overlaps_segment_segment.hpp

#ifndef PASTELGEOMETRY_OVERLAPS_SEGMENT_SEGMENT_HPP
#define PASTELGEOMETRY_OVERLAPS_SEGMENT_SEGMENT_HPP

#include "pastel/geometry/overlap/overlaps_segment_segment.h"
#include "pastel/geometry/predicates.h"
#include "pastel/geometry/shape/segment.h"

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

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

namespace Pastel
{

    template <typename Real>
    bool overlaps(
        const Segment<Real, 1>& aSegment,
        const Segment<Real, 1>& bSegment)
    {
        Real aMin(0);
        Real aMax(0);

        minMax(aSegment.start()[0], aSegment.end()[0],
            aMin, aMax);

        if ((aMin <= bSegment.start()[0] &&
            bSegment.start()[0] <= aMax) ||
            (aMin <= bSegment.end()[0] &&
            bSegment.end()[0] <= aMax))
        {
            return true;
        }

        return false;
    }

    template <typename Real>
    bool overlaps(
        const Segment<Real, 2>& aSegment,
        const Segment<Real, 2>& bSegment)
    {
        // The segments intersect if and only if
        // 1) The endpoints of segment A are
        // on the different sides of the line B.
        // and
        // 2) The endpoints of segment B are
        // on the different sides of the line A.

        // Note: endpoint exactly on the line
        // is not considered an intersection.

        Plane<Real, 2> aPlane(
            aSegment.start(),
            cross(aSegment.end() - aSegment.start()));

        Plane<Real, 2> bPlane(
            bSegment.start(),
            cross(bSegment.end() - bSegment.start()));

        bool aCondition =
            (side(aSegment.start(), bPlane) *
            side(aSegment.end(), bPlane) < 0);

        bool bCondition =
            (side(bSegment.start(), aPlane) *
            side(bSegment.end(), aPlane) < 0);

        return aCondition && bCondition;
    }

}

#endif