How to get the intersection volume of two meshes (faces & vertices)?

Question

Do you know how to get the intersection (corresponding) volume/meshes of two polygon meshes consisting of the set of faces and vertices in Matlab?

Answer 1

I am not aware of a builtin MATLAB method to do this. But via mex functions you can make use of ready-made C++ libraries.

The following example uses libigl's boolean mesh operation.

It has some dependencies, I installed them on Ubuntu Linux using:

$ sudo apt-get install libcgal-dev git mercurial
$ cd /opt/
$ hg clone https://bitbucket.org/eigen/eigen/
$ git clone https://github.com/libigl/libigl.git

---

get_intersection_mesh.cpp

#include "mex.h"

#include <Eigen/Core>
#include <igl/matlab/prepare_lhs.h>
#include <igl/matlab/parse_rhs.h>
#include <igl/boolean/mesh_boolean.h>

void mexFunction(
     int          nlhs,
     mxArray      *plhs[],
     int          nrhs,
     const mxArray *prhs[]
     )
{
  using namespace Eigen;
  if (nrhs != 4) 
  {
    mexErrMsgIdAndTxt("MATLAB:mexcpp:nargin",
        "get_intersection_mesh requires 4 input parameters: F1, V1, F2, V2");
  }
  if (nlhs != 2) 
  {
    mexErrMsgIdAndTxt("MATLAB:mexcpp:nargout",
        "get_intersection_mesh requires 2 output parameters: F, V");
  }

  MatrixXd V1, V2, V_i;
  MatrixXi F1, F2, F_i;

  // read input meshes
  igl::matlab::parse_rhs_index(prhs+0, F1);
  igl::matlab::parse_rhs_double(prhs+1,V1);
  igl::matlab::parse_rhs_index(prhs+2, F2);
  igl::matlab::parse_rhs_double(prhs+3,V2);

  // calculate intersection
  igl::boolean::mesh_boolean(V1,F1,V2,F2,igl::boolean::MESH_BOOLEAN_TYPE_INTERSECT,V_i,F_i);

  // write output
  igl::matlab::prepare_lhs_index(F_i,plhs+1);
  igl::matlab::prepare_lhs_double(V_i,plhs);
}

---

You compile it in MATLAB using:

mex get_intersection_mesh.cpp -I/opt/libigl/include -I/opt/eigen -lboost_thread -lCGAL -lmpfr -lgmp -lboost_system

---

You would then use it like this:

[V_i, F_i] = get_intersection_mesh(fv1.faces, fv1.vertices, fv2.faces, fv2.vertices);

% plot intersection mesh
patch('Faces',F_i,'Vertices',V_i, 'FaceColor','w');