:vj)PddlZddlmZddlmZddlmZd dZ d dZ ded e fd Z y) N)res_path)tol_path)Integerc <tj|tj}|tjj tj |ddj }tj|tj|zz }ttj|tjt|ztjt|z}t|}tjdd|}d|z }t|dz }t!t#|tj$t||}|D cgc])\}} } || z||| z zzj'd| z|z+} } }} tj | d} t(j*rZtj | ddg|ddgz d zd} | t(j,kj/sJt| d k\sJ|ddg| ddg<| Scc} } }w) ak Parameters ---------- points : (order, dimension) float Control points of the bezier curve For a 2D cubic bezier, order=3, dimension=2 count : int, or None Number of segments scale : float Scale of curve Returns ---------- discrete: (n, dimension) float Points forming a a polyline representation dtyperaxisg?)r rr)np asanyarrayfloat64linalgnormdiffsumceilresseg_fracintclip min_sectionslen max_sectionslinspacezipbinomialarangereshapetolstrictmergeall)pointscountscalertt_dniterablecipstackedresulttests c/workspace/moltex-experiments/.pixi/envs/default/lib/python3.12/site-packages/trimesh/path/curve.pydiscretize_bezierr5s"]]6 4F }yy~~bggf15A~>BBD u 456 GGE3++c&k93;K;KcRXk;Y Z  JE Ce$A 'C F aA8A; #f+ 6?HMULTAq!Q$31q5> "++G4q81QGsyy %%'''6{aaWoFAr7O Ms.Hc |ddlm}tj|tj}t |t |z dz }|tj jtj|ddj}ttj|tj|zz tjt |ztjt |z}tj |d|d|}||||j"|g}tj$|}|S)a Given a B-Splines control points and knot vector, return a sampled version of the curve. Parameters ---------- control : (o, d) float Control points of the b- spline knots : (j,) float B-spline knots count : int Number of line segments to discretize the spline If not specified will be calculated as something reasonable Returns ---------- discrete : (count, dimension) float Points on a polyline version of the B-spline r)splevrr r r)scipy.interpolater7rrrrrrrrrrrrrrrT column_stack) controlknotsr(r)r7degreeripldiscretes r4discretize_bspliner@?s,(mmG2::6G Z#g, & *F }yy~~bgggA6Q~?CCE GG u,-  3w</  3w</   ++eAhb 5 1CS5'))V45Hx(H Or,returnc|dk(rddgS|dk(rgdS|dk(rgdS|dk(rgdS|dk(rgd Sd d lm}||tj|dzS) a+ Return all binomial coefficients for a given order. For n > 5, scipy.special.binom is used, below we hardcode. Parameters -------------- n : int Order of binomial Returns --------------- binom : (n + 1,) int Binomial coefficients of a given order r r)r rr )r rDrDr )r rErEr )r rG rHrGr r)binom) scipy.specialrIrr!)r,rIs r4r r kse  Av1v a a a a##'Q !a%())rA)Nr ) numpyr constantsrrrr#typedrr5r@listr rAr4rPs0''4n)X**D*rA