jdZddlZddlmZddlmZ 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 >/DATA/.local/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'$B"ctj|tj}tj|ds t dtj ||z ||zf}|Dcgc]&}t|jj|(}}tjt|}tt||D]\}\}} |j|j| } t!| dddf| dddf||} |j"| } tj$|j&| dd} | | z| zj)d z ||<|Scc}w) 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$Nrr)centerr-r"r)rr%r&rr'r( column_stacklistface_adjacency_tree intersectionzeroslen enumeratezipr/face_adjacency_edgesline_ball_intersectionface_adjacency_angleswhereface_adjacency_convexr)rr,r-boundsb candidates mean_curvix x_candidates endpointslengthsanglessignss rdiscrete_mean_curvature_measurerLYsJ,]]6 4F == )011__fvov? @FKQQ&Q$t//<rhsf0'  &"B*Z*Z I0,,,Q/J0s-AAA