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import matplotlib.delaunay as delaunay
import matplotlib._tri as _tri
import numpy as np
class Triangulation(object):
"""
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.
Read-only attributes:
*x*: array of shape (npoints).
x-coordinates of grid points.
*y*: array of shape (npoints).
y-coordinates of grid points.
*triangles*: integer array of shape (ntri,3).
For each triangle, the indices of the three points that make
up the triangle, ordered in an anticlockwise manner.
*mask*: optional boolean array of shape (ntri).
Which triangles are masked out.
*edges*: integer array of shape (?,2).
All edges of non-masked triangles. Each edge is the start
point index and end point index. Each edge (start,end and
end,start) appears only once.
*neighbors*: integer array of shape (ntri,3).
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].
"""
def __init__(self, x, y, triangles=None, mask=None):
"""
Create a Triangulation object.
The first two arguments must be:
*x*, *y*: arrays of shape (npoints).
Point coordinates.
Optional arguments (args or keyword args):
*triangles*: integer array of shape (ntri,3).
For each triangle, the indices of the three points that make
up the triangle. If the points are ordered in a clockwise
manner, they are converted to anticlockwise.
If not specified, matplotlib.delaunay is used to create a
Delaunay triangulation of the points.
*mask*: optional boolean array of shape (ntri).
Which triangles are masked out.
"""
self.x = np.asarray(x, dtype=np.float64)
self.y = np.asarray(y, dtype=np.float64)
if self.x.shape != self.y.shape or len(self.x.shape) != 1:
raise ValueError("x and y must be equal-length 1-D arrays")
self.mask = None
self._edges = None
self._neighbors = None
if triangles is None:
# No triangulation specified, so use matplotlib.delaunay.
dt = delaunay.Triangulation(self.x, self.y)
self.triangles = np.asarray(dt.triangle_nodes, dtype=np.int32)
if mask is None:
self._edges = np.asarray(dt.edge_db, dtype=np.int32)
# Delaunay triangle_neighbors uses different edge indexing,
# so convert.
neighbors = np.asarray(dt.triangle_neighbors, dtype=np.int32)
self._neighbors = np.roll(neighbors, 1, axis=1)
else:
# Triangulation specified.
self.triangles = np.asarray(triangles, dtype=np.int32)
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=np.bool)
if len(self.mask.shape) != 1 or \
self.mask.shape[0] != 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
@property
def edges(self):
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.
"""
if self._cpp_triangulation is None:
self._cpp_triangulation = _tri.Triangulation(
self.x, self.y, self.triangles, self.mask, self._edges,
self._neighbors)
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.compress(1-self.mask, axis=0)
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[0]
args = args[1:]
else:
x = args[0]
y = args[1]
args = args[2:] # Consumed first two args.
ignore_remaining_args = True
# Check triangles in kwargs then args.
triangles = kwargs.pop('triangles', None)
from_args = False
if triangles is None and len(args) > 0:
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.
ignore_remaining_args = False
# Check for mask in kwargs then args.
mask = kwargs.pop('mask', None)
from_args = False
if mask is None and not ignore_remaining_args and len(args) > 0:
mask = args[0]
from_args = True
if mask is not None:
try:
mask = np.asarray(mask, dtype=np.bool)
except ValueError:
mask = None
if mask is not None and mask.ndim != 1:
mask = None
if mask is not None and triangles is not None and \
len(mask) != triangles.shape[0]:
mask = None
if mask is not None and from_args:
args = args[1:] # Consumed first item in args.
triangulation = Triangulation(x, y, triangles, mask)
return triangulation, args, kwargs
@property
def neighbors(self):
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=np.bool)
if len(self.mask.shape) != 1 or \
self.mask.shape[0] != 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