+ £‡iO)ãó>€Rt^RIt^RIHt^RIHt!RR4tR#)z Tools for triangular grids. N)Ú_api)Ú Triangulationcóda€]tRt^ toRtRt]R4tR RltR Rlt Rt ] R4t Rt VtR #) Ú TriAnalyzeraT 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. cóJ€\P!\VR7WnR#))Ú triangulationN)rÚcheck_isinstancerÚ_triangulation)Úselfrs&&Úx/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/matplotlib/tri/_tritools.pyÚ__init__ÚTriAnalyzer.__init__s€Ü ×Òœm¸=ÕIØ+Öóc ó°€VPP4p\P!\P!V4VPP P R7^8gp^\P!VPP V,4, ^\P!VPPV,4, 3#)zí 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. ©Ú minlength) r Úget_masked_trianglesÚnpÚbincountÚravelÚxÚsizeÚptpÚy)r Úcompressed_trianglesÚ node_useds& r Ú scale_factorsÚTriAnalyzer.scale_factors s €ð $×2Ñ2×GÑGÓIÐÜ—[’[¤§¢Ð*>Ó!?Ø+/×+>Ñ+>×+@Ñ+@×+EÑ+EôGØJKñLˆ à”B—F’F˜4×.Ñ.×0Ñ0°Õ;Ó<Õ<Ø”B—F’F˜4×.Ñ.×0Ñ0°Õ;Ó<Õ<ð>ð >rc óÄ€V'dVPwr#MRRr2\P!VPPV,VPP V,.4P pW@PP,pVR,VR,, pVR ,VR,, pVR,VR ,, p\P!VR ,VR ,4p\P!VR ,VR ,4p\P!VR ,VR ,4pWg,V,R,p W–V,V , ,Wh,V , ,Wx,V , ,p V R8Hp \P!V 4'd‘VP^,p \P!V \PR7p \PWÛ&Wg,V,pWë(,R\P!W«(,4,, WÛ(&M1Wg,V,R\P!V 4,, p Wg,V,RV ,V ,, pWý, pVPPpVfV#\P P#VVR7#) a¦ Return a measure of the triangulation triangles flatness. The ratio of the incircle radius over the circumcircle radius is a widely used indicator of a triangle flatness. It is always ``<= 0.5`` and ``== 0.5`` only for equilateral triangles. Circle ratios below 0.01 denote very flat triangles. To avoid unduly low values due to a difference of scale between the 2 axis, the triangular mesh can first be rescaled to fit inside a unit square with `scale_factors` (Only if *rescale* is True, which is its default value). Parameters ---------- rescale : bool, default: True If True, internally rescale (based on `scale_factors`), so that the (unmasked) triangles fit exactly inside a unit square mesh. Returns ------- masked array Ratio of the incircle radius over the circumcircle radius, for each 'rescaled' triangle of the encapsulated triangulation. Values corresponding to masked triangles are masked out. gð?gà?g©Údtypeg@)Úmask)ºNNNér")r"ér")r"ér")r"r$)r"r#)rrÚvstackr rrÚTÚ trianglesÚhypotÚanyÚshapeÚemptyÚfloat64ÚinfÚsqrtr!ÚmaÚarray)r ÚrescaleÚkxÚkyÚptsÚtri_ptsÚaÚbÚcÚsÚprodÚ bool_flatÚntriÚ circum_radiusÚabcÚ in_radiusÚ circle_ratior!s&& r Ú circle_ratiosÚTriAnalyzer.circle_ratios2s€÷: Ø×)Ñ)‰HˆRà˜SÜiŠi˜×,Ñ,×.Ñ.¨rÕ1Ø×,Ñ,×.Ñ.¨rÕ1ð3ó4ß45±Að à×)Ñ)×3Ñ3Õ4ˆà GÕ ˜w wÕ/Õ /ˆØ GÕ ˜w wÕ/Õ /ˆØ GÕ ˜w wÕ/Õ /ˆÜ HŠHQt•W˜a gÓ &ˆÜ HŠHQt•W˜a gÓ &ˆÜ HŠHQt•W˜a gÓ &ˆà SUCKˆØA•#a•%y˜!#˜a%Õ  !¥# a¥%Õ(ˆà˜R‘Zˆ Ü 6Š6)× Ò à—=‘= Õ#ˆDÜŸHšH T´·±Ô<ˆMÜ')§v¡vˆMÑ $Ø•#a•%ˆCØ(+¨J­Ø”B—G’G˜D Õ,Ó-Õ-õ)/ˆM˜*Ò %ðS U s¬2¯7ª7°4«=Õ'8Õ9ˆMØ•S˜•U˜s =Õ0°Õ2Õ3ˆ Ø Õ.ˆ Ø×"Ñ"×'Ñ'ˆØ Š<ØÐ ä—5‘5—;‘;˜|°$;Ó7Ð 7rc ó€VPPP^,pVPV4V8pVPPpVf\ P !V\R7p\ P!VPP4p\ P!V\ PR7pRpV^8wdw\ P!V^R7R8HV(,p W”,p W¥,p\ P!V 4pRWjR3&RWz&\ P!VR8HRWv,4pK}\ PP!VR4#)aÓ 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. r)Úaxisr"Téÿÿÿÿ)r r(r+rBr!rÚzerosÚboolÚcopyÚ neighborsÚarangeÚint32ÚminÚsumÚwherer0Úfilled) r Úmin_circle_ratior2r=Úmask_bad_ratioÚ current_maskÚvalid_neighborsÚrenum_neighborsÚnaddÚ wavefrontÚ added_masks &&& r Úget_flat_tri_maskÚTriAnalyzer.get_flat_tri_maskus!€ð`×"Ñ"×,Ñ,×2Ñ2°1Õ5ˆØ×+Ñ+¨GÓ4Ð7GÑGˆà×*Ñ*×/Ñ/ˆ Ø Ò ÜŸ8š8 D´Ô5ˆLÜŸ'š' $×"5Ñ"5×"?Ñ"?Ó@ˆÜŸ)š) D´·±Ô9ˆØˆØaŒiôŸš °aÔ8¸BÑ>À<À-ÕOˆIð#Õ3ˆJØ%Õ4ˆLÜ—6’6˜*Ó%ˆDð.0ˆO¨˜MÑ *Ø*,ˆOÑ 'Ü Ÿhšh ¸"Ñ'<¸bØ'6Õ'GóIŠOôu‰u|‰|˜L¨$Ó/Ð/rc ót€VPPpVPP4pVPPP^,pVeVP V(4pM&\ P!V\ PR7p\ P!\ P!V4VPPPR7^8gpVPPV,pVPPV,pVP V4pW‚,pW&WtV3#)aä 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*). rr)r r!rr(r+Ú_total_to_compress_renumrrKrLrrrrr) r Útri_maskrr=Ú tri_renumÚ valid_nodeÚ compressed_xÚ compressed_yÚ node_renums & r Ú_get_compressed_triangulationÚ)TriAnalyzer._get_compressed_triangulationÀs€ð8×&Ñ&×+Ñ+ˆØ#×2Ñ2×GÑGÓIÐØ×"Ñ"×,Ñ,×2Ñ2°1Õ5ˆØ Ò Ø×5Ñ5°x°iÓ@‰IäŸ š  $¬b¯h©hÔ7ˆIô—k’k¤"§(¢(Ð+?Ó"@Ø,0×,?Ñ,?×,AÑ,A×,FÑ,FôHØKLñMˆ à×*Ñ*×,Ñ,¨ZÕ8ˆ Ø×*Ñ*×,Ñ,¨ZÕ8ˆ Ø×2Ñ2°:Ó>ˆ ð *Õ?Ðà$°LØðð rc óø€\P!\P!V4R\PR7p\P!V4p\P !V\PR7W&V#)ah 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) rrF)rÚfullrrLrNrK)ÚvalidÚrenumÚn_valids& r r\Ú$TriAnalyzer._total_to_compress_renumñsJ€ô&—’œŸš ›¨´"·(±(Ô;ˆÜ—&’&˜“-ˆÜ—y’y ´·±Ô9ˆ‰ ؈ r)r N)T)g{®Gáz„?T)Ú__name__Ú __module__Ú __qualname__Ú__firstlineno__Ú__doc__r ÚpropertyrrBrYrcÚ staticmethodr\Ú__static_attributes__Ú__classdictcell__)Ú __classdict__s@r rr sKø‡€ñò ,ðñ>óð>ô"A8ôFI0òV/ðbñóörr)roÚnumpyrÚ matplotlibrÚmatplotlib.trirr©rr Úrys!ðñóåÝ(÷|ó|r