l0jTdZddlmZddlZddlmZddlmZddl m Z ddl m Z m Z mZdd lmZmZd e d e fd Zdd ZddZdZdZdZeGddZ d d efdZdZdZddZd!dZdZd"dZdZdZ dS)#z` triangles.py ------------- Functions for dealing with triangle soups in (n, 3, 3) float form. ) dataclassN)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)r vectorsabs T/home/wildlama/miniconda3/envs/lam/lib/python3.11/site-packages/trimesh/triangles.pyrrs122qqq!Iaaa!QQQh$77GqQx1 wqqq!t}555  q AAAqDM AAAqDMAw111a4 1QQQT7Qqqq!tW#444 Y_ % %%c|-ttj|tj}tj|dzddz S)a Calculates the sum area of input triangles Parameters ---------- triangles : (n, 3, 3) float Vertices of triangles crosses : (n, 3) float or None As a speedup don't re- compute cross products sum : bool Return summed area or individual triangle area Returns ---------- area : (n,) float or float Individual or summed area depending on `sum` argument Ndtyperraxisg@)rr asanyarrayr sqrtsum)r crossess rarear$-sQ$ irzBBBCC 7GQJ###++ , ,s 22rc|5|jddkr$tjgd|jddfS|t|}t |d\}}||fS) aV Calculates the normals of input triangles Parameters ------------ triangles : (n, 3, 3) float Vertex positions crosses : (n, 3) float Cross products of edge vectors Returns ------------ normals : (m, 3) float Normal vectors valid : (n,) bool Was the face nonzero area or not Nr)r'?rrT) check_valid)rrtilerr )r r#unitvalids rnormalsr-Dso$!4!9!9w);Q(?@@@ ""'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 zeroslenarccosclipr pirmergeany)r uvwresults ranglesr:_s  irz:::I  !!!Q$)AAAqD/122A !!!Q$)AAAqD/122A !!!Q$)AAAqD/122AXs9~~q) < < r?r)rr r rrCrr-rrDr5rErFrrG)r rHrIrJ any_coplanars rrMrMs  irz:::I =J / /97888)$$Q'KA,q/K$}$$W--  I 6"& (9(9'(B(BSX(M!N!NUVWWWXXL rcpeZdZUeed<eed<eed<eeed<dZeeeed<dZ dS)MassPropertiesdensitymassvolume center_massNinertiac"t||SN)getattr)selfitems r __getitem__zMassProperties.__getitem__stT"""r) __name__ __module__ __qualname__float__annotations__rr rTr rZrrrOrOsuNNN KKK MMM!!!!+/GXgg& '...#####rrOFc tj|tj}tj|dst d|t |}|d}|dddddf|dddddfz|dddddfz}|dddddfdz|dddddfdzz|dddddf|dddddfzz|dddddf|zz}|dddddfd z|dddddfdz|dddddfzz|dddddf|dddddfdzzz|dddddfd zz|dddddf|zz}||dddddf|z|dddddfzz}||dddddf|z|dddddfzz} ||dddddf|z|dddddfzz} tjd t|f} |dddf|dddfz| d<||zj | dd <||zj | d d <td D]}} tj | dzd } |dd| f|ddd| f|dd| fz|ddd| f| dd| fzz|ddd| f| dd| fzzz| | d z<~| d tj gdtjz }|d}|Ptj|tjkr!tjd tj}n |dd |z }t#|||z||}|r|Stjd}|d|dz||ddgdz zz |d<|d |dz||ddgdz zz |d<|d |dz||ddgdz zz |d<|d |tj|ddgzz |d<|d|tj|ddgzz |d<|d|tj|ddgzz |d<|d|d<|d|d<|d|d<||z|_|S)aL Calculate the mass properties of a group of triangles. Implemented from: http://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf Parameters ---------- triangles : (n, 3, 3) float Triangle vertices in space crosses : (n,) float Optional cross products of triangles density : float Optional override for density center_mass : (3,) float Optional override for center mass skip_inertia : bool if True will not return moments matrix Returns --------- info : dict Mass properties rr<r=Nr(rrrr r) rfrf<rgrgxrhrh)rPrQrRrS)rrre)rr)rr)rr)rr)rr )rr)rr)rr)rr)rr r rrCrrr/r0Trangemodr"arrayrFrrGrOprodrT)r r#rPrS skip_inertiaf1f2f3g0g1g2integrali triangle_i integratedrRr9rTs rmass_propertiesr|s26 irz:::I =J / /97888 "" 111a7 i1aaa0 09QQQ111W3E EB !!!Q'a AAAq!!!G  ! " AAAq!!!G yAqqq1 1 2 AAAq!!!G r ! " 111a7 q QQQ111W  "yAqqq'9 : ; QQQ111W )AAAq!!!G"4"9 : ; QQQ111W  " $ QQQ111W  "  $ yAqqq!B&)AAAq!!!G*<< >CH $ $(1BJ777KK%QqS/F2K  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 rrCrrr-dotr r/r0bool)r normals_compare calculatedr, differencealigneds rwindings_alignedrDs" 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 rr<r=rr) rr r rrCr column_stackminmax bounds_tree)r triangle_boundstrees rrrhs irz:::I =J / /97888oy}}!}'<'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<r=N)r areasrr) rr r rrCrrr4extentsrE)r rheightoks 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<r=N)r rrrrg?) rr r rrCrr$r"rr4r/r0) r rrrlength_alength_b nonzero_a nonzero_bboxs rrrsh  irz:::I =J / /97888 }y))) !!!Q$)AAAqD/)A!!!Q$)AAAqD/)A1zzqz!!S(H1zzqz!!S(H39$I39$I (C NNA&bj 9 9 9C!),q0HY4GGC1Ii!),q0HY4GGC1Ii Jrc6tj|tj}tj|tj}||ddz}||dzd}|S)aG Convert a list of barycentric coordinates on a list of triangles to cartesian points. Parameters ------------ triangles : (n, 3, 3) float Triangles in space barycentric : (n, 2) float Barycentric coordinates Returns ----------- points : (m, 3) float Points in space rrrr&r)r&rr)rror r r"rD)r barycentricr@s rbarycentric_to_pointsrs"(;bj999K irz:::I;???**227;;;K+--j999 > >A > F FF Mrcramercjfd}fd}tjtjtj|tj}tjdkrt djd}t|jdks-|jd|ks|jdjdkrt d d d dd fd d d dfz |d d dfd |fz |d kr |S|S) a; Find the barycentric coordinates of points relative to triangles. The Cramer's rule solution implements: http://blackpawn.com/texts/pointinpoly The cross product solution implements: https://www.cs.ubc.ca/~heidrich/Papers/JGT.05.pdf Parameters ----------- triangles : (n, 3, 2 | 3) float Triangles vertices in space points : (n, 2 | 3) float Point in space associated with a triangle method : str Which method to compute the barycentric coordinates with: - 'cross': uses a method using cross products, roughly 2x slower but different numerical robustness properties - anything else: uses a cramer's rule solution Returns ----------- barycentric : (n, 3) float Barycentric coordinates of each point ctjdddfdddf}t||}tjt dftj}ttjdddf||z |dddf<ttjdddf||z |dddf<d|dddfz |dddfz |dddf<|S)Nrrrrr)rrr r/r0r )n denominatorr edge_vectorsr r8s r method_crossz+points_to_barycentric..method_cross s H\!!!Q$'aaad); < <"1a(( hI2"*EEE (,qqq!t2Da)H)H!LL{Z AAAqD(!\!!!Q$5G)H)H!LL{Z AAAqD AAAqD 11K14EE AAAqDrc\tdddfdddf}tdddfdddf}tdddf }tdddfdddf}tdddf }d||z||zz z }tjtdftj}||z||zz |z|dddf<||z||zz |z|dddf<d|dddfz |dddfz |dddf<|S)Nrrr(rrr)r rr/r0r ) dot00dot01dot02dot11dot12inverse_denominatorrrr r8s r method_cramerz,points_to_barycentric..method_cramersu\!!!Q$/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 r0rrrD)r r@methodrrdimrr8s` @@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 rrCrr0 zeros_likeonesrr logical_andrrGr5rD) r r@r9remainrrrcabacapd1d2is_abpd3d4is_bvcis_abr7cpd5d6is_cvbis_acr8vais_bcd43denoms r closest_pointr<s0 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<r=r>)verticesfaces) rr r rrCrrDaranger0)r rrkwargss r to_kwargsrs( irz:::I =J / /97888  ))H Ic(mm $ $ , ,W 5 5E"U 3 3F Mr)NN)NNNFrV)r)!__doc__ dataclassesrnumpyrr constantsrr@rtypedrr r r r rr$r-r:rKrMrOr|rrrrrrrrr`rrrs"!!!!!((((((----------''''''''&W&&&&&43333.6###L:* ####### #.KPssssssl!!!H2!!!!H****Z6LLLL^ssslr