Sparse Voxel Grid (#937)

* Add a utility function which computes a sparse set of epsilon-sized grid cells surrounding an input surface. The function takes a point on the surface as input and finds all those epsilon grid cells that intersect the surface using a breadth first search over the grid space.

* Add a utility function which computes a sparse set of epsilon-sized grid cells surrounding an input surface. The function takes a point on the surface as input and finds all those epsilon grid cells that intersect the surface using a breadth first search over the grid space.

tutorial/715_MeshImplicitFunction/main.cpp

@@ -0,0 +1,50 @@
+#include <igl/copyleft/marching_cubes.h>
+#include <igl/sparse_voxel_grid.h>
+#include <igl/opengl/glfw/Viewer.h>
+
+#include <Eigen/Core>
+#include <iostream>
+
+#include "tutorial_shared_path.h"
+
+int main(int argc, char * argv[])
+{
+  // An implicit function which is zero on the surface of a sphere centered at the origin with radius 1
+  // This function is negative inside the surface and positive outside the surface
+  std::function<double(const Eigen::RowVector3d&)> scalar_func = [](const Eigen::RowVector3d& pt) -> double {
+    return pt.norm() - 1.0;
+  };
+
+  // We know that the point (0, 0, 1) lies on the implicit surface
+  Eigen::RowVector3d p0(0., 0., 1.);
+
+  // Construct a sparse voxel grid whose cubes have edge length eps = 0.1.
+  // The cubes will form a thin shell around the implicit surface
+  const double eps = 0.1;
+
+  // CS will hold one scalar value at each cube vertex corresponding
+  // the value of the implicit at that vertex
+  Eigen::VectorXd CS;
+
+  // CV will hold the positions of the corners of the sparse voxel grid
+  Eigen::MatrixXd CV;
+
+  // CI is a #cubes x 8 matrix of indices where each row contains the
+  // indices into CV of the 8 corners of a cube
+  Eigen::MatrixXi CI;
+
+  // Construct the voxel grid, populating CS, CV, and CI
+  igl::sparse_voxel_grid(p0, scalar_func, eps, CS, CV, CI);
+
+  // Given the sparse voxel grid, use Marching Cubes to construct a triangle mesh of the surface
+  Eigen::MatrixXi F;
+  Eigen::MatrixXd V;
+  igl::copyleft::marching_cubes(CS, CV, CI, V, F);
+
+  // Draw the meshed implicit surface
+  igl::opengl::glfw::Viewer viewer;
+  viewer.data().clear();
+  viewer.data().set_mesh(V,F);
+  viewer.data().set_face_based(true);
+  viewer.launch();
+}