overlaps_alignedbox_plane.h

// Description: Overlap tests between an aligned box and a plane

#ifndef PASTELGEOMETRY_OVERLAPS_ALIGNEDBOX_PLANE_H
#define PASTELGEOMETRY_OVERLAPS_ALIGNEDBOX_PLANE_H

#include "pastel/sys/mytypes.h"
#include "pastel/sys/vector.h"

#include "pastel/geometry/shape/alignedbox.h"
#include "pastel/geometry/shape/plane.h"

namespace Pastel
{

    //! Tests if an aligned box and a plane overlap.
    /*!
   Preconditions:
   alignedBox.n() == plane.n()

   Returns:
   Whether the box and the plane overlap.

   Time complexity:
   O(n), where n is dimension.

   Note: Currently the box is assumed closed.
   */
    template <typename Real, int N>
    bool overlaps(
        const AlignedBox<Real, N>& alignedBox,
        const Plane<Real, N>& plane)
    {
        PENSURE_OP(alignedBox.n(), ==, plane.n());

        integer n = alignedBox.n();

        // Find maximal and minimal signed distances
        // of the vertices in V along the normal vector
        // of the plane.

        // FIX: Box topologies are not handled correctly.
        // The box is now treated as closed. I do
        // not see how this could be handled.

        Real minDistance = 
            dot(alignedBox.min() - plane.position(), plane.normal());
        Real maxDistance = 
            minDistance;
        for (integer i = 0;i < n;++i)
        {
            Real deltaAxisDistance =
                alignedBox.extent(i) * plane.normal()[i];
            if (deltaAxisDistance < 0)
            {
                minDistance += deltaAxisDistance;
            }
            else
            {
                maxDistance += deltaAxisDistance;
            }
        }

        return (minDistance <= 0 && maxDistance >= 0);
    }

}

#endif