visibility.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
 *                                                                           *
 * Copyright(C) 2021-2025                                                    *
 * Visual Computing Lab                                                      *
 * ISTI - Italian National Research Council                                  *
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of            *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
 * (https://www.mozilla.org/en-US/MPL/2.0/) for more details.                *
 ****************************************************************************/
 
#ifndef VCL_ALGORITHMS_CORE_VISIBILITY_H
#define VCL_ALGORITHMS_CORE_VISIBILITY_H
 
#include <vclib/space/core.h>
 
namespace vcl {
 
template<Point3Concept PointType>
auto halfSpaceDeterminant(
    const PointType& p0,
    const PointType& p1,
    const PointType& p2,
    const PointType& p)
{
    return (p1 - p0).cross(p2 - p0).dot(p - p0);
}
 
template<Triangle3Concept TriangleType, Point3Concept PointType>
auto halfSpaceDeterminant(const TriangleType& triangle, const PointType& point)
{
    return halfSpaceDeterminant(
        triangle.point(0), triangle.point(1), triangle.point(2), point);
}
 
template<Point3Concept PointType>
bool arePointsCollinear(
    const PointType& p0,
    const PointType& p1,
    const PointType& p2)
{
    PointType c = (p1 - p0).cross(p2 - p0);
    return c.squaredNorm() == 0;
}
 
template<Point3Concept PointType>
bool arePointsCoplanar(
    const PointType& p0,
    const PointType& p1,
    const PointType& p2,
    const PointType& p3)
{
    return halfSpaceDeterminant(p0, p1, p2, p3) == 0;
}
 
template<Triangle3Concept TriangleType, Point3Concept PointType>
bool trianglePointVisibility(
    const TriangleType& triangle,
    const PointType&    point)
{
    return halfSpaceDeterminant(triangle, point) > 0;
}
 
template<Point3Concept PointType>
auto trianglePointVisibility(
    const PointType& p0,
    const PointType& p1,
    const PointType& p2,
    const PointType& p)
{
    return halfSpaceDeterminant(p0, p1, p2, p) > 0;
}
 
} // namespace vcl
 
#endif // VCL_ALGORITHMS_CORE_VISIBILITY_H