libigl/tutorial/805_MeshImplicitFunction/contours.cpp

#include "contours.h"
#include <igl/unique_simplices.h>
#include <igl/dual_contouring.h>
#include <igl/get_seconds.h>
#include <igl/grid.h>
#include <igl/marching_cubes.h>
#include <igl/per_corner_normals.h>
#include <igl/parallel_for.h>
#include <igl/per_corner_normals.h>
#include <igl/per_face_normals.h>
#include <igl/polygon_corners.h>
#include <igl/sparse_voxel_grid.h>

void contours(
    Eigen::MatrixXd & V,
    Eigen::MatrixXi & E,
    Eigen::MatrixXd & VV,
    Eigen::MatrixXi & FF,
    Eigen::MatrixXd & NN,
    Eigen::MatrixXd & mcV,
    Eigen::MatrixXi & mcF,
    Eigen::MatrixXd & mcN)
{
  const auto & tictoc = []()
  {
    static double t_start = igl::get_seconds();
    double diff = igl::get_seconds()-t_start;
    t_start += diff;
    return diff;
  };

  // Create an interesting shape with sharp features using SDF CSG with spheres.
  const auto & sphere = [](
      const Eigen::RowVector3d & c,
      const double r,
      const Eigen::RowVector3d & x)->double
  {
    return (x-c).norm() - r;
  };
  const std::function<double(const Eigen::RowVector3d & x)> f = 
    [&](const Eigen::RowVector3d & x)->double
  {
    return 
      std::min(
      std::min(std::max(
      sphere(Eigen::RowVector3d(-0.2,0,-0.2),0.5,x),
      -sphere(Eigen::RowVector3d(+0.2,0,0.2),0.5,x)),
       sphere(Eigen::RowVector3d(-0.15,0,-0.15),0.3,x)
      ),
      std::max(
      std::max(
        sphere(Eigen::RowVector3d(-0.2,-0.5,-0.2),0.6,x),x(1)+0.45),-0.6-x(1))
      );
  };
  Eigen::RowVector3d p0(-0.2,0.5,-0.2);
  assert(abs(f(p0)) < 1e-10 && "p0 should be on zero level-set");

  // Simple finite difference gradients
  const auto & fd = [](
    const std::function<double(const Eigen::RowVector3d&)> & f,
    const Eigen::RowVector3d & x)
  {
    const double eps = 1e-10;
    Eigen::RowVector3d g;
    for(int c = 0;c<3;c++)
    {
      const Eigen::RowVector3d xp = x+eps*Eigen::RowVector3d(c==0,c==1,c==2);
      const double fp = f(xp);
      const Eigen::RowVector3d xn = x-eps*Eigen::RowVector3d(c==0,c==1,c==2);
      const double fn = f(xn);
      g(c) = (fp-fn)/(2*eps);
    }
    return g;
  };
  const auto & f_grad = [&fd,&f](const Eigen::RowVector3d & x)
  {
    return fd(f,x).normalized();
  };

  // Quads
  Eigen::MatrixXi Q;

  // Grid parameters
  const Eigen::RowVector3d min_corner(-2,-2,-2);
  const Eigen::RowVector3d max_corner(+2,+2,+2);
  const int s = 256;
  int nx = s+1;
  int ny = s+1;
  int nz = s+1;
  const Eigen::RowVector3d step =
    (max_corner-min_corner).array()/(Eigen::RowVector3d(nx,ny,nz).array()-1);
  // Sparse grid below assumes regular grid
  assert((step(0) == step(1))&&(step(0) == step(2)));

  // Dual contouring parameters
  bool constrained = false;
  bool triangles = false;
  bool root_finding = true;
  for(int pass = 0;pass<2;pass++)
  {
    const bool sparse = pass == 1;
    printf("Using %s grid..\n",sparse?"sparse":"dense");
    if(sparse)
    {
      // igl::sparse_voxel_grid assumes (0,0,0) lies on the grid. But dense igl::grid
      // below won't necessarily do that depending on nx,ny,nz.
      tictoc();
      Eigen::MatrixXd GV;
      Eigen::VectorXd Gf;
      Eigen::Matrix<int,Eigen::Dynamic,8> GI;
      igl::sparse_voxel_grid(p0,f,step(0),16.*pow(step(0),-2.),Gf,GV,GI);
      const auto t_Gf = tictoc();
      printf("  %5f secs to populate sparse grid of %ld cells\n",t_Gf+tictoc(),GI.rows());
      // Dual contouring requires list of sparse edges (not cells)
      // extract _all_ edges from sparse_voxel_grid (conservative)
      Eigen::Matrix<int,Eigen::Dynamic,2> GI2;
      {
        Eigen::Matrix<int,Eigen::Dynamic,2> all_GI2(GI.rows()*12,2);
        all_GI2 << 
          // front
          GI.col(0),GI.col(1),
          GI.col(1),GI.col(2),
          GI.col(2),GI.col(3),
          GI.col(3),GI.col(0),
          // back
          GI.col(4+0),GI.col(4+1),
          GI.col(4+1),GI.col(4+2),
          GI.col(4+2),GI.col(4+3),
          GI.col(4+3),GI.col(4+0),
          // sides
          GI.col(0),GI.col(4+0), 
          GI.col(1),GI.col(4+1), 
          GI.col(2),GI.col(4+2),
          GI.col(3),GI.col(4+3);
        Eigen::VectorXi _1,_2;
        igl::unique_simplices(all_GI2,GI2,_1,_2);
      }
      tictoc();
      Eigen::RowVector3d step =
        (max_corner-min_corner).array()/(Eigen::RowVector3d(nx,ny,nz).array()-1);
      igl::dual_contouring(
        f,f_grad,step,Gf,GV,GI2,constrained,triangles,root_finding,V,Q);
      printf("  %5f secs dual contouring\n",t_Gf+tictoc());
      tictoc();
      igl::marching_cubes(Gf,GV,GI,0.0,mcV,mcF);
      printf("  %5f secs marching cubes\n",t_Gf+tictoc());
    }else
    {

      tictoc();
      igl::dual_contouring(
        f,f_grad,min_corner,max_corner,nx,ny,nz,constrained,triangles,root_finding,V,Q);
      printf("  %5f secs dual contouring\n",tictoc());
      // build and sample grid
      tictoc();
      Eigen::MatrixXd GV;
      igl::grid(Eigen::RowVector3i(nx,ny,nz),GV);
      Eigen::VectorXd Gf(GV.rows());
      igl::parallel_for(GV.rows(),[&](const int i)
      {
        GV.row(i).array() *= (max_corner-min_corner).array();
        GV.row(i) += min_corner;
        Gf(i) = f(GV.row(i));
      },1000ul);
      const auto t_grid = tictoc();
      igl::marching_cubes(Gf,GV,nx,ny,nz,0,mcV,mcF);
      const auto t_mc = tictoc();
      printf("  %5f secs (%5f + %5f) marching cubes\n",t_grid+t_mc,t_grid,t_mc);
    }
  }

  // Crisp (as possible) rendering of resulting MC triangle mesh
  igl::per_corner_normals(mcV,mcF,20,mcN);
  // Crisp rendering of resulting DC quad mesh with edges
  Eigen::MatrixXd N;
  Eigen::VectorXi J;
  if(triangles)
  {
    VV = V;
    FF = Q;
    E.resize(Q.rows()*3,2);
    E<<
      Q.col(0), Q.col(1), 
      Q.col(1), Q.col(2), 
      Q.col(2), Q.col(0);
  }else
  {
    Eigen::VectorXi I,C;
    igl::polygon_corners(Q,I,C);
    E.resize(Q.rows()*4,2);
    E<<
      Q.col(0), Q.col(1), 
      Q.col(1), Q.col(2), 
      Q.col(2), Q.col(3), 
      Q.col(3), Q.col(0);
    igl::per_face_normals(V,I,C,N,VV,FF,J);
    NN = N(J,Eigen::all);
    igl::per_corner_normals(V,I,C,20,N,VV,FF,J,NN);
  }

}