Ti/VddlZddlmZddlmZddlmZm Z d dZ d dZ d ed e fd Z dS) N)res_path)tol_path)IntegerList?c  tj|tj}|tjtj|dd}tj|tj |zz }ttj |tj t|ztjt|z}t|}tjdd| d z t|dz t!t#tjt||} fd|D}tj|d}t&jretj|dd g|dd gz d zd}|t&jksJt|d ksJ|dd g|dd g<|S) 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 dtypeNraxisgrcfg|]-\}}}|z|z zzd|z|z.S))r)reshape).0cipntt_ds L/DATA/AppData/hermes/venv/lib/python3.11/site-packages/trimesh/path/curve.py z%discretize_bezier..-sUAHAq!Q$31q5> "++G44q81<rr)np asanyarrayfloat64linalgnormdiffsumceilresseg_fracintclip min_sectionslen max_sectionslinspacezipbinomialarangetolstrictmergeall) pointscountscaler iterablestackedresulttestrrrs @@@rdiscretize_bezierr:s"]6 4 4 4F }y~~bgf1555A~>>BBDD u 4566 GE3+c&kk93;KcRXkk;Y Z Z   JJE Ce$$A 'C F aA8A;; #f++ 6 6??HLTGVG! $ $ $F z vvq"gB8Q>QGGGsy %%'''''6{{aaWoFAr7O Mrc ddlm}tj|tj}t |t |z dz }|tjtj|dd }ttj |tj |zz tjt |ztjt |z}tj|d|d|}||||j|g}tj|}|S)a Given a B-Splines control points and knot vector, return a sampled version of the curve. Parameters ---------- control : (o, d) float Control points of the b- spline knots : (j,) float B-spline knots count : int Number of line segments to discretize the spline If not specified will be calculated as something reasonable Returns ---------- discrete : (count, dimension) float Points on a polyline version of the B-spline r)splevr rNr r)scipy.interpolater<rrrr)rr r!r"r&r'r$r%r(r*r+T column_stack) controlknotsr4r5r<degreer ipldiscretes rdiscretize_bsplinerE?s,('''''mG2:666G ZZ#g,, & *F }y~~bggA666Q~??CCEE G u,- 3w<</ 3w<</     +eAhb 5 1 1CuS5')V455Hx((H Orrreturnc|dkrddgS|dkrgdS|dkrgdS|dkrgdS|dkrgd 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 rr)rrr)rrHrHr)rrIrIr)rrK rLrKrr)binom) scipy.specialrMrr.)rrMs rr-r-ks  Avv1v ayy a|| a a####''''''uQ !a%(()))r)Nr) numpyr constantsrr$rr/typedrrr:rEr-rrrSs''''''''''''!!!!!!!!4444n))))X**D******r