add hausdorff lower bound

include/hausdorff_lower_bound.h

@@ -1,6 +1,9 @@
 #ifndef HAUSDORFF_LOWER_BOUND_H
 #define HAUSDORFF_LOWER_BOUND_H
 #include <Eigen/Core>
+#include <point_mesh_distance.h>
+#include <random_points_on_mesh.h>
+
 // Compute a lower bound on the _directed_ Hausdorff distance from a given mesh
 // (VX,FX) to another mesh (VY,FY).
 //

src/hausdorff_lower_bound.cpp

@@ -7,6 +7,11 @@ double hausdorff_lower_bound(
   const Eigen::MatrixXi & FY,
   const int n)
 {
-  // Replace with your code
-  return 0;
-}
+  Eigen::MatrixXd pointsX, P, N;
+  Eigen::VectorXd D;
+
+  random_points_on_mesh(n, VX, FX, pointsX);
+  point_mesh_distance(pointsX, VY, FY, D, P, N);
+
+  return D.maxCoeff();
+}

src/point_mesh_distance.cpp

@@ -1,5 +1,5 @@
 #include "point_mesh_distance.h"
-#include <iostream>
+// #include <iostream>
 
 void point_mesh_distance(
   const Eigen::MatrixXd & X,