intersect_triangle_triangle.hpp

#ifndef PASTELGEOMETRY_INTERSECT_TRIANGLE_TRIANGLE_HPP
#define PASTELGEOMETRY_INTERSECT_TRIANGLE_TRIANGLE_HPP

#include "pastel/geometry/intersect/intersect_triangle_triangle.h"
#include "pastel/geometry/shape/segment.h"
#include "pastel/geometry/shape/plane.h"
#include "pastel/geometry/shape/flat.h"
#include "pastel/geometry/overlap/overlaps_plane_triangle.h"
#include "pastel/geometry/intersect/intersect_flat_plane.h"
#include "pastel/geometry/intersect/intersect_alignedbox_alignedbox.h"
#include "pastel/geometry/shape/linear_projection.h"

#include "pastel/sys/ensure.h"
#include "pastel/sys/vector/vector_tools.h"

#include "pastel/sys/math/minmax.h"

namespace Pastel
{

    template <typename Real>
    bool intersect(
        const PASTEL_TRIANGLE(Real, 3)& aTriangle,
        const PASTEL_TRIANGLE(Real, 3)& bTriangle,
        Line<Real, 3>& intersectionLine,
        AlignedBox<Real, 1>& intersectionRange)
    {
        Plane<Real, 3> aPlane(
            aTriangle[0],
            cross(aTriangle[1] - aTriangle[0],
            aTriangle[2] - aTriangle[0]));

        if (!overlaps(aPlane, bTriangle))
        {
            return false;
        }

        Plane<Real, 3> bPlane(
            bTriangle[0],
            cross(bTriangle[1] - bTriangle[0],
            bTriangle[2] - bTriangle[0]));

        if (!overlaps(bPlane, aTriangle))
        {
            return false;
        }

        Flat<Real, 3, 2> aFlat;
        aFlat.setPosition(aTriangle[0]);
        aFlat[0] = aTriangle[1] - aTriangle[0];
        aFlat[1] = aTriangle[2] - aTriangle[0];

        // Since we already tested that the triangles
        // intersect each others planes, there
        // should be an intersection between the
        // planes.

        Line<Real, 3> line;
        bool intersected =
            Pastel::intersect(aFlat, bPlane, line);
        ASSERT(intersected);

        // Project the vertices on the intersection line.
        // See what their parametric position
        // is on that line..

        AlignedBox<Real, 1> aInterval = 
            projectAxis(aTriangle, line.direction());
        AlignedBox<Real, 1> bInterval = 
            projectAxis(bTriangle, line.direction());

        // If the parameter ranges intersect
        // then the triangles also intersect,
        // otherwise they don't.

        AlignedBox<Real, 1> sharedInterval;
        if (!intersect(aInterval, bInterval, sharedInterval))
        {
            return false;
        }

        intersectionLine = line;
        intersectionRange = sharedInterval - 
            Vector<Real, 1>(dot(line.position(), line.direction()));

        return true;
    }

}

#endif