overlaps_plane_box.h

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

#ifndef PASTELGEOMETRY_OVERLAPS_PLANE_BOX_H
#define PASTELGEOMETRY_OVERLAPS_PLANE_BOX_H

#include "pastel/geometry/shape/plane.h"
#include "pastel/geometry/shape/box.h"
#include "pastel/geometry/distance/distance_plane_point.h"

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

#include "pastel/math/matrix/matrix.h"

namespace Pastel
{

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

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

   Returns:
   Whether the plane and the box overlap.
   */
    template <typename Real, int N>
    bool overlaps(
        const Plane<Real, N>& plane,
        const Box<Real, N>& box)
    {
        ENSURE_OP(plane.n(), ==, box.n());

        integer n = plane.n();

        // FIX: The topology of the box is not
        // handled correctly. The box is assumed
        // closed.

        // A plane and a box intersect if
        // the projection of the box onto the
        // plane normal intersects the projection
        // of the plane.

        // Find the radius of the projection
        // of the box.
        Real d = 0;
        for (integer i = 0;i < n;++i)
        {
            d += abs(dot(box.rotation()[i], plane.normal()));
        }

        // Calculate the distance of the center
        // point and the plane.
        Real planeDistance2 = 
            distance2(plane, box.position());

        // If the distance of the center to the
        // plane is less than or equal to the box's
        // projected radius, then we have an 
        // intersection.

        return (planeDistance2 <= square(d));
    }

    //! Tests if a plane and an box overlap.
    /*!
   boxOnPositiveSide:
   Set true, if the center point of the box
   is on the positive side of the plane.
   Otherwise set to false.

   Returns:
   overlaps(plane, box)
   */
    template <typename Real, int N>
    bool overlaps(
        const Plane<Real, N>& plane,
        const Box<Real, N>& box,
        bool &boxOnPositiveSide)
    {
        ENSURE_OP(plane.n(), ==, box.n());

        // Check if the box's center point
        // is on the positive side of the plane.

        boxOnPositiveSide = dot(plane.normal(),
            box.position() - plane.position()) > 0;

        return Pastel::overlaps(plane, box);
    }

}

#endif