ó ÀMóiçãó°•SrSSKrSSKJr SSKJr SSKJr Sr S r S rS rS rS rg!\a"r SSKJ r \ R"\ 5rSr C N6Sr C ff=f)z5 curvature.py --------------- Query mesh curvature. éNé)Úutil)Ú diagonal_dot)Ú coo_matrix)Ú exceptionscóΕ[URR5URRURR 44URR 5nU$)zž A sparse matrix representation of the face angles. Returns ---------- sparse : scipy.sparse.coo_matrix matrix is float shaped (len(vertices), len(faces)) )rÚ face_anglesÚflattenÚ faces_sparseÚrowÚcolÚshape)ÚmeshÚmatrixs Úk/var/www/eduai.edurigo.com/storigo/production/storigo_env/lib/python3.13/site-packages/trimesh/curvature.pyÚface_angles_sparsersX€ôØ × Ñ × !Ñ !Ó # d×&7Ñ&7×&;Ñ&;¸T×=NÑ=N×=RÑ=RÐ%SÐTØ ×Ñ×Ñó€Fð €Mócó¨•[R"URRSS95R 5nS[R -U- nU$)a` Return the vertex defects, or (2*pi) minus the sum of the angles of every face that includes that vertex. If a vertex is only included by coplanar triangles, this will be zero. For convex regions this is positive, and concave negative. Returns -------- vertex_defect : (len(self.vertices), ) float Vertex defect at the every vertex r)Úaxisé)ÚnpÚarrayrÚsumr Úpi)rÚ angle_sumÚdefects rÚvertex_defectsr%sF€ô—’˜×0Ñ0×4Ñ4¸!Ð4Ð<Ó=×EÑEÓG€IØ”"—%‘%‰i˜9Ñ $€FØ €MrcóZ•[R"U[RS9n[R"US5(d [ S5eUR RX5nUVs/sHo@RUR5PM! nn[R"U5$s snf)aú Return the discrete gaussian curvature measure of a sphere centered at a point as detailed in 'Restricted Delaunay triangulations and normal cycle'- Cohen-Steiner and Morvan. This is the sum of the vertex defects at all vertices within the radius for each point. Parameters ---------- points : (n, 3) float Points in space radius : float , The sphere radius, which can be zero if vertices passed are points. Returns -------- gaussian_curvature: (n,) float Discrete gaussian curvature measure. ©Údtype©éÿÿÿÿéúpoints must be (n,3)!) rÚ asanyarrayÚfloat64rÚis_shapeÚ ValueErrorÚkdtreeÚquery_ball_pointrrÚasarray)rÚpointsÚradiusÚnearestÚverticesÚ gauss_curvs rÚ#discrete_gaussian_curvature_measurer18s„€ô.]Š]˜6¬¯©Ñ 4€FÜ =Š=˜ × )Ñ )ÜÐ0Ó1Ð1àk‰k×*Ñ*¨6Ó:€GÙFMÓNÂg¸(×%Ñ% hÑ/×3Ñ3Ö5Ág€JÐNä :Š:jÓ !Ð!ùòOsÁ*&B(cóÈ•[R"U[RS9n[R"US5(d [ S5e[R "X- X-45nUVs/sH'n[URRU55PM) nn[R"[U55n[[X55H‹unup‰URURU n [!U SS2S4U SS2S4X‚S9n UR"U n [R$"UR&U SS5n X¼-U -R)5S - Xg'M U$s snf) aÚ Return the discrete mean curvature measure of a sphere centered at a point as detailed in 'Restricted Delaunay triangulations and normal cycle'- Cohen-Steiner and Morvan. This is the sum of the angle at all edges contained in the sphere for each point. Parameters ---------- points : (n, 3) float Points in space radius : float Sphere radius which should typically be greater than zero Returns -------- mean_curvature : (n,) float Discrete mean curvature measure. rr!r$Nrr)Úcenterr-r"r)rr%r&rr'r(Ú column_stackÚlistÚface_adjacency_treeÚ intersectionÚzerosÚlenÚ enumerateÚzipr/Úface_adjacency_edgesÚline_ball_intersectionÚface_adjacency_anglesÚwhereÚface_adjacency_convexr)rr,r-ÚboundsÚbÚ candidatesÚ mean_curvÚiÚxÚ x_candidatesÚ endpointsÚlengthsÚanglesÚsignss rÚdiscrete_mean_curvature_measurerLYs?€ô,]Š]˜6¬¯©Ñ 4€FÜ =Š=˜ × )Ñ )ÜÐ0Ó1Ð1ô_Š_˜f™o¨v©Ð?Ó @€FñKQÓQÊ&ÀQ”$t×/Ñ/×<Ñ<¸QÓ?Ö@É&€JÐQä—’œ˜V›Ó%€IÜ )¬#¨fÓ*AÖ BÑˆÑ ˆAØ—M‘M $×";Ñ";¸LÑ"IÑJˆ Ü(Ø ’a˜d‰O˜Y¢q¨! t™_°Qñ ˆð×+Ñ+¨LÑ9ˆÜ—’˜×3Ñ3°LÑAÀ1ÀbÓIˆØÑ(¨5Ñ0×5Ñ5Ó7¸!Ñ;ˆ ‹ ñ!Cð ÐùòRsÁ+.Ecóî•X- nX- nUn[XD5n[XE5n[XU5n US-XyUS-- -- n [R"[U55n U S:„n XŒ*[R"X¬5- X|- n XŒ*[R"X¬5-X|- n[R "U SS5n [R "USS5nXí- [R"X|5-X¼'U $)aP Compute the length of the intersection of a line segment with a ball. Parameters ---------- start_points : (n,3) float, list of points in space end_points : (n,3) float, list of points in space center : (3,) float, the sphere center radius : float, the sphere radius Returns -------- lengths: (n,) float, the lengths. rrr)rrr8r9ÚsqrtÚclip)Ú start_pointsÚ end_pointsr3r-ÚLÚocÚrÚldotlÚldotocÚocdotocÚdiscrimsrIÚmÚd1Úd2s rr=r=†sô€ð( Ñ!€AØ Ñ €BØ€AÜ ˜Ó €EÜ ˜!Ó €Fܘ2Ó"€GØq‰y˜5¨a°©d¡NÑ3Ñ3€HôhŠh”s˜<Ó(Ó)€Gà1‰ €AØ ‰9ˆ*”r—w’w˜x™{Ó+Ñ +¨u©xÑ 7€BØ ‰9ˆ*”r—w’w˜x™{Ó+Ñ +¨u©xÑ 7€Bô ŠQ˜Ó €BÜ ŠQ˜Ó €Bð‘'œRŸWšW U¡XÓ.Ñ.€GJà €Nrcó¬•SUS--US-- SU-- nX *:¼aS[R-U-X- -$X *:aS[R-US--$g)a Compute the surface area of the intersection of sphere of radius R centered at (0, 0, 0) with a ball of radius r centered at (R, 0, 0). Parameters ---------- R : float, sphere radius r : float, ball radius Returns -------- area: float, the surface are. réN)rr)ÚRrTrFs rÚsphere_ball_intersectionr_³se€ð ˆQ‰T‰Aq‘D‰˜Q ™UÑ#€A؈BƒwØ”2—5‘5‰y˜1‰} ¡Ñ&Ð&؈2ƒvØ”2—5‘5‰y˜1˜a™4ÑÐðr)Ú__doc__ÚnumpyrÚrrÚ scipy.sparserÚ ImportErrorÚErÚExceptionWrapperrrr1rLr=r_©rrÚrhsdðñóåÝð0Ý'ò ò ò&"òB*òZ*óZ øðIó0Ýà×,Ò,¨QÓ/…Jûð0ús”-­A³AÁA