a EbN)@s6dZddlZddlmZddlmZGdddZdS)z Tools for triangular grids. N)_api) Triangulationc@sLeZdZdZddZeddZdddZdd d Zd d Z e ddZ dS) TriAnalyzera Define basic tools for triangular mesh analysis and improvement. A TriAnalyzer encapsulates a `.Triangulation` object and provides basic tools for mesh analysis and mesh improvement. Attributes ---------- scale_factors Parameters ---------- triangulation : `~matplotlib.tri.Triangulation` The encapsulated triangulation to analyze. cCstjt|d||_dS)N) triangulation)rZcheck_isinstancer_triangulation)selfrrW/home/ja/django-apps/lartica_env/lib/python3.9/site-packages/matplotlib/tri/tritools.py__init__szTriAnalyzer.__init__cCsT|j}tjt||jjjddk}dt|jj|dt|jj|fS)a- Factors to rescale the triangulation into a unit square. Returns ------- (float, float) Scaling factors (kx, ky) so that the triangulation ``[triangulation.x * kx, triangulation.y * ky]`` fits exactly inside a unit square. Z minlengthr) rget_masked_trianglesnpbincountravelxsizeZptpy)rcompressed_trianglesZ node_usedrrr scale_factors s  zTriAnalyzer.scale_factorsTcCs:|r|j\}}nd\}}t|jj||jj|gj}||jj}|dddddf|dddddf}|dddddf|dddddf}|dddddf|dddddf}t|dddf|dddf}t|dddf|dddf}t|dddf|dddf}|||d} | ||| ||| ||| } | dk} t | r|j d} tj | tj d} tj | | <|||}|| d t| | | | <n|||d t| } |||d | | }|| }|jj}|dur&|Stjj||d SdS) aN Return 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 `scale_factors` (Only if *rescale* is True, which is its default value). Parameters ---------- rescale : bool, default: True If True, internally rescale (based on `scale_factors`), so that the (unmasked) triangles fit exactly inside a unit square mesh. Returns ------- 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. )?rNr rg?gZdtypeg@)mask)rrZvstackrrrT triangleshypotanyshapeemptyZfloat64infsqrtrmaarray)rrescaleZkxkyZptsZtri_ptsabcsprodZ bool_flatntriZ circum_radiusabcZ in_radiusZ circle_ratiorrrr circle_ratios2s>   ,,,$$$(      zTriAnalyzer.circle_ratios{Gz?c Cs|jjjd}|||k}|jj}|dur:tj|td}t|jj }tj |tj d}d}|dkrtj |dddk|@} | |@} | |B}t | }d|| ddf<d|| <t|dkd||}q\tj|dS)a Eliminate 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 `.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, default: 0.01 Border triangles with incircle/circumcircle radii ratio r/R will be removed if r/R < *min_circle_ratio*. rescale : bool, default: True If True, first, internally rescale (based on `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. Returns ------- array of bool 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. rNrr )ZaxisT)rrrr-rrZzerosboolcopyZ neighborsarangeint32minsumwherer"Zfilled) rZmin_circle_ratior$r+Zmask_bad_ratioZ current_maskZvalid_neighborsZrenum_neighborsZnaddZ wavefrontZ added_maskrrr get_flat_tri_maskus&0  zTriAnalyzer.get_flat_tri_maskc Cs|jj}|j}|jjjd}|dur6||}ntj|tjd}tj t ||jj j ddk}|jj |}|jj |}||}||}|||||fS)a Compress (if masked) the encapsulated triangulation. Returns minimal-length triangles array (*compressed_triangles*) and coordinates arrays (*compressed_x*, *compressed_y*) that can still describe the unmasked triangles of the encapsulated triangulation. Returns ------- compressed_triangles : array-like the returned compressed triangulation triangles compressed_x : array-like the returned compressed triangulation 1st coordinate compressed_y : array-like the returned compressed triangulation 2nd coordinate tri_renum : int array renumbering table to translate the triangle numbers from the encapsulated triangulation into the new (compressed) renumbering. -1 for masked triangles (deleted from *compressed_triangles*). node_renum : int array renumbering table to translate the point numbers from the encapsulated triangulation into the new (compressed) renumbering. -1 for unused points (i.e. those deleted from *compressed_x* and *compressed_y*). rNrr )rrr rr_total_to_compress_renumrr2r3rrrrr) rZtri_maskrr+Z tri_renumZ valid_nodeZ compressed_xZ compressed_yZ node_renumrrr _get_compressed_triangulations$     z)TriAnalyzer._get_compressed_triangulationcCs:tjt|dtjd}t|}tj|tjd||<|S)a Parameters ---------- valid : 1D bool array Validity mask. Returns ------- int array Array so that (`valid_array` being a compressed array based on a `masked_array` with mask ~*valid*): - For all i with valid[i] = True: valid_array[renum[i]] = masked_array[i] - For all i with valid[i] = False: renum[i] = -1 (invalid value) r/r)rfullrr3r5r2)ZvalidZrenumZn_validrrr r8s z$TriAnalyzer._total_to_compress_renumN)T)r.T) __name__ __module__ __qualname____doc__r propertyrr-r7r9 staticmethodr8rrrr r s  C K1r)r>numpyrZ matplotlibrZmatplotlib.trirrrrrr s