visibility.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
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 * Copyright(C) 2021-2025                                                    *
 * Visual Computing Lab                                                      *
 * ISTI - Italian National Research Council                                  *
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
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 ****************************************************************************/
 
#ifndef VCL_ALGORITHMS_CORE_VISIBILITY_H
#define VCL_ALGORITHMS_CORE_VISIBILITY_H
 
#include <vclib/concepts/space/plane.h>
#include <vclib/concepts/space/point.h>
#include <vclib/concepts/space/triangle.h>
#include <vclib/space/core/triangle_wrapper.h>
 
namespace vcl {
 
template<Triangle3Concept TriangleType, Point3Concept PointType>
auto halfSpaceDeterminant(const TriangleType& triangle, const PointType& point)
{
    return (triangle.point(1) - triangle.point(0))
        .cross(triangle.point(2) - triangle.point(0))
        .dot(point - triangle.point(0));
}
 
template<FaceConcept FaceType, Point3Concept PointType>
auto halfSpaceDeterminant(const FaceType& face, const PointType& point)
{
    // TODO: don't just check the first three vertices: first check if the face
    // is a triangle, then:
    // - if it is a triangle, keep the current implementation
    // - if it is a polygon, use its normal to compute the determinant
    return halfSpaceDeterminant(
        face.vertex(0)->coord(),
        face.vertex(1)->coord(),
        face.vertex(2)->coord(),
        point);
}
 
template<Point3Concept PointType>
auto halfSpaceDeterminant(
    const PointType& p1,
    const PointType& p2,
    const PointType& p3,
    const PointType& p)
{
    return halfSpaceDeterminant(TriangleWrapper(p1, p2, p3), p);
}
 
template<Point3Concept PointType>
bool arePointsCoplanar(
    const PointType& p1,
    const PointType& p2,
    const PointType& p3,
    const PointType& p4)
{
    return halfSpaceDeterminant(p1, p2, p3, p4) == 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& p1,
    const PointType& p2,
    const PointType& p3,
    const PointType& p)
{
    return halfSpaceDeterminant(p1, p2, p3, p) > 0;
}
 
template<FaceConcept FaceType, Point3Concept PointType>
bool facePointVisibility(const FaceType& face, const PointType& point)
{
    return halfSpaceDeterminant(face, point) > 0;
}
 
} // namespace vcl
 
#endif // VCL_ALGORITHMS_CORE_VISIBILITY_H