:vjdZddlZddlmZddlmZ ddlmZdZ d Z d Zd Zd Zd Zy#e$r"Z ddlm Z e je ZYdZ [ 5dZ [ wwxYw)z5 curvature.py --------------- Query mesh curvature. N)util) diagonal_dot) coo_matrix) exceptionsct|jj|jj|jj ff|jj }|S)z A sparse matrix representation of the face angles. Returns ---------- sparse : scipy.sparse.coo_matrix matrix is float shaped (len(vertices), len(faces)) )r face_anglesflatten faces_sparserowcolshape)meshmatrixs b/workspace/moltex-experiments/.pixi/envs/default/lib/python3.12/site-packages/trimesh/curvature.pyface_angles_sparsersX   ! ! #d&7&7&;&;T=N=N=R=R%ST F Mctj|jjdj }dtj z|z }|S)a Return the vertex defects, or (2*pi) minus the sum of the angles of every face that includes that vertex. If a vertex is only included by coplanar triangles, this will be zero. For convex regions this is positive, and concave negative. Returns -------- vertex_defect : (len(self.vertices), ) float Vertex defect at the every vertex r)axis)nparrayrsumr pi)r angle_sumdefects rvertex_defectsr%sF0044!4<=EEGI"%%i9 $F MrcNtj|tj}tj|ds t d|j j||}|Dcgc]}|j|j!}}tj|Scc}w)a> Return the discrete gaussian curvature measure of a sphere centered at a point as detailed in 'Restricted Delaunay triangulations and normal cycle'- Cohen-Steiner and Morvan. This is the sum of the vertex defects at all vertices within the radius for each point. Parameters ---------- points : (n, 3) float Points in space radius : float , The sphere radius, which can be zero if vertices passed are points. Returns -------- gaussian_curvature: (n,) float Discrete gaussian curvature measure. dtypepoints must be (n,3)!) r asanyarrayfloat64ris_shape ValueErrorkdtreequery_ball_pointrrasarray)rpointsradiusnearestvertices gauss_curvs r#discrete_gaussian_curvature_measurer18s.]]6 4F == )011kk**66:GFMNg($%%h/335gJN ::j !!Os'$B"c tj|tj}tj|ds t dtj |j}tj |j}tj |j}tj |j}|j}||z }||z} |j|| \} } tj | tj} tj | tj} t'| dk(rtj.t'|Stj0tj2t'|| }||| }t5|dddf|dddf||| }tj6|| dd }tj8|||| z|zt'| d z S#t$rtj|| fDcgc]}t!|j#|ncc}w}}tj$|Dcgc] }t'|ncc}wc}tj} tj(d|Dtjt+| j-} YwxYw) a Return the discrete mean curvature measure of a sphere centered at a point as detailed in 'Restricted Delaunay triangulations and normal cycle'- Cohen-Steiner and Morvan. This is the sum of the angle at all edges contained in the sphere for each point. Parameters ---------- points : (n, 3) float Points in space radius : float Sphere radius which should typically be greater than zero Returns -------- mean_curvature : (n,) float Discrete mean curvature measure. rr!r$c3.K|] }|D]}|yw)N).0cis r z2discrete_mean_curvature_measure..s - 11aQ1Q s)r countrNr)centerr-r")weights minlengthr)rr%r&rr'r(r+r/face_adjacency_edgesface_adjacency_anglesface_adjacency_convexface_adjacency_treeintersection_vint64 BaseException column_stacklist intersectionrlenfromiterintrzerosrepeatarangeline_ball_intersectionwherebincount)rr,r-r/adjacency_edgesadjacency_anglesadjacency_convextreeminsmaxshit_ids hit_counts candidatescountsb per_pointr6owner endpointslengthssignss rdiscrete_mean_curvature_measurer`YsI,]]6 4F == )011zz$--(Hjj!:!:;Ozz$"<"<=zz$"<"<=  # #D F?D F?D  "11$=ZZrxx8 Jbhh7 :!xxF $$ IIbiiF ,f 5E45I%!Q$1a4vG HH%j11b 9E .z::UB&k  -  9;$PT9VW9VAT$++A./9VW W959a3q695RXXF[[ - -RXXSEV  s,AH"K(!I  K$I7 6A!KKc||z }||z }|}t||}t||}t||} |dz|| |dzz zz } tjt|} | dkD} ||  tj| | z || z } ||  tj| | z|| z }tj | dd} tj |dd}|| z tj|| z| | <| S)a| Compute the length of the intersection of a line segment with a ball. Parameters ---------- start_points : (n,3) float, list of points in space end_points : (n,3) float, list of points in space center : (3,) float, the sphere center radius : float, the sphere radius Returns -------- lengths: (n,) float, the lengths. rrr)rrrJrGsqrtclip) start_points end_pointsr:r-Locrldotlldotococdotocdiscrimsr^md1d2s rrMrMs( \!A  BA A E !R F2r"Gqy5GadN33Hhhs<()G1 A !9*rwwx{+ +uQx 7B !9*rwwx{+ +uQx 7B Q B Q Br'RWWU1X..GAJ Nrcd|dzz|dzz d|zz }|| k\rdtjz|z||z zS|| krdtjz|dzzSy)a( Compute the surface area of the intersection of sphere of radius R centered at (0, 0, 0) with a ball of radius r centered at (R, 0, 0). Parameters ---------- R : float, sphere radius r : float, ball radius Returns -------- area: float, the surface are. rN)rr)Rrhxs rsphere_ball_intersectionrtsk QTAqDQU#AQBw255y1}A&&A2v255y1a4r)__doc__numpyrrr scipy.sparser ImportErrorErExceptionWrapperrrr1r`rMrtr4rrr|sg0'  &"BGT*Z C0,,,Q/J0s-AAA