MiV&SrSSKJr SSKJr SSKrSSKJr SSK J r SSK J r SS K JrJrJr SS KJrJr \"\5rS \S \4S jrSSjrSSjrSrSrSr\"SS55rSS \4SjjrSrSrSSjrS Sjr Sr!S!Sjr"Sr#Sr$g)"z` triangles.py ------------- Functions for dealing with triangle soups in (n, 3, 3) float form. ) dataclass) getLoggerN)util)tol)point_plane_distance)NDArrayOptionalfloat64) diagonal_dotunitize trianglesreturncnUSS2SS2SS24USS2SS2SS24- nURSS:Xa%[R"USS2S4USS2S45$URSS:Xa9USS2S4nUSS2S4nUSS2S4USS2S4-USS2S4USS2S4-- $[UR5e)z Returns the cross product of two edges from input triangles Parameters -------------- triangles: (n, 3, 3) float Vertices of triangles Returns -------------- crosses : (n, 3) float Cross product of two edge vectors Nrr)shapenpcross ValueError)rvectorsabs k/var/www/eduai.edurigo.com/storigo/production/storigo_env/lib/python3.13/site-packages/trimesh/triangles.pyrrs12q!Ia!Qh$77GqQxx1 wq!t}55  q AqDM AqDMAw1a4 1QT7Qq!tW#444 Y__ %%cUc,[[R"U[RS95n[ UR 5S:Xa[R "U5S- $[R"US-RSS95S- $)ai Calculates the sum area of input triangles Parameters ---------- triangles : (n, 3, 3) float Vertices of triangles crosses : (n, 3) float or None As a speedup don't re- compute cross products sum : bool Return summed area or individual triangle area Returns ---------- area : (n,) float or float Individual or summed area depending on `sum` argument dtyperg@raxis) rr asanyarrayr lenrabssqrtsum)rcrossess rarear'0sl$ irzzBC 7==Qvvg$$ 77GQJ###+ ,s 22rcHUb[R"U[RS9nURSS:XaM[R"/SQURSS45n[R "[ U5[S9nX#4$Uc [U5n[USS9up#X#4$) a Calculates the normals of input triangles Parameters ------------ triangles : (n, 3, 3) float Vertex positions crosses : (n, 3) float Cross products of edge vectors Returns ------------ normals : (m, 3) float Normal vectors valid : (n,) bool Was the face nonzero area or not rr)r*?rrT) check_valid) rr!r rtileonesr"boolrr )rr&unitvalids rnormalsr2Js$MM)2::> ??2 ! #77?Y__Q-?,CDDGGC N$7E;  "'t4KD ;rc[R"U[RS9n[USS2S4USS2S4- 5n[USS2S4USS2S4- 5n[USS2S4USS2S4- 5n[R"[ U5S4[RS9n[R "[R"[X5SS55USS2S4'[R "[R"[U*U5SS55USS2S4'[RUSS2S4- USS2S4- USS2S4'SXD[R:RSS 9SS24'U$) z Calculates the angles of input triangles. Parameters ------------ triangles : (n, 3, 3) float Vertex positions Returns ------------ angles : (n, 3) float Angles at vertex positions in radians Degenerate angles will be returned as zero rNrrrrr)r*r) rr!r r zerosr"arccosclipr pirmergeany)ruvwresults ranglesr>js@  irzz:I  !Q$)AqD/12A !Q$)AqD/12A !Q$)AqD/12AXXs9~q) CHH $ IIX Y 1o.    F hhvG1 1 %1v3F!3K2P2P2R)RS DM 1 1 %1v3F!3K2P2P2R)RS DM 1 1 %1v3F!3K2P2P2R)RS DM!mv QF8K0L'LMNGDM mv QF8K0L'LMNGDM mv QF8K0L'LMNGDMDMGDMDMGDMDMGDMw&FN Mrc[R"U[RS9n[R"USSS9(d[ SUR <35e[R"U[RS9n[U5up#UR S:Xa[R"X!5nO[X!U5n[R"[U5[S9nUS:XS'U$)a* Given a list of triangles and a list of normals determine if the two are aligned Parameters ---------- triangles : (n, 3, 3) float Vertex locations in space normals_compare : (n, 3) float List of normals to compare Returns ---------- aligned : (n,) bool Are normals aligned with triangles rr@T) allow_zerosz)triangles must have shape (n, 3, 3), got )rr*) rr!r rrGrrr2dotr r4r"r/)rnormals_compare calculatedr1 differencealigneds rwindings_alignedrOs" irzz:I ==JD ADY__DWXYYmmO2::FO *J$VVJ8 "*e.DE hhs9~T2G#%GN Nrc*[R"U[RS9n[R"US5(d [ S5e[R "URSS9URSS945n[R"U5nU$)z Given a list of triangles, create an r-tree for broad- phase collision detection Parameters --------- triangles : (n, 3, 3) float Triangles in space Returns --------- tree : rtree.Rtree One node per triangle r)r)r)rrrArr) rr!r rrGr column_stackminmax bounds_tree)rtriangle_boundstrees rrrssv irzz:I ==O 4 4788ooy}}!}'S&TUO   O ,D Krc[R"U[RS9n[R"US5(d [ S5eUc[ Rn[XS9U:RSS9nU$)a Find all triangles which have an oriented bounding box where both of the two sides is larger than a specified height. Degenerate triangles can be when: 1) Two of the three vertices are colocated 2) All three vertices are unique but colinear Parameters ---------- triangles : (n, 3, 3) float Triangles in space height : float Minimum edge length of a triangle to keep Returns ---------- nondegenerate : (n,) bool True if a triangle meets required minimum height rr@rA)rareasrr) rr!r rrGrrr8extentsrI)rrheightoks r nondegeneratersg, irzz:I ==J / /788 ~ I 3f < A Aq A IB IrcR[R"U[RS9n[R"US5(d [ S5eUc [ US9nUSS2S4USS2S4- nUSS2S4USS2S4- nUS-RSS 9S -nUS-RSS 9S -nU[R:nU[R:n[R"[U5S4[RS9nXS-XF- USS2S4U'XS-XW- USS2S4U'U$) a Return the 2D bounding box size of each triangle. Parameters ---------- triangles : (n, 3, 3) float Triangles in space areas : (n,) float Optional area of input triangles Returns ---------- box : (n, 2) float The size of each triangle's 2D oriented bounding box rr@rAN)rrrrrg?) rr!r rrGrr'r%rr8r4r") rrrrlength_alength_b nonzero_a nonzero_bboxs rrrs4  irzz:I ==J / /788 }y) !Q$)AqD/)A!Q$)AqD/)A1zzqz!S(H1zzqz!S(H399$I399$I ((C NA&bjj 9C!,q0H4GGC1Ii!,q0H4GGC1Ii Jrc[R"U[RS9n[R"U[RS9nXR SS9R S5-nXR S5-R SS9nU$)a Convert a list of barycentric coordinates on a list of triangles to cartesian points. Parameters ------------ triangles : (n, 3, 3) float Triangles in space barycentric : (n, 2) float Barycentric coordinates Returns ----------- points : (m, 3) float Points in space rrrr)r)r)rr)rrwr r!r%rH)r barycentricrDs rbarycentric_to_pointsrsr"((;bjj9K irzz:I???*227;;K--j99 > >A > FF MrcX^^^UUU4SjnUUU4Sjn[R"T[RS9m[R"U[RS9n[TR5S:wa [ S5eTRSn[UR5S:wd3URSU:wd URSTRS:wa [ S 5eTS S 2SS 24TS S 2S S24- mUTS S 2S4R S U45- mUS :XaU"5$U"5$) a Find the barycentric coordinates of points relative to triangles. The Cramer's rule solution implements: http://blackpawn.com/texts/pointinpoly The cross product solution implements: https://www.cs.ubc.ca/~heidrich/Papers/JGT.05.pdf Parameters ----------- triangles : (n, 3, 2 | 3) float Triangles vertices in space points : (n, 2 | 3) float Point in space associated with a triangle method : str Which method to compute the barycentric coordinates with: - 'cross': uses a method using cross products, roughly 2x slower but different numerical robustness properties - anything else: uses a cramer's rule solution Returns ----------- barycentric : (n, 3) float Barycentric coordinates of each point c>[R"TSS2S4TSS2S45n[X5n[R"[ T5S4[R S9n[[R"TSS2S4T5U5U- USS2S4'[[R"TTSS2S45U5U- USS2S4'SUSS2S4- USS2S4- USS2S4'U$)Nrrrrr)rrr r4r"r )n denominatorr edge_vectorsrr<s r method_cross+points_to_barycentric..method_crosss HH\!Q$'ad); <"1( hhI2"**E (,q!t2Da)H!L{Z AqD(!\!Q$5G)H!L{Z AqD AqD 11K14EE AqDrc>[TSS2S4TSS2S45n[TSS2S4TSS2S45n[TSS2S4T 5n[TSS2S4TSS2S45n[TSS2S4T 5nSX-X-- - n[R"[T5S4[RS9nX-X-- U-USS2S4'X2-X-- U-USS2S4'SUSS2S4- USS2S4- USS2S4'U$)Nrrr+rrr)r rr4r"r ) dot00dot01dot02dot11dot12inverse_denominatorrrrr<s r method_cramer,points_to_barycentric..method_cramers"\!Q$/ad1CD\!Q$/ad1CD\!Q$/3\!Q$/ad1CD\!Q$/3!U]U]%BChhI2"**E "]U]:>QQ AqD"]U]:>QQ AqD AqD 11K14EE AqDrrrtriangles shape incorrectrrrz$triangles and points must correspondNr)r)rr!r r"rrrH)rrDmethodrrdimrr<s` @@rpoints_to_barycentricrs:   irzz:I ]]6 4F 9??q 455 //! C FLLQ <<?c ! <<?iooa0 0?@@QU#i2A2&66L1a4(("c33A ~ ?rcH [R"U[RS9n[R"U[RS9n[R"US5(d [ S5e[R"U[ U5S45(d [ S5e[R"U5n[R"[ U5[S9n/SQnUSS2SSS24nUSS2S SS24nUSS2S SS24nXe- nXu- n X- n [R"X-U5n [R"X-U5n [R"U [R:U [R:5n [U 5(a X]X-'S X='X- n[R"X-U5n[R"X-U5nU[R*:UU:*-U-n[U5(a UUUU'S UU'U U-X-- nU[R:U [R*:-U[R:-U-n[U5(a6U UU UUU- - RS 5nUUUUU--UU'S UU'X- n[R"UU-U5n[R"U U-U5nU[R*:UU:*-U-n[U5(a UUUU'S UU'UU -U U-- nU[R:U [R*:-U[R:-U-n[U5(a6U UU UUU- - RS 5nUUUU U--UU'S UU'UU-UU-- nU[R:UU- [R*:-UU- [R*:-U-n[U5(aGUUUU- nUUUUUU- -- RS 5nUUUUUUU- --UU'S UU'[U5(aXS UUUU-UU-- nUUU-RS 5nUUU-RS 5nXSXU--XU--X#'U$)a Return the closest point on the surface of each triangle for a list of corresponding points. Implements the method from "Real Time Collision Detection" and use the same variable names as "ClosestPtPointTriangle" to avoid being any more confusing. Parameters ---------- triangles : (n, 3, 3) float Triangle vertices in space points : (n, 3) float Points in space Returns ---------- closest : (n, 3) float Point on each triangle closest to each point rr@rrz)need same number of triangles and points!)r+r+r+NrrrFrr+)rr!r rrGrr" zeros_liker.r/r logical_andrrJr9rH) rrDr=remainr.rrcabacapd1d2is_abpd3d4is_bvcis_abr;cpd5d6is_cvbis_acr<vais_bcd43denoms r closest_pointrGs0 irzz:I ]]6 4F ==J / /455 ==#i.!!4 5 5DEE]]6 "F WWS[ -F D !Q'A!Q'A!Q'A B B B  B  B >>"sxx-chh 7D 4yyw   B  B  B #((NrRx (6 1D 4yywt t  r'bg B #((]rSXXI~ ."sxx- @6 IE 5zz Y"U)bi/ 0 9 9' B%A5 M2u u  B R B R B #((NrRx (6 1D 4yywt t  r'b2g B #((]rSXXI~ ."sxx- @6 IE 5zz Y"U)bi/ 0 9 9' B%1r%y=0u u  r'b2g B #((]RCHH94 5"r'chhY9N ORX XE 5zzi"U)# C2e9r%y01 2 ; ;G D%1%1U8(;#<<u u  6{{r&zBvJ.F;< Z%  ( ( 1 Z%  ( ( 1bj1n5aH Mrc [R"U[RS9n[R"US5(d [ S5eUR S5n[R"[U55R S5nXS.nU$)ah Convert a list of triangles to the kwargs for the Trimesh constructor. Parameters --------- triangles : (n, 3, 3) float Triangles in space Returns --------- kwargs : dict Keyword arguments for the trimesh.Trimesh constructor Includes keys 'vertices' and 'faces' Examples --------- >>> mesh = trimesh.Trimesh(**trimesh.triangles.to_kwargs(triangles)) rr@rArB)verticesfaces) rr!r rrGrrHaranger")rrrkwargss r to_kwargsrso( irzz:I ==J / /788  )H IIc(m $ , ,W 5E" 3F Mr)NN)NNNFr[)cramer)%__doc__ dataclassesrloggingrnumpyrr constantsrrDrtypedr r r r r rarxrr'r2r>rNrPrRrrrrrrrrrr`rrrs"(--'&W&&434@#L:* ## #.KPssl!H2!H*Z6L^slr