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""" 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. """ 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
""" 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)
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
""" Return the underlying C++ Triangulation object, creating it if necessary. """ 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
""" Return an array of triangles that are not masked. """ if self.mask is not None: return self.triangles.compress(1 - self.mask, axis=0) else: return self.triangles
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[0] args = args[1:] else: x = args[0] y = args[1] args = args[2:] # Consumed first two 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
""" 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
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
""" 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() |