h0SrSSKJr SSKJr SSKJr SSKrSSKrSSKJrJ r Sr Sr S r S r S rSS jrS rSSjrSSjrSrSrSrSrSrg)a[ Functions about transforming mesh(changing the position: modify vertices). 1. forward: transform(transform, camera, project). 2. backward: estimate transform matrix from correspondences. Preparation knowledge: transform&camera model: https://cs184.eecs.berkeley.edu/lecture/transforms-2 Part I: camera geometry and single view geometry in MVGCV )absolute_import)division)print_functionN)cossinc [R"US5[R"US5[R"US5p2n[R"/SQS[U5[ U5*/S[ U5[U5//5n[R"[U5S[ U5//SQ[ U5*S[U5//5n[R"[U5[ U5*S/[ U5[U5S//SQ/5nUR UR U55nUR [R5$)aget rotation matrix from three rotation angles(degree). right-handed. Args: angles: [3,]. x, y, z angles x: pitch. positive for looking down. y: yaw. positive for looking left. z: roll. positive for tilting head right. Returns: R: [3, 3]. rotation matrix. rr rrrr rrrr )npdeg2radarrayrrdotastypefloat32anglesxyzRxRyRzRs l/var/www/fran/franai/venv/lib/python3.13/site-packages/insightface/thirdparty/face3d/mesh_numpy/transform.py angle2matrixrsjj#RZZq %:BJJvay/33ACC8 rc"UR5$)ascaled orthographic projection(just delete z) assumes: variations in depth over the object is small relative to the mean distance from camera to object x -> x*f/z, y -> x*f/z, z -> f. for point i,j. zi~=zj. so just delete z ** often used in face Homo: P = [[1,0,0,0], [0,1,0,0], [0,0,1,0]] Args: vertices: [nver, 3] Returns: projected_vertices: [nver, 3] if isKeepZ=True. [nver, 2] if isKeepZ=False. copy)r$s rorthographic_projectrEs ==?rc [R"U5nU[R"U5-nU*nXR-nU*n[R"X7- SSS/SX5- SS/SSXC-*XC- - SU-U-XC- - //SQ/5n [R"U[R "UR SS4545n U RU R5n XSS2SS24- n U SS2SS24n U SS2S4*U SS2S4'U $)aperspective projection. Args: vertices: [nver, 3] fovy: vertical angular field of view. degree. aspect_ratio : width / height of field of view near : depth of near clipping plane far : depth of far clipping plane Returns: projected_vertices: [nver, 3] r)rrrr Nr ) rrtanrhstackonesshaperr#) r$fovy aspect_rationearfartopbottomrightleftP vertices_homoprojected_verticess rperspective_projectrYs ::d D rvvd| CTF  E 6D 4:q!Q'TXq!$Q#( SX.3t SX0FG  !AIIx(..2CQ1G)HIJM&**133/+qt,DD+AbqbD11!A#66qs rcUR5nU(a,USS2S4U-S- USS2S4'USS2S4U-S- USS2S4'USS2S4US- -USS2S4'USS2S4US- -USS2S4'XSS2S4- S- USS2S4'U$)achange vertices to image coord system 3d system: XYZ, center(0, 0, 0) 2d image: x(u), y(v). center(w/2, h/2), flip y-axis. Args: vertices: [nver, 3] h: height of the rendering w : width of the rendering Returns: projected_vertices: [nver, 3] Nrr r rC)r$hwis_perspectiveimage_verticess rto_imager_s]]_N,QqS1!3A5qs,QqS1!3A5qs(1-!3N1Q3(1-!3N1Q3QqS11A5N1Q3 rc[R"U[R"URSS/545n[RR X!5SR nU$)zUsing least-squares solution Args: X: [n, 3]. 3d points(fixed) Y: [n, 3]. corresponding 3d points(moving). Y = PX Returns: P_Affine: (3, 4). Affine camera matrix (the third row is [0, 0, 0, 1]). r r)rrKrLrMlinalglstsqr#)XYX_homorVs restimate_affine_matrix_3d23drfsNYY277AGGAJq>23 4F "1%''A Hrc@URoRnURSURS:XdeURSnUS:de[R"US5nU[R"USS2[R 4SU/5- n[R"[R "[R"US-S555n[R "S5U- nXQ-n[R"S[RS9nU=US'US 'U*U-USS2S4'SUS '[R"U[R"SU4545n[R"US5nU[R"USS2[R 4SU/5- nUSS 2SS24U- n[R"[R "[R"US-S555n[R "S 5U- nXP-n[R"S [RS9n U=U S'=U S 'U S 'U*U-U SS 2S 4'SU S'[R"US-S 4[RS9n [R"U[R"SU4545RnXzSU2SS24'XzUS2SS24'[R"USS/5n [RRU 5RU 5n [R"S[RS9n U SS2S4U SSS24'U SS2S4U SSS24'SU S'[RR!U5RU RU 55nU$)aUsing Golden Standard Algorithm for estimating an affine camera matrix P from world to image correspondences. See Alg.7.2. in MVGCV Code Ref: https://github.com/patrikhuber/eos/blob/master/include/eos/fitting/affine_camera_estimation.hpp x_homo = X_homo.dot(P_Affine) Args: X: [n, 3]. corresponding 3d points(fixed) x: [n, 2]. n>=4. 2d points(moving). x = PX Returns: P_Affine: [3, 4]. Affine camera matrix r Nr r)rIrIr(rrr r r r rI)rhrhrH)rIrh)rHrH)r#rMrmeantiler+r2r3zerosrvstackrLreshaperapinvrinv)rcrnrm average_normscaler#remUAbp_8rVP_Affines restimate_affine_matrix_3d22dr}s AQ 771: #$ #  A 6N6 771a=D BGGDBJJ'!Q 00A77277266!Q$?34L GGAJ %E A  +AAdGaguU{Abqb!eHAdGYY277Aq6?+ ,F 771a=D BGGDBJJ'!Q 00Arr!t qA77277266!Q$?34L GGAJ %E A  +A"''AdG'ag$uU{Abqb!eHAdG !A#q2::.A YY277Aq6?+ , . .Fbqb"1"fIab!"fI 1r1gA ))..    "C ,A"1"a%jAadG!"a%jAadGAfIyy}}Q##AEE!H-H OrcUSS2S4nUSS2SS24nUSS2SS24n[RRU5[RRU5-S- nU[RRU5- nU[RRU5- n[R"XV5n[R"XVU4S5nXHU4$)zdecompositing camera matrix P Args: P: (3, 4). Affine Camera Matrix. Returns: s: scale factor. R: (3, 3). rotation matrix. t: (3,). translation. NrIrr r g@)rrar6r9 concatenate) rVtR1R2r,r1r2r3rs rP2sRtr/s !Q$A 1Q37B 1Q37B  biinnR0 0#5A BIINN2  B BIINN2  B " B |Q'A 7Nrc[R"U5n[R"X5n[R"SURS9n[R R X2- 5nUS:$)zMchecks if a matrix is a valid rotation matrix(whether orthogonal or not) rIr(ư>)r transposeridentityr)rar6)rRtshouldBeIdentityIrts risRotationMatrixrDsQ aBvvb} Aqww'A q+,A t8Orc6[(de[R"USUS-USUS--5nUS:nU(dV[R"USUS5n[R"US*U5n[R"USUS5nO;[R"US*US5n[R"US*U5nS nUS -[R - US -[R - US -[R - pnXgU4$) z}get three Euler angles from Rotation Matrix Args: R: (3,3). rotation matrix Returns: x: pitch y: yaw z: roll ri)r rr)r r rk)r r)r r rjr)rmathr2atan2rpi) rsysingularrrrrxryrzs r matrix2anglerMs    1S6AcF?afqvo5 6BDyH  JJqv# ' JJ#w # JJqvqv & JJ#w# ' JJ#w # 3ruuaeBEEk1S5;BB 2:r)NN)g?g?g@@)F)__doc__ __future__rrrnumpyrrrrrr!r&r/r7rArErYr_rfr}rrrrrrsg '%  6 >" (  D  F2  <|*r