overlaps_box_sphere.h

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

#ifndef PASTELGEOMETRY_OVERLAPBOXSPHERE_H
#define PASTELGEOMETRY_OVERLAPBOXSPHERE_H

#include "pastel/geometry/shape/box.h"
#include "pastel/geometry/shape/sphere.h"
#include "pastel/geometry/overlap/overlaps_alignedbox_sphere.h"

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

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

namespace Pastel
{

    //! Tests if an box and a sphere overlap.
    template <typename Real, int N>
    bool overlaps(
        const Box<Real, N>& box,
        const Sphere<Real, N>& sphere)
    {
        // FIX: This can be made faster by
        // using projected distances.

        // The coordinates are transformed such that
        // the box becomes an origin centered aligned box.
        // Then the test for aligned box-sphere overlap
        // is used.

        // Transpose of an orthogonal matrix
        // is its inverse..

        Matrix<Real, N, N> boxRotationInverse(
            transpose(box.rotation()));

        // The radius is not affected by a
        // rotation.

        Sphere<Real, N> transformedSphere(
            (sphere.position() - box.position()) *
            boxRotationInverse,
            sphere.radius());

        AlignedBox<Real, N> transformedBox(
            Vector<Real, N>(-box.width()),
            Vector<Real, N>(box.width()));

        return overlaps(transformedBox,
            transformedSphere);
    }

}

#endif