triangulation.py

import numpy as np


class Triangulation:
    """
    An unstructured triangular grid consisting of npoints points and
    ntri triangles.  The triangles can either be specified by the user
    or automatically generated using a Delaunay triangulation.

    Parameters
    ----------
    x, y : array-like of shape (npoints)
        Coordinates of grid points.
    triangles : integer array-like of shape (ntri, 3), optional
        For each triangle, the indices of the three points that make
        up the triangle, ordered in an anticlockwise manner.  If not
        specified, the Delaunay triangulation is calculated.
    mask : boolean array-like of shape (ntri), optional
        Which triangles are masked out.

    Attributes
    ----------
    edges : int array of shape (nedges, 2)
        See `~.Triangulation.edges`
    neighbors : int array of shape (ntri, 3)
        See `~.Triangulation.neighbors`
    mask : bool array of shape (ntri, 3)
        Masked out triangles.
    is_delaunay : bool
        Whether the Triangulation is a calculated Delaunay
        triangulation (where *triangles* was not specified) or not.

    Notes
    -----
    For a Triangulation to be valid it must not have duplicate points,
    triangles formed from colinear points, or overlapping triangles.
    """
    def __init__(self, x, y, triangles=None, mask=None):
        from matplotlib import _qhull

        self.x = np.asarray(x, dtype=np.float64)
        self.y = np.asarray(y, dtype=np.float64)
        if self.x.shape != self.y.shape or self.x.ndim != 1:
            raise ValueError("x and y must be equal-length 1-D arrays")

        self.mask = None
        self._edges = None
        self._neighbors = None
        self.is_delaunay = False

        if triangles is None:
            # No triangulation specified, so use matplotlib._qhull to obtain
            # Delaunay triangulation.
            self.triangles, self._neighbors = _qhull.delaunay(x, y)
            self.is_delaunay = True
        else:
            # Triangulation specified. Copy, since we may correct triangle
            # orientation.
            self.triangles = np.array(triangles, dtype=np.int32, order='C')
            if self.triangles.ndim != 2 or self.triangles.shape[1] != 3:
                raise ValueError('triangles must be a (?,3) array')
            if self.triangles.max() >= len(self.x):
                raise ValueError('triangles max element is out of bounds')
            if self.triangles.min() < 0:
                raise ValueError('triangles min element is out of bounds')

        if mask is not None:
            self.mask = np.asarray(mask, dtype=bool)
            if self.mask.shape != (self.triangles.shape[0],):
                raise ValueError('mask array must have same length as '
                                 'triangles array')

        # Underlying C++ object is not created until first needed.
        self._cpp_triangulation = None

        # Default TriFinder not created until needed.
        self._trifinder = None

    def calculate_plane_coefficients(self, z):
        """
        Calculate plane equation coefficients for all unmasked triangles from
        the point (x, y) coordinates and specified z-array of shape (npoints).
        The returned array has shape (npoints, 3) and allows z-value at (x, y)
        position in triangle tri to be calculated using
        ``z = array[tri, 0] * x  + array[tri, 1] * y + array[tri, 2]``.
        """
        return self.get_cpp_triangulation().calculate_plane_coefficients(z)

    @property
    def edges(self):
        """
        Return integer array of shape (nedges, 2) containing all edges of
        non-masked triangles.

        Each row defines an edge by it's start point index and end point
        index.  Each edge appears only once, i.e. for an edge between points
        *i*  and *j*, there will only be either *(i, j)* or *(j, i)*.
        """
        if self._edges is None:
            self._edges = self.get_cpp_triangulation().get_edges()
        return self._edges

    def get_cpp_triangulation(self):
        """
        Return the underlying C++ Triangulation object, creating it
        if necessary.
        """
        from matplotlib import _tri
        if self._cpp_triangulation is None:
            self._cpp_triangulation = _tri.Triangulation(
                self.x, self.y, self.triangles, self.mask, self._edges,
                self._neighbors, not self.is_delaunay)
        return self._cpp_triangulation

    def get_masked_triangles(self):
        """
        Return an array of triangles that are not masked.
        """
        if self.mask is not None:
            return self.triangles[~self.mask]
        else:
            return self.triangles

    @staticmethod
    def get_from_args_and_kwargs(*args, **kwargs):
        """
        Return a Triangulation object from the args and kwargs, and
        the remaining args and kwargs with the consumed values removed.

        There are two alternatives: either the first argument is a
        Triangulation object, in which case it is returned, or the args
        and kwargs are sufficient to create a new Triangulation to
        return.  In the latter case, see Triangulation.__init__ for
        the possible args and kwargs.
        """
        if isinstance(args[0], Triangulation):
            triangulation, *args = args
        else:
            x, y, *args = args

            # Check triangles in kwargs then args.
            triangles = kwargs.pop('triangles', None)
            from_args = False
            if triangles is None and args:
                triangles = args[0]
                from_args = True

            if triangles is not None:
                try:
                    triangles = np.asarray(triangles, dtype=np.int32)
                except ValueError:
                    triangles = None

            if triangles is not None and (triangles.ndim != 2 or
                                          triangles.shape[1] != 3):
                triangles = None

            if triangles is not None and from_args:
                args = args[1:]  # Consumed first item in args.

            # Check for mask in kwargs.
            mask = kwargs.pop('mask', None)

            triangulation = Triangulation(x, y, triangles, mask)
        return triangulation, args, kwargs

    def get_trifinder(self):
        """
        Return the default :class:`matplotlib.tri.TriFinder` of this
        triangulation, creating it if necessary.  This allows the same
        TriFinder object to be easily shared.
        """
        if self._trifinder is None:
            # Default TriFinder class.
            from matplotlib.tri.trifinder import TrapezoidMapTriFinder
            self._trifinder = TrapezoidMapTriFinder(self)
        return self._trifinder

    @property
    def neighbors(self):
        """
        Return integer array of shape (ntri, 3) containing neighbor triangles.

        For each triangle, the indices of the three triangles that
        share the same edges, or -1 if there is no such neighboring
        triangle.  ``neighbors[i, j]`` is the triangle that is the neighbor
        to the edge from point index ``triangles[i,j]`` to point index
        ``triangles[i,(j+1)%3]``.
        """
        if self._neighbors is None:
            self._neighbors = self.get_cpp_triangulation().get_neighbors()
        return self._neighbors

    def set_mask(self, mask):
        """
        Set or clear the mask array.  This is either None, or a boolean
        array of shape (ntri).
        """
        if mask is None:
            self.mask = None
        else:
            self.mask = np.asarray(mask, dtype=bool)
            if self.mask.shape != (self.triangles.shape[0],):
                raise ValueError('mask array must have same length as '
                                 'triangles array')

        # Set mask in C++ Triangulation.
        if self._cpp_triangulation is not None:
            self._cpp_triangulation.set_mask(self.mask)

        # Clear derived fields so they are recalculated when needed.
        self._edges = None
        self._neighbors = None

        # Recalculate TriFinder if it exists.
        if self._trifinder is not None:
            self._trifinder._initialize()