medial_mesh_from_spheres

medial_mesh_from_spheres(V, T, C, R)

Connect medial spheres into a medial mesh with the restricted power diagram (CUDA).

The power diagram of the spheres is clipped by the input tet mesh on the GPU (restricted power diagram, RPD). Two spheres are connected by a medial edge when their restricted power cells share a face, and three spheres span a medial face when their cells share an edge.

Requires a build with CUDA (LIBMAT_WITH_CUDA=ON).

Parameters:

Name	Type	Description	Default
V	(n,3) numpy double array	Tet mesh vertex positions.	required
T	(m,4) numpy int array	Tetrahedra.	required
C	(s,3) numpy double array	Medial sphere centers (same coordinates as V).	required
R	(s,) numpy double array	Medial sphere radii.	required

Returns:

Name	Type	Description
E	(e,2) numpy int array	Medial edges (indices into C).
F	(f,3) numpy int array	Medial faces (indices into C).
importance	(f,) numpy double array	Face importance (dual RPD edge length over the average sphere diameter), to be used with thin_medial_mesh.

Raises:

Type	Description
RuntimeError	If libmat was built without CUDA.

Notes

C++: void libmat::medial_mesh_from_spheres(V, T, C, R, E, F, importance) in <libmat/medial_mesh_from_spheres.h>, implemented in src/cuda/api/.

Examples:

import libmat
V, T = libmat.read_tet_mesh("data/lblock.tet")
SV, SF, _ = libmat.extract_surface(V, T)
C, R, _ = libmat.shrink_spheres(SV, SF, num_spheres=1000)
if libmat.has_cuda():
    E, F, importance = libmat.medial_mesh_from_spheres(V, T, C, R)
    E, F = libmat.thin_medial_mesh(C, R, E, F, importance, 0.3)

Requires CUDA

Only available when libmat is built with LIBMAT_WITH_CUDA=ON, see Installation.

C++

#include <libmat/medial_mesh_from_spheres.h>

// [CUDA] Compute the medial mesh connecting a set of medial spheres, as the
// dual of their power diagram restricted to the input tet mesh (RPD): two
// spheres are connected by an edge if their
// restricted power cells share a face, and three spheres span a medial face
// if their restricted power cells share an edge.
//
// Requires a build with LIBMAT_WITH_CUDA=ON, throws std::runtime_error
// otherwise.
//
// Inputs:
//   V  #V by 3 tet mesh vertex positions
//   T  #T by 4 tetrahedra
//   C  #S by 3 medial sphere centers (same coordinates as V)
//   R  #S medial sphere radii
// Outputs:
//   E           #E by 2 medial edges (indices into C)
//   F           #F by 3 medial faces (indices into C)
//   importance  #F face importance (dual RPD edge length over the average
//               sphere diameter), to be used with thin_medial_mesh()
void medial_mesh_from_spheres(const Eigen::MatrixXd& V,
                              const Eigen::MatrixXi& T,
                              const Eigen::MatrixXd& C,
                              const Eigen::VectorXd& R, Eigen::MatrixXi& E,
                              Eigen::MatrixXi& F, Eigen::VectorXd& importance);