import sys import numpy as np from matplotlib import _api 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 : (npoints,) array-like Coordinates of grid points. triangles : (ntri, 3) array-like of int, 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 : (ntri,) array-like of bool, optional Which triangles are masked out. Attributes ---------- triangles : (ntri, 3) array of int For each triangle, the indices of the three points that make up the triangle, ordered in an anticlockwise manner. If you want to take the *mask* into account, use `get_masked_triangles` instead. mask : (ntri, 3) array of bool or None 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 1D arrays, but " f"found shapes {self.x.shape!r} and " f"{self.y.shape!r}") 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, sys.flags.verbose) self.is_delaunay = True else: # Triangulation specified. Copy, since we may correct triangle # orientation. try: self.triangles = np.array(triangles, dtype=np.int32, order='C') except ValueError as e: raise ValueError('triangles must be a (N, 3) int array, not ' f'{triangles!r}') from e if self.triangles.ndim != 2 or self.triangles.shape[1] != 3: raise ValueError( 'triangles must be a (N, 3) int array, but found shape ' f'{self.triangles.shape!r}') if self.triangles.max() >= len(self.x): raise ValueError( 'triangles are indices into the points and must be in the ' f'range 0 <= i < {len(self.x)} but found value ' f'{self.triangles.max()}') if self.triangles.min() < 0: raise ValueError( 'triangles are indices into the points and must be in the ' f'range 0 <= i < {len(self.x)} but found value ' f'{self.triangles.min()}') # Underlying C++ object is not created until first needed. self._cpp_triangulation = None # Default TriFinder not created until needed. self._trifinder = None self.set_mask(mask) 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 its 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( # For unset arrays use empty tuple which has size of zero. self.x, self.y, self.triangles, self.mask if self.mask is not None else (), self._edges if self._edges is not None else (), self._neighbors if self._neighbors is not None else (), not self.is_delaunay) return self._cpp_triangulation def get_masked_triangles(self): """ Return an array of triangles taking the mask into account. """ 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 if 'triangles' in kwargs: _api.warn_external( "Passing the keyword 'triangles' has no effect when also " "passing a Triangulation") if 'mask' in kwargs: _api.warn_external( "Passing the keyword 'mask' has no effect when also " "passing a Triangulation") else: x, y, triangles, mask, args, kwargs = \ Triangulation._extract_triangulation_params(args, kwargs) triangulation = Triangulation(x, y, triangles, mask) return triangulation, args, kwargs @staticmethod def _extract_triangulation_params(args, kwargs): 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) return x, y, triangles, mask, args, kwargs def get_trifinder(self): """ Return the default `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. Parameters ---------- mask : None or bool array of length 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 if self.mask is not None else ()) # 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()