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""" Tools for triangular grids. """
""" Define basic tools for triangular mesh analysis and improvement.
A TriAnalizer encapsulates a :class:`~matplotlib.tri.Triangulation` object and provides basic tools for mesh analysis and mesh improvement.
Parameters ---------- triangulation : :class:`~matplotlib.tri.Triangulation` object The encapsulated triangulation to analyze.
Attributes ---------- `scale_factors`
""" if not isinstance(triangulation, Triangulation): raise ValueError("Expected a Triangulation object") self._triangulation = triangulation
def scale_factors(self): """ Factors to rescale the triangulation into a unit square.
Returns *k*, tuple of 2 scale factors.
Returns ------- k : tuple of 2 floats (kx, ky) Tuple of floats that would rescale the triangulation : ``[triangulation.x * kx, triangulation.y * ky]`` fits exactly inside a unit square.
""" compressed_triangles = self._triangulation.get_masked_triangles() node_used = (np.bincount(np.ravel(compressed_triangles), minlength=self._triangulation.x.size) != 0) return (1 / np.ptp(self._triangulation.x[node_used]), 1 / np.ptp(self._triangulation.y[node_used]))
""" Returns a measure of the triangulation triangles flatness.
The ratio of the incircle radius over the circumcircle radius is a widely used indicator of a triangle flatness. It is always ``<= 0.5`` and ``== 0.5`` only for equilateral triangles. Circle ratios below 0.01 denote very flat triangles.
To avoid unduly low values due to a difference of scale between the 2 axis, the triangular mesh can first be rescaled to fit inside a unit square with :attr:`scale_factors` (Only if *rescale* is True, which is its default value).
Parameters ---------- rescale : boolean, optional If True, a rescaling will be internally performed (based on :attr:`scale_factors`, so that the (unmasked) triangles fit exactly inside a unit square mesh. Default is True.
Returns ------- circle_ratios : masked array Ratio of the incircle radius over the circumcircle radius, for each 'rescaled' triangle of the encapsulated triangulation. Values corresponding to masked triangles are masked out.
""" # Coords rescaling if rescale: (kx, ky) = self.scale_factors else: (kx, ky) = (1.0, 1.0) pts = np.vstack([self._triangulation.x*kx, self._triangulation.y*ky]).T tri_pts = pts[self._triangulation.triangles] # Computes the 3 side lengths a = tri_pts[:, 1, :] - tri_pts[:, 0, :] b = tri_pts[:, 2, :] - tri_pts[:, 1, :] c = tri_pts[:, 0, :] - tri_pts[:, 2, :] a = np.sqrt(a[:, 0]**2 + a[:, 1]**2) b = np.sqrt(b[:, 0]**2 + b[:, 1]**2) c = np.sqrt(c[:, 0]**2 + c[:, 1]**2) # circumcircle and incircle radii s = (a+b+c)*0.5 prod = s*(a+b-s)*(a+c-s)*(b+c-s) # We have to deal with flat triangles with infinite circum_radius bool_flat = (prod == 0.) if np.any(bool_flat): # Pathologic flow ntri = tri_pts.shape[0] circum_radius = np.empty(ntri, dtype=np.float64) circum_radius[bool_flat] = np.inf abc = a*b*c circum_radius[~bool_flat] = abc[~bool_flat] / ( 4.0*np.sqrt(prod[~bool_flat])) else: # Normal optimized flow circum_radius = (a*b*c) / (4.0*np.sqrt(prod)) in_radius = (a*b*c) / (4.0*circum_radius*s) circle_ratio = in_radius/circum_radius mask = self._triangulation.mask if mask is None: return circle_ratio else: return np.ma.array(circle_ratio, mask=mask)
""" Eliminates excessively flat border triangles from the triangulation.
Returns a mask *new_mask* which allows to clean the encapsulated triangulation from its border-located flat triangles (according to their :meth:`circle_ratios`). This mask is meant to be subsequently applied to the triangulation using :func:`matplotlib.tri.Triangulation.set_mask`. *new_mask* is an extension of the initial triangulation mask in the sense that an initially masked triangle will remain masked.
The *new_mask* array is computed recursively; at each step flat triangles are removed only if they share a side with the current mesh border. Thus no new holes in the triangulated domain will be created.
Parameters ---------- min_circle_ratio : float, optional Border triangles with incircle/circumcircle radii ratio r/R will be removed if r/R < *min_circle_ratio*. Default value: 0.01 rescale : boolean, optional If True, a rescaling will first be internally performed (based on :attr:`scale_factors` ), so that the (unmasked) triangles fit exactly inside a unit square mesh. This rescaling accounts for the difference of scale which might exist between the 2 axis. Default (and recommended) value is True.
Returns ------- new_mask : array-like of booleans Mask to apply to encapsulated triangulation. All the initially masked triangles remain masked in the *new_mask*.
Notes ----- The rationale behind this function is that a Delaunay triangulation - of an unstructured set of points - sometimes contains almost flat triangles at its border, leading to artifacts in plots (especially for high-resolution contouring). Masked with computed *new_mask*, the encapsulated triangulation would contain no more unmasked border triangles with a circle ratio below *min_circle_ratio*, thus improving the mesh quality for subsequent plots or interpolation. """ # Recursively computes the mask_current_borders, true if a triangle is # at the border of the mesh OR touching the border through a chain of # invalid aspect ratio masked_triangles. ntri = self._triangulation.triangles.shape[0] mask_bad_ratio = self.circle_ratios(rescale) < min_circle_ratio
current_mask = self._triangulation.mask if current_mask is None: current_mask = np.zeros(ntri, dtype=bool) valid_neighbors = np.copy(self._triangulation.neighbors) renum_neighbors = np.arange(ntri, dtype=np.int32) nadd = -1 while nadd != 0: # The active wavefront is the triangles from the border (unmasked # but with a least 1 neighbor equal to -1 wavefront = ((np.min(valid_neighbors, axis=1) == -1) & ~current_mask) # The element from the active wavefront will be masked if their # circle ratio is bad. added_mask = np.logical_and(wavefront, mask_bad_ratio) current_mask = (added_mask | current_mask) nadd = np.sum(added_mask)
# now we have to update the tables valid_neighbors valid_neighbors[added_mask, :] = -1 renum_neighbors[added_mask] = -1 valid_neighbors = np.where(valid_neighbors == -1, -1, renum_neighbors[valid_neighbors])
return np.ma.filled(current_mask, True)
return_node_renum=False): """ Compress (if masked) the encapsulated triangulation.
Returns minimal-length triangles array (*compressed_triangles*) and coordinates arrays (*compressed_x*, *compressed_y*) that can still describe the unmasked triangles of the encapsulated triangulation.
Parameters ---------- return_tri_renum : boolean, optional Indicates whether a renumbering table to translate the triangle numbers from the encapsulated triangulation numbering into the new (compressed) renumbering will be returned. return_node_renum : boolean, optional Indicates whether a renumbering table to translate the nodes numbers from the encapsulated triangulation numbering into the new (compressed) renumbering will be returned.
Returns ------- compressed_triangles : array-like the returned compressed triangulation triangles compressed_x : array-like the returned compressed triangulation 1st coordinate compressed_y : array-like the returned compressed triangulation 2nd coordinate tri_renum : array-like of integers renumbering table to translate the triangle numbers from the encapsulated triangulation into the new (compressed) renumbering. -1 for masked triangles (deleted from *compressed_triangles*). Returned only if *return_tri_renum* is True. node_renum : array-like of integers renumbering table to translate the point numbers from the encapsulated triangulation into the new (compressed) renumbering. -1 for unused points (i.e. those deleted from *compressed_x* and *compressed_y*). Returned only if *return_node_renum* is True.
""" # Valid triangles and renumbering tri_mask = self._triangulation.mask compressed_triangles = self._triangulation.get_masked_triangles() ntri = self._triangulation.triangles.shape[0] tri_renum = self._total_to_compress_renum(tri_mask, ntri)
# Valid nodes and renumbering node_mask = (np.bincount(np.ravel(compressed_triangles), minlength=self._triangulation.x.size) == 0) compressed_x = self._triangulation.x[~node_mask] compressed_y = self._triangulation.y[~node_mask] node_renum = self._total_to_compress_renum(node_mask)
# Now renumbering the valid triangles nodes compressed_triangles = node_renum[compressed_triangles]
# 4 cases possible for return if not return_tri_renum: if not return_node_renum: return compressed_triangles, compressed_x, compressed_y else: return (compressed_triangles, compressed_x, compressed_y, node_renum) else: if not return_node_renum: return (compressed_triangles, compressed_x, compressed_y, tri_renum) else: return (compressed_triangles, compressed_x, compressed_y, tri_renum, node_renum)
""" Parameters ---------- mask : 1d boolean array or None mask n : integer length of the mask. Useful only id mask can be None
Returns ------- renum : integer array array so that (`valid_array` being a compressed array based on a `masked_array` with mask *mask*) :
- For all i such as mask[i] = False: valid_array[renum[i]] = masked_array[i] - For all i such as mask[i] = True: renum[i] = -1 (invalid value)
""" if n is None: n = np.size(mask) if mask is not None: renum = -np.ones(n, dtype=np.int32) # Default num is -1 valid = np.arange(n, dtype=np.int32).compress(~mask, axis=0) renum[valid] = np.arange(np.size(valid, 0), dtype=np.int32) return renum else: return np.arange(n, dtype=np.int32) |