[geometry] Enhance Half_plane object based interface. openMVG#517

- Add a Box construction in order to build Rectangular parallelepiped
- Add viewing debugging functions to export as PLY the Bounding Box & Frustum (Infinite or truncated)

- Add a contains function to test if a point is inside the volume build by the HalfPlanes
  - Add it's corresponding unit test

src/openMVG/geometry/box.hpp

@@ -8,6 +8,7 @@
 #define OPENMVG_GEOMETRY_BOX_HPP_
 
 #include "openMVG/geometry/half_space_intersection.hpp"
+#include <fstream>
 
 namespace openMVG
 {
@@ -29,7 +30,8 @@ struct Box : public HalfPlaneObject
 {
   /// Points that define the bounding box
   Vec3 points[8];
-
+
+  /// Define a Square bounding box from a center position and radius (center to corner distance)
   Box
   (
     const Vec3 & center,
@@ -41,25 +43,111 @@ struct Box : public HalfPlaneObject
     {
       // Top face
       (R * Vec3(-1,-1,1).normalized()) * radius + center,
-      (R * Vec3(-1,1,1).normalized())  * radius + center,
-      (R * Vec3(1,1,1).normalized())   * radius + center,
-      (R * Vec3(1,-1,1).normalized())  * radius + center,
+      (R * Vec3(-1, 1,1).normalized()) * radius + center,
+      (R * Vec3( 1, 1,1).normalized()) * radius + center,
+      (R * Vec3( 1,-1,1).normalized()) * radius + center,
       // Bottom face
       (R * Vec3(-1,-1,-1).normalized()) * radius + center,
-      (R * Vec3(-1,1,-1).normalized())  * radius + center,
-      (R * Vec3(1,1,-1).normalized())   * radius + center,
-      (R * Vec3(1,-1,-1).normalized())  * radius + center
+      (R * Vec3(-1, 1,-1).normalized()) * radius + center,
+      (R * Vec3( 1, 1,-1).normalized()) * radius + center,
+      (R * Vec3( 1,-1,-1).normalized()) * radius + center
     };
     std::copy(directions, directions + 8, points);
-
-    // Defines the 6 half_planes that defines the supporting volume
-    planes.push_back( Half_plane_p( directions[0], directions[1], directions[3] ) ); // Top
-    planes.push_back( Half_plane_p( directions[4], directions[7], directions[5] ) ); // Bottom
+
+    // Defines the supporting volume thanks to 6 half_planes
+    planes.push_back( Half_plane_p( points[0], points[1], points[3] ) ); // Top
+    planes.push_back( Half_plane_p( points[4], points[7], points[5] ) ); // Bottom
+    // Define remaining supporting planes (box borders)
+    planes.push_back( Half_plane_p( points[0], points[4], points[1] ) );
+    planes.push_back( Half_plane_p( points[0], points[3], points[4] ) );
+    planes.push_back( Half_plane_p( points[3], points[2], points[7] ) );
+    planes.push_back( Half_plane_p( points[1], points[5], points[2] ) );
+  }
+
+  /// Define a Rectangular parallelepiped bounding box from min/max axis aligned positions
+  Box
+  (
+    const double x_min,
+    const double y_min,
+    const double z_min,
+    const double x_max,
+    const double y_max,
+    const double z_max
+  )
+  {
+    const Vec3 points_[8] =
+    {
+      // Top face
+      Vec3(x_min, y_min, z_max),
+      Vec3(x_min, y_max, z_max),
+      Vec3(x_max, y_max, z_max),
+      Vec3(x_max, y_min, z_max),
+      // Bottom face
+      Vec3(x_min, y_min, z_min),
+      Vec3(x_min, y_max, z_min),
+      Vec3(x_max, y_max, z_min),
+      Vec3(x_max, y_min, z_min),
+    };
+    std::copy(points_, points_ + 8, points);
+
+    // Defines the supporting volume thanks to 6 half_planes
+    planes.push_back( Half_plane_p( points[0], points[1], points[3] ) ); // Top
+    planes.push_back( Half_plane_p( points[4], points[7], points[5] ) ); // Bottom
     // Define remaining supporting planes (box borders)
-    planes.push_back( Half_plane_p( directions[0], directions[4], directions[1] ) );
-    planes.push_back( Half_plane_p( directions[0], directions[3], directions[4] ) );
-    planes.push_back( Half_plane_p( directions[3], directions[2], directions[7] ) );
-    planes.push_back( Half_plane_p( directions[1], directions[5], directions[2] ) );
+    planes.push_back( Half_plane_p( points[0], points[4], points[1] ) );
+    planes.push_back( Half_plane_p( points[0], points[3], points[4] ) );
+    planes.push_back( Half_plane_p( points[3], points[2], points[7] ) );
+    planes.push_back( Half_plane_p( points[1], points[5], points[2] ) );
+  }
+
+  /**
+  * @brief Export the Box as a PLY file
+  * @return true if the file can be saved on disk
+  */
+  static bool export_Ply
+  (
+    const Box & box,
+    const std::string & filename,
+    const Vec3 color = Vec3(0, 255, 0)
+  )
+  {
+    std::ofstream of(filename.c_str());
+    if (!of.is_open())
+      return false;
+
+    of << "ply" << '\n'
+      << "format ascii 1.0" << '\n'
+      << "element vertex 8\n"
+      << "property float x" << '\n'
+      << "property float y" << '\n'
+      << "property float z" << '\n'
+      << "property uchar red" << '\n'
+      << "property uchar green" << '\n'
+      << "property uchar blue" << '\n'
+      << "element face 6 \n"
+      << "property list uchar int vertex_index" << '\n'
+      << "end_header" << '\n';
+
+    // Export box points
+    {
+      for (int i = 0; i < 8; ++i)
+        of << box.points[i].transpose() << " " << color.cast<int>() << '\n';
+    }
+
+    of
+      // top & bottom planes
+      << "3 0 1 3\n"
+      << "3 4 7 5\n"
+      // remaining planes
+      << "3 0 4 1\n"
+      << "3 0 3 4\n"
+      << "3 3 2 7\n"
+      << "3 1 5 2\n";
+
+    of.flush();
+    const bool bOk = of.good();
+    of.close();
+    return bOk;
   }
 };