jVdZddlmZddlmZddlZddlmZddl m Z ddl m Z dd l mZmZmZdd lmZmZeeZd ed efd ZddZddZdZdZdZeGddZ dd efdZdZdZddZd dZ dZ!d!dZ"dZ#dZ$y)"z` triangles.py ------------- Functions for dealing with triangle soups in (n, 3, 3) float form. ) dataclass) getLoggerN)util)tol)point_plane_distance)NDArrayOptionalfloat64) diagonal_dotunitize trianglesreturnch|ddddddf|ddddddfz }|jddk(r$tj|dddf|dddfS|jddk(r9|dddf}|dddf}|dddf|dddfz|dddf|dddfzz St|j)a 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 >/DATA/.local/lib/python3.12/site-packages/trimesh/triangles.pyrrs12q!Ia!Qh$77GqQxx1 wq!t}55  q AqDM AqDMAw1a4 1QT7Qq!tW#444 Y__ %%c|.ttj|tj}t |j dk(rtj |dz Stj|dzjddz S)a Calculates the sum area of input triangles Parameters ---------- triangles : (n, 3, 3) float Vertices of triangles crosses : (n, 3) float or None As a speedup don't re- compute cross products sum : bool Return summed area or individual triangle area Returns ---------- area : (n,) float or float Individual or summed area depending on `sum` argument dtyperg@raxis) rr asanyarrayr lenrabssqrtsum)rcrossess rarear'0sl$ irzzBC 7==Qvvg$$ 77GQJ###+ ,s 22rcT|tj|tj}|jddk(rOtjgd|jddf}tj t |t}||fS| t|}t|d\}}||fS) aV 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$7E;  "'t4KD% ;rctj|tj}t|dddf|dddfz }t|dddf|dddfz }t|dddf|dddfz }tjt |dftj}tj tjt||dd|dddf<tj tjt| |dd|dddf<tj|dddfz |dddfz |dddf<d||tjkjd ddf<|S) a  Calculates the angles of input triangles. Parameters ------------ triangles : (n, 3, 3) float Vertex positions Returns ------------ angles : (n, 3) float Angles at vertex positions in radians Degenerate angles will be returned as zero rNrrrrr)r*r) rr!r r zerosr"arccosclipr pirmergeany)ruvwresults ranglesr>jsD  irzz:I  !Q$)AqD/12A !Q$)AqD/12A !Q$)AqD/12AXXs9~q) CHH $ IIX Y 1o.  v  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 Mrctj|tj}tj|ddst d|j tj|tj}t|\}}|j dk(rtj||}nt|||}tjt|t}|dkD||<|S)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$VVJ8 "*oe.DE hhs9~T2G#%GEN Nrc*tj|tj}tj|ds t dtj |jd|jdf}tj|}|S)a Given a list of triangles, create an r-tree for broad- phase collision detection Parameters --------- triangles : (n, 3, 3) float Triangles in space Returns --------- tree : rtree.Rtree One node per triangle r)r)r)rrrArr) rr!r rrGr column_stackminmax bounds_tree)rtriangle_boundstrees rrrsss irzz:I ==O 4788ooy}}!}'S&TUO   O ,D Krctj|tj}tj|ds t d|t j}t|||kDjd}|S)a Find all triangles which have an oriented bounding box where both of the two sides is larger than a specified height. Degenerate triangles can be when: 1) Two of the three vertices are colocated 2) All three vertices are unique but colinear Parameters ---------- triangles : (n, 3, 3) float Triangles in space height : float Minimum edge length of a triangle to keep Returns ---------- nondegenerate : (n,) bool True if a triangle meets required minimum height rr@rA)rareasrr) rr!r rrGrrr8extentsrI)rrheightoks r nondegeneratersf, irzz:I ==J /788 ~ IU 3f < A Aq A IB Ircftj|tj}tj|ds t d| t |}|dddf|dddfz }|dddf|dddfz }|dzjd d z}|dzjd d z}|tjkD}|tjkD}tjt|dftj}||dz||z |dddf|<||dz||z |dddf|<|S) a@ Return the 2D bounding box size of each triangle. Parameters ---------- triangles : (n, 3, 3) float Triangles in space areas : (n,) float Optional area of input triangles Returns ---------- box : (n, 2) float The size of each triangle's 2D oriented bounding box rr@rAN)rrrrrg?) rr!r rrGrr'r%rr8r4r") rrrrlength_alength_b nonzero_a nonzero_bboxs rrrs9  irzz:I ==J /788 }y) !Q$)AqD/)A!Q$)AqD/)A1zzqz!S(H1zzqz!S(H399$I399$I ((C NA&bjj 9C!),q0HY4GGC1Ii!),q0HY4GGC1Ii Jrc*tj|tj}tj|tj}||j dj dz}||j dzj d}|S)aG Convert a list of barycentric coordinates on a list of triangles to cartesian points. Parameters ------------ triangles : (n, 3, 3) float Triangles in space barycentric : (n, 2) float Barycentric coordinates Returns ----------- points : (m, 3) float Points in space rrrr)r)r)rr)rrsr r!r%rH)r barycentricrDs rbarycentric_to_pointsrsv"((;bjj9K irzz:I;???*227;;K+--j99 > >A > FF MrcRfd}fd}tjtjtj|tj}tjdk7r t djd}t|jdk7s1|jd|k7s|jdjdk7r t d d d dd fd d d dfz |d d dfj d |fz |d k(r|S|S) a; Find the barycentric coordinates of points relative to triangles. The Cramer's rule solution implements: http://blackpawn.com/texts/pointinpoly The cross product solution implements: https://www.cs.ubc.ca/~heidrich/Papers/JGT.05.pdf Parameters ----------- triangles : (n, 3, 2 | 3) float Triangles vertices in space points : (n, 2 | 3) float Point in space associated with a triangle method : str Which method to compute the barycentric coordinates with: - 'cross': uses a method using cross products, roughly 2x slower but different numerical robustness properties - anything else: uses a cramer's rule solution Returns ----------- barycentric : (n, 3) float Barycentric coordinates of each point ctjdddfdddf}t||}tjt dftj }ttjdddf||z |dddf<ttjdddf||z |dddf<d|dddfz |dddfz |dddf<|S)Nrrrrr)rrr r4r"r )n denominatorr edge_vectorsrr<s r method_crossz+points_to_barycentric..method_crosss HH\!Q$'ad); <"1a( hhI2"**E (,q!t2Da)H!L{Z AqD(!\!Q$5G)H!L{Z AqD AqD 11K14EE AqDrctdddfdddf}tdddfdddf}tdddf }tdddfdddf}tdddf }d||z||zz z }tjtdftj}||z||zz |z|dddf<||z||zz |z|dddf<d|dddfz |dddfz |dddf<|S)Nrrr+rrr)r rr4r"r ) dot00dot01dot02dot11dot12inverse_denominatorrrrr<s r method_cramerz,points_to_barycentric..method_cramers.\!Q$/ad1CD\!Q$/ad1CD\!Q$/3\!Q$/ad1CD\!Q$/3!UU]UU]%BChhI2"**E "U]UU]:>QQ AqD"U]UU]:>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 ~ ?rc tj|tj}tj|tj}tj|ds t dtj|t |dfs t dtj|}tjt |t}gd}|dddddf}|ddd ddf}|ddd ddf}||z }||z } ||z } tj|| z|} tj| | z|} tj| tjk| tjk} t| r || || <d || <||z }tj||z|}tj| |z|}|tj kD||kz|z}t|r ||||<d ||<| |z|| zz }|tjk| tj kDz|tjkz|z}t|r6| || |||z z jd }|||||zz||<d ||<||z }tj||z|}tj| |z|}|tj kD||kz|z}t|r ||||<d ||<|| z| |zz }|tjk| tj kDz|tjkz|z}t|r6| || |||z z jd }|||| |zz||<d ||<||z||zz }|tjk||z tj kDz||z tj kDz|z}t|rG||||z }||||||z zz jd }|||||||z zz||<d ||<t|r\d ||||z||zz }|||zjd }|||zjd }|||||zz| ||zz||<|S)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 5DEE]]6 "F WWS[ -F D !Q'A!Q'A!Q'A QB QB !B R B R B >>"sxx-chh 7D 4ywt t  !B R B R B #((NrRx (6 1D 4ywt t  r'b2g B #((]rSXXI~ ."sxx- @6 IE 5z Y"U)bi/ 0 9 9' B%A5 M2u u  !B R B R B #((NrRx (6 1D 4ywt t  r'b2g B #((]rSXXI~ ."sxx- @6 IE 5z Y"U)bi/ 0 9 9' B%1r%y=0u u  r'b2g B #((]RCHH94 5"r'chhY9N ORX XE 5zi"U)# C2e9r%y01 2 ; ;G D%1%1U8(;#<<u u  6{r&zBvJ.F;< Z%  ( ( 1 Z%  ( ( 16bj1n5FaHv Mrctj|tj}tj|ds t d|j d}tjt|j d}||d}|S)a 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_kwargsrsn( irzz:I ==J /788  )H IIc(m $ , ,W 5E"U 3F Mr)NN)NNNFrZ)cramer)%__doc__ dataclassesrloggingrnumpyrr constantsrrDrtypedr r r r r r^rtrr'r2r>rNrPrRrrrrrrrrrrdrrrs"(--'&W&&434@#L:* ## #.KPssl!H2!H*Z6L^slr