l0jdZddlZddlmZ ddlmZn(#e$r Zddlm Z e j eZYdZ[ndZ[wwxYwdZ dZ d Z d Zd Zd ZdS) z5 curvature.py --------------- Query mesh curvature. N)util) coo_matrix) exceptionsct|j|jj|jjff|jj}|S)z A sparse matrix representation of the face angles. Returns ---------- sparse : scipy.sparse.coo_matrix matrix is float shaped (len(vertices), len(faces)) )r face_anglesflatten faces_sparserowcolshape)meshmatrixs T/home/wildlama/miniconda3/envs/lam/lib/python3.11/site-packages/trimesh/curvature.pyface_angles_sparsersK  ! ! # #d&7&;T=N=R%ST F Mctj|jd}dtjz|z }|S)a Return the vertex defects, or (2*pi) minus the sum of the angles of every face that includes that vertex. If a vertex is only included by coplanar triangles, this will be zero. For convex regions this is positive, and concave negative. Returns -------- vertex_defect : (len(self.vertices), ) float Vertex defect at the every vertex r)axis)nparrayrsumr pi)r angle_sumdefects rvertex_defectsr$sH044!4<<==EEGGI"%i9 $F Mrctj|tj}tj|dst dj||}fd|D}tj|S)a> Return the discrete gaussian curvature measure of a sphere centered at a point as detailed in 'Restricted Delaunay triangulations and normal cycle'- Cohen-Steiner and Morvan. This is the sum of the vertex defects at all vertices within the radius for each point. Parameters ---------- points : (n, 3) float Points in space radius : float , The sphere radius, which can be zero if vertices passed are points. Returns -------- gaussian_curvature: (n,) float Discrete gaussian curvature measure. dtypepoints must be (n,3)!cNg|]!}j|"S)rr).0verticesrs r z7discrete_gaussian_curvature_measure..Ss-NNN($%h/3355NNNr) r asanyarrayfloat64ris_shape ValueErrorkdtreequery_ball_pointasarray)rpointsradiusnearest gauss_curvs` r#discrete_gaussian_curvature_measurer47s~.]6 4 4 4F = ) )20111k**66::GNNNNgNNNJ :j ! !!rctj|tj}tj|dst dtj||z ||zf}fd|D}tjt|}tt||D]\}\}}j j |} t| dddf| dddf||} j|} tjj|dd } | | z| zd z ||<|S) 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#c^g|])}tj|*Sr%)listface_adjacency_tree intersection)r&brs rr(z3discrete_mean_curvature_measure..vs2QQQQ$t/<irrr)reinsumr=r>sqrtclip) start_points end_pointsr;r1LocrldotlldotococdotocdiscrimsrMmd1d2s rrBrBs0( \!A  BA Ik1a ( (E Y{Ar * *Fi R,,Gqy5GadN33Hhs<(())G1 A !9*rwx{++ +uQx 7B !9*rwx{++ +uQx 7B Q  B Q  Br'RWU1X...GAJ Nrcd|dzz|dzz d|zz }|| krdtjz|z||z zS|| krdtjz|dzzSdS)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)RrYrJs rsphere_ball_intersectionrdsm QTAqDQU#AQBww25y1}A&&A2vv25y1a4vr)__doc__numpyrr scipy.sparser ImportErrorErExceptionWrapperrrr4rPrBrdr%rrrls0'''''''000,,Q//JJJJJJ0    &"""B***Z***Z     s:5: