TiV*dZddlmZddlmZddlZddlmZddl m Z ddl m Z dd l mZmZmZdd lmZmZeeZd ed efd Zd dZd dZdZdZdZeGddZ d!d efdZdZdZd dZd"dZ dZ!d#dZ"dZ#dZ$dS)$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 trianglesreturnc|ddddddf|ddddddfz }|jddkr)tj|dddf|dddfS|jddkrK|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 K/DATA/AppData/hermes/venv/lib/python3.11/site-packages/trimesh/triangles.pyrrs122qqq!Iaaa!QQQh$77GqQx1 wqqq!t}555  q AAAqDM AAAqDMAw111a4 1QQQT7Qqqq!tW#444 Y_ % %%c|-ttj|tj}t |jdkrtj|dz Stj|dzddz S)a Calculates the sum area of input triangles Parameters ---------- triangles : (n, 3, 3) float Vertices of triangles crosses : (n, 3) float or None As a speedup don't re- compute cross products sum : bool Return summed area or individual triangle area Returns ---------- area : (n,) float or float Individual or summed area depending on `sum` argument Ndtyperg@raxis) rr asanyarrayr lenrabssqrtsum)rcrossess rarear'0sy$ irzBBBCC 7=Qvg$$ 7GQJ###++ , ,s 22rcZ|tj|tj}|jddkrPtjgd|jddf}tjt |t}||fS|t|}t|d \}}||fS) aV Calculates the normals of input triangles Parameters ------------ triangles : (n, 3, 3) float Vertex positions crosses : (n, 3) float Cross products of edge vectors Returns ------------ normals : (m, 3) float Normal vectors valid : (n,) bool Was the face nonzero area or not Nrr)r*?rrT) check_valid) rr!r rtileonesr"boolrr )rr&unitvalids rnormalsr2Js$M)2:>>> ?2 ! # #7???Y_Q-?,CDDDGC NN$777E;  ""'t444KD% ;rc.tj|tj}t|dddf|dddfz }t|dddf|dddfz }t|dddf|dddfz }tjt |dftj}tjtjt||dd|dddf<tjtjt| |dd|dddf<tj |dddfz |dddfz |dddf<d||tj k d ddf<|S) a  Calculates the angles of input triangles. Parameters ------------ triangles : (n, 3, 3) float Vertex positions Returns ------------ angles : (n, 3) float Angles at vertex positions in radians Degenerate angles will be returned as zero rNrrrrr)r*r) rr!r r zerosr"arccosclipr pirmergeany)ruvwresults ranglesr>js  irz:::I  !!!Q$)AAAqD/122A !!!Q$)AAAqD/122A !!!Q$)AAAqD/122AXs9~~q) < < >CH $ $ IIX Y Y Y 1o.  v  F hvG1 1 %;1v3F!3K2P2P2R2R)RS DM 1 1 %;1v3F!3K2P2P2R2R)RS DM 1 1 %;1v3F!3K2P2P2R2R)RS DM!mv QF8K0L0L'LMNGDM mv QF8K0L0L'LMNGDM mv QF8K0L0L'LMNGDMDMGDMDMGDMDMGDMw&FN Mrctj|tj}tj|ddst d|jtj|tj}t|\}}|jdkrtj||}nt|||}tj t|t}|dk||<|S)a^ Given a list of triangles and a list of normals determine if the two are aligned Parameters ---------- triangles : (n, 3, 3) float Vertex locations in space normals_compare : (n, 3) float List of normals to compare Returns ---------- aligned : (n,) bool Are normals aligned with triangles rr@T) allow_zerosz)triangles must have shape (n, 3, 3), got )rr*) rr!r rrGrrr2dotr r4r"r/)rnormals_compare calculatedr1 differencealigneds rwindings_alignedrOs" irz:::I =JD A A AZXY_XXYYYmO2:FFFO **J$$VJ88 "*oe.DEE hs9~~T222G#%GEN Nrc2tj|tj}tj|dst dtj|d|df}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 rrrss irz:::I =O 4 497888oy}}!}'<'S>S&TUUO  O , ,D Krctj|tj}tj|dst d| t j}t|||k d}|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@rAN)rareasrr) rr!r rrGrrr8extentsrI)rrheightoks r nondegeneratersx, irz:::I =J / /97888 ~ IU 3 3 3f < A Aq A I IB Irctj|tj}tj|dst d|t |}|dddf|dddfz }|dddf|dddfz }|dzd d z}|dzd d z}|tj k}|tj k}tj t|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 rrrsh  irz:::I =J / /97888 }y))) !!!Q$)AAAqD/)A!!!Q$)AAAqD/)A1zzqz!!S(H1zzqz!!S(H39$I39$I (C NNA&bj 9 9 9C!),q0HY4GGC1Ii!),q0HY4GGC1Ii Jrc6tj|tj}tj|tj}||ddz}||dzd}|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_pointsrs"(;bj999K irz:::I;???**227;;;K+--j999 > >A > F FF Mrcramercjfd}fd}tjtjtj|tj}tjdkrt djd}t|jdks-|jd|ks|jdjdkrt d d d dd fd d d dfz |d d dfd |fz |d kr |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 H\!!!Q$'aaad); < <"1a(( hI2"*EEE (,qqq!t2Da)H)H!LL{Z AAAqD(!\!!!Q$5G)H)H!LL{Z AAAqD AAAqD 11K14EE AAAqDrc\tdddfdddf}tdddfdddf}tdddf }tdddfdddf}tdddf }d||z||zz z }tjtdftj}||z||zz |z|dddf<||z||zz |z|dddf<d|dddfz |dddfz |dddf<|S)Nrrr+rrr)r rr4r"r ) dot00dot01dot02dot11dot12inverse_denominatorrrrr<s r method_cramerz,points_to_barycentric..method_cramersu\!!!Q$/aaad1CDD\!!!Q$/aaad1CDD\!!!Q$/33\!!!Q$/aaad1CDD\!!!Q$/33!UU]UU]%BChI2"*EEE "U]UU]:>QQ AAAqD"U]UU]:>QQ AAAqD AAAqD 11K14EE AAAqDrrrtriangles shape incorrectrrrz$triangles and points must correspondNr)r)rr!r r"rrrH)rrDmethodrrdimrr<s` @@rpoints_to_barycentricrsq:         irz:::I ]6 4 4 4F 9?q  4555 /! C FLQ <?c ! ! <?ioa0 0 0?@@@QQQU#i2A2&66L111a4(("c333A |~~ =??rc tj|tj}tj|tj}tj|dst dtj|t |dfst dtj|}tjt |t}gd}|dddddf}|ddd ddf}|ddd ddf}||z }||z } ||z } tj || z|} tj | | z|} tj | tj k| tj k} t| r|| || <d || <||z }tj ||z|}tj | |z|}|tj k||kz|z}t|r||||<d ||<| |z|| zz }|tj k| tj kz|tj kz|z}t|rI| || |||z z d }|||||zz||<d ||<||z }tj ||z|}tj | |z|}|tj k||kz|z}t|r||||<d ||<|| z| |zz }|tj k| tj kz|tj kz|z}t|rI| || |||z z d }|||| |zz||<d ||<||z||zz }|tj k||z tj kz||z tj kz|z}t|r`||||z }||||||z zz d }|||||||z zz||<d ||<t|r|d ||||z||zz }|||zd }|||zd }|||||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 irz:::I ]6 4 4 4F =J / /64555 =#i..!!4 5 5FDEEE]6 " "F WS[[ - - -F ??D !!!Q'A!!!Q'A!!!Q'A QB QB !B R  B R  B >"sx-ch 7 7D 4yywt t  !B R  B R  B #(NrRx (6 1D 4yywt t  r'b2g B #(]rSXI~ ."sx- @6 IE 5zz Y"U)bi/ 0 9 9' B B%A5 M2u u  !B R  B R  B #(NrRx (6 1D 4yywt t  r'b2g B #(]rSXI~ ."sx- @6 IE 5zz Y"U)bi/ 0 9 9' B B%1r%y=0u u  r'b2g B #(]RCH94 5"r'chY9N ORX XE 5zzi"U)# C2e9r%y01 2 ; ;G D D%1%1U8(;#<<u u  6{{Ir&zBvJ.F;< Z%  ( ( 1 1 Z%  ( ( 1 16bj1n5FaHv Mrc*tj|tj}tj|dst d|d}tjt|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_kwargsrs( irz:::I =J / /97888  ))H Ic(mm $ $ , ,W 5 5E"U 3 3F Mr)NN)NNNFrZ)r)%__doc__ dataclassesrloggingrnumpyrr constantsrrDrtypedr r r r r r^rtrr'r2r>rNrPrRrrrrrrrrrrdrrrs5"!!!!!((((((----------''''''''i&W&&&&&433334@###L:* ####### #.KPssssssl!!!H2!!!!H****Z6LLLL^ssslr