Fast mesh-to-mesh intersection and mesh self intersection without CGAL (#2109)

* Added code for fast triangle-triangle intersection checking and function for fast detection of mesh self-intersections and mesh-to-mesh intersections withoug CGAL

* Fixed auto parameters in lambda helper function

* Replaced cbegin/cend with begin/end

* Fixed auto parameters in lambda helper function

* Added tests for igl::tri_tri_intersection_test_3d

* Added more tests, converted macros in Guigue2003_tri_tri_intersect.cpp to proper c++

* Renamed files and function names to follow IGL guidelines,
added reference to the original license for tri_tri_intersect

tutorial/724_FastFindIntersections/main.cpp

@@ -0,0 +1,98 @@
+#include <igl/readOFF.h>
+#include <igl/combine.h>
+
+#include <igl/opengl/glfw/Viewer.h>
+#include <igl/opengl/glfw/imgui/ImGuiMenu.h>
+
+#include <igl/fast_find_intersections.h>
+
+Eigen::MatrixXd V1,V2;
+Eigen::MatrixXi F1,F2;
+
+igl::AABB<Eigen::MatrixXd,3> tree;
+
+double min_z,max_z;
+double slice_z;
+
+
+void update_visualization(igl::opengl::glfw::Viewer & viewer)
+{
+  Eigen::MatrixXi I;
+  Eigen::MatrixXd edges;
+
+  //shifted intersection object
+  Eigen::MatrixXd V2_(V2.rows(),V2.cols());
+  V2_<< V2.col(0), V2.col(1), V2.col(2).array()+slice_z;
+
+  igl::fast_find_intersections(tree, V1,F1, V2_,F2, I,edges);
+  Eigen::MatrixXi edges_link=Eigen::MatrixXi::NullaryExpr(edges.rows()/2,2, [](int i,int j) { return i*2+j;});
+ 
+  // Plot the edges of the intersects
+  viewer.data().set_edges ( edges, edges_link, Eigen::RowVector3d(1,0,0));
+  
+  // show faces which are intersected
+  Eigen::VectorXd face_data=Eigen::VectorXd::Zero(F1.rows());
+
+  for(int i=0; i<I.rows(); ++i)
+    face_data(I(i,0)) = 1.0;
+  
+  viewer.data().set_data(face_data);
+}
+
+
+bool key_down(igl::opengl::glfw::Viewer& viewer, unsigned char key, int mod)
+{
+  switch(key)
+  {
+    default:
+      return false;
+    case '.':
+      slice_z = std::min(slice_z+0.01,max_z);
+      break;
+    case ',':
+      slice_z = std::max(slice_z-0.01,min_z);
+      break;
+  }
+  update_visualization(viewer);
+  return true;
+}
+
+
+int main(int argc, char *argv[])
+{
+  // Load two meshes 
+  igl::readOFF(TUTORIAL_SHARED_PATH "/cow.off",     V1, F1);
+  igl::readOFF(TUTORIAL_SHARED_PATH "/planexy.off", V2, F2);
+
+  // initialize AABB tree with first mesh (it doesn't move)
+  tree.init(V1,F1);
+
+  std::cout<<"Usage:"<<std::endl;
+  std::cout<<"'.'/','  push back/pull forward slicing plane."<<std::endl;
+  std::cout<<std::endl;
+
+  min_z=V1.col(2).minCoeff();
+  max_z=V1.col(2).maxCoeff();
+  slice_z=(max_z+min_z)/2;
+
+  //center slicing object
+  V2.col(2).array() -= V2.col(2).array().mean();
+
+  // Plot the mesh
+  igl::opengl::glfw::Viewer viewer;
+  viewer.data().set_mesh(V1, F1);
+  
+
+  update_visualization(viewer);
+
+  igl::opengl::glfw::imgui::ImGuiMenu menu;
+  //plugin.widgets.push_back(&menu);
+  menu.callback_draw_viewer_window = [](){};
+  viewer.callback_key_down = &key_down;
+
+  // show the cow closer
+  viewer.core().camera_zoom = 2.0;
+
+  // Launch the viewer
+  viewer.launch();
+}