:

      0

  get_faces()

    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()

    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)

    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)

    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

    The number of vertices of the mesh, \(n_{\mathrm{v}}\).

    Default:

      0

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 uniformily 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=VoxelGridVis(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))

  property domain

    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

    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

    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 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.

    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])

    New in version 3.9.0.