thin_medial_mesh

thin_medial_mesh(C, R, E, F, importance, threshold)

Remove medial tets and unimportant faces by topology-preserving thinning.

Medial meshes computed from a power diagram may contain medial tets: four spheres whose four triangles are all medial faces. Each tet is removed by collapsing a tet-face simple pair (the face with the smallest importance first); then, among the faces of those tets, faces with importance < threshold are pruned through their free edges (face-edge simple pairs). Collapsing simple pairs does not change the topology of the medial mesh.

Parameters:

Name	Type	Description	Default
C	(n,3) numpy double array	Sphere centers.	required
R	(n,) numpy double array	Sphere radii.	required
E	(e,2) numpy int array	Medial edges.	required
F	(f,3) numpy int array	Medial faces.	required
importance	(f,) numpy double array	Importance of each face, for example the length of the dual edge of the restricted power diagram over the average sphere diameter, as returned by medial_mesh_from_spheres.	required
threshold	float	Faces of medial tets with importance >= threshold are kept.	required

Returns:

Name	Type	Description
E_out	(e',2) numpy int array	Remaining medial edges (indices into C).
F_out	(f',3) numpy int array	Remaining medial faces (indices into C).

Notes

Only faces that belong to a medial tet are candidates for pruning; a medial mesh without tets is returned unchanged.

C++: void libmat::thin_medial_mesh(C, R, E, F, importance, threshold, E_out, F_out) in <libmat/thin_medial_mesh.h>.

Examples:

import numpy as np
import libmat
# four spheres forming a medial tet, plus one extra face
C = np.array([[0., 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1]])
R = np.full(5, 0.3)
F = np.array([[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3], [1, 2, 4]])
importance = np.array([0.9, 0.1, 0.2, 0.8, 1.0])
E_out, F_out = libmat.thin_medial_mesh(C, R, None, F, importance, 0.5)
print(F_out)   # the low-importance faces of the tet are gone

C++

#include <libmat/thin_medial_mesh.h>

// Topology-preserving thinning of a medial mesh: medial tetrahedra (four vertices
// whose four triangles are all medial faces) are removed by collapsing
// tet-face simple pairs in order of increasing face importance, then faces of
// those tets with importance below `threshold` are pruned through their free
// edges (face-edge simple pairs). Pruning simple pairs preserves topology.
//
// Inputs:
//   C           #V by 3 sphere centers
//   R           #V sphere radii
//   E           #E by 2 medial edges
//   F           #F by 3 medial faces
//   importance  #F importance of each face (e.g. the length of the dual
//               power-diagram edge over the average sphere diameter)
//   threshold   faces with importance >= threshold are kept
// Outputs:
//   E_out  #E' by 2 remaining edges (indices into C)
//   F_out  #F' by 3 remaining faces (indices into C)
void thin_medial_mesh(const Eigen::MatrixXd& C, const Eigen::VectorXd& R,
                      const Eigen::MatrixXi& E, const Eigen::MatrixXi& F,
                      const Eigen::VectorXd& importance, double threshold,
                      Eigen::MatrixXi& E_out, Eigen::MatrixXi& F_out);