overlaps_box_box.h

// Description: Overlap tests between two boxes

#ifndef PASTELGEOMETRY_OVERLAPS_BOX_BOX_H
#define PASTELGEOMETRY_OVERLAPS_BOX_BOX_H

#include "pastel/geometry/shape/box.h"
#include "pastel/geometry/overlap/overlaps_alignedbox_box.h"
#include "pastel/geometry/shape/alignedbox.h"
#include "pastel/geometry/shape/box.h"

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

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

namespace Pastel
{

    //! Tests if two box's overlap.
    template <typename Real, int N>
    bool overlaps(
        const Box<Real, N>& aBox,
        const Box<Real, N>& bBox)
    {
        // Transform boxes such that the
        // aBox becomes an aligned box. Then
        // run the aligned box-box test.

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

        Matrix<Real, N, N> aRotationInverse(
            transpose(aBox.rotation()));

        Box<Real, N> bBoxTransformed(
            (bBox.position() - aBox.position()) *
            aRotationInverse,
            bBox.width(),
            bBox.rotation() * aRotationInverse);

        AlignedBox<Real, N> aBoxTransformed(
            Vector<Real, N>(-aBox.width()),
            Vector<Real, N>(aBox.width()));

        return overlaps(
            aBoxTransformed,
            bBoxTransformed);
    }

    template <typename Real, int N>
    bool overlaps(
        const Box<Real, N>& aBox,
        const Box<Real, N>& bBox,
        const Vector<Real, N>& bVelocity,
        Tuple<Real, 2>& intersectionRange)
    {
        // Transform boxes such that the
        // aBox becomes an aligned box. Then
        // run the aligned box-box test.

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

        Matrix<Real, N, N> aRotationInverse(
            transpose(aBox.rotation()));

        Box<Real, N> bBoxTransformed(
            (bBox.position() - aBox.position()) *
            aRotationInverse,
            bBox.width(),
            bBox.rotation() * aRotationInverse);

        AlignedBox<Real, N> aBoxTransformed(
            Vector<Real, N>(-aBox.width()),
            Vector<Real, N>(aBox.width()));

        return overlaps(
            aBoxTransformed,
            bBoxTransformed,

            bVelocity * aRotationInverse,
            intersectionRange);
    }

    //! Tests if two box's overlap and returns the projection vector.
    /*!
   projection (out):
   If the boxes intersect,
   the shortest vector by which
   the bBox must be translated for the boxes
   to become separated.

   commonPoint (out):
   If the boxes intersect, a point in the
   intersection
   */
    template <typename Real, int N>
    bool overlaps(
        const Box<Real, N>& aBox,
        const Box<Real, N>& bBox,
        Vector<Real, N>& projection,
        Vector<Real, N>& commonPoint)
    {
        // Transform boxes such that the
        // aBox becomes an aligned box. Then
        // run the aligned box-box test.

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

        Matrix<Real, N, N> aRotationInverse(
            transpose(aBox.rotation()));

        Box<Real, N> bBoxTransformed(
            (bBox.position() - aBox.position()) *
            aRotationInverse,
            bBox.width(),
            bBox.rotation() * aRotationInverse);

        AlignedBox<Real, N> aBoxTransformed(
            Vector<Real, N>(-aBox.width()),
            Vector<Real, N>(aBox.width()));

        Vector<Real, N> transformedProjection;
        Vector<Real, N> transformedCommonPoint;
        if (overlaps(
            aBoxTransformed,
            bBoxTransformed,
            transformedProjection,
            transformedCommonPoint))
        {
            projection =
                transformedProjection * aBox.rotation();
            commonPoint =
                transformedCommonPoint * aBox.rotation() + aBox.position();

            return true;
        }

        return false;
    }

}

#endif