B ]t\0@s,dZddlZddlmZGdddeZdS)z Tools for triangular grids. N) Triangulationc@sPeZdZdZddZeddZdddZdd d Zdd dZ e dddZ dS) TriAnalyzera 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` cCst|tstd||_dS)NzExpected a Triangulation object) isinstancer ValueError_triangulation)selfZ triangulationr6lib/python3.7/site-packages/matplotlib/tri/tritools.py__init__s zTriAnalyzer.__init__cCsT|j}tjt||jjjddk}dt|jj|dt|jj|fS)ar 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. ) minlengthr) rget_masked_trianglesnpbincountravelxsizeZptpy)rcompressed_trianglesZ node_usedrrr scale_factors s   zTriAnalyzer.scale_factorsTcCsX|r|j\}}nd\}}t|jj||jj|gj}||jj}|dddddf|dddddf}|dddddf|dddddf}|dddddf|dddddf}t|dddfd|dddfd}t|dddfd|dddfd}t|dddfd|dddfd}|||d} | ||| ||| ||| } | dk} t | r|j d} tj | tj d} tj | | <|||}|| d t| | | | <n|||d t| } |||d | | }|| }|jj}|dkrD|Stjj||d SdS) a 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. )g?g?Nr rg?g)dtypeg@)mask)rrZvstackrrrT trianglesZsqrtanyshapeemptyZfloat64infrmaZarray)rrescaleZkxZkyZptsZtri_ptsabcsZprodZ bool_flatntriZ circum_radiusabcZ in_radiusZ circle_ratiorrrr circle_ratios5s:  ,,,...(     zTriAnalyzer.circle_ratios{Gz?c Cs|jjjd}|||k}|jj}|dkr:tj|td}t|jj }tj |tj d}d}xp|dkrtj |dddk|@} t | |} | |B}t| }d|| ddf<d|| <t|dkd||}q^Wtj|dS)a 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. rN)rr )axisT)rrrr'rrZzerosboolcopyZ neighborsarangeint32minZ logical_andsumwhererZfilled) rZmin_circle_ratior r%Zmask_bad_ratioZ current_maskZvalid_neighborsZrenum_neighborsZnaddZ wavefrontZ added_maskrrr get_flat_tri_maskzs&1    zTriAnalyzer.get_flat_tri_maskFc Cs|jj}|j}|jjjd}|||}tjt||jj j ddk}|jj |}|jj |} ||} | |}|s|s||| fS||| | fSn|s||| |fS||| || fSdS)a8 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. r)r N) rrr rr_total_to_compress_renumrrrrrr) rZreturn_tri_renumZreturn_node_renumZtri_maskrr%Z tri_renumZ node_maskZ compressed_xZ compressed_yZ node_renumrrr _get_compressed_triangulations()     z)TriAnalyzer._get_compressed_triangulationNcCs||dkrt|}|dk rhtj|tjd }tj|tjdj|dd}tjt|dtjd||<|Stj|tjdSdS)aT 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) N)rr)r*)rrZonesr.r-compress)rnZrenumZvalidrrr r3s z$TriAnalyzer._total_to_compress_renum)T)r(T)FF)N) __name__ __module__ __qualname____doc__r propertyrr'r2r4 staticmethodr3rrrr r s  E M Fr)r:ZnumpyrZmatplotlib.trirobjectrrrrr s