isLinePolyhedronIntersection

Determine whether a 3D line primitive (segment, ray, or infinite line) intersects a polyhedron.

---

Function Signatures

// Test intersection and collect all intersection points.
template<typename LineT>
bool isLinePolyhedronIntersection(
    const Eigen::MatrixX3d& polyhedronVertices,
    const LineT& geoAB,
    std::vector<Eigen::RowVector3d>& intersections
)

// Overload without computing intersection coordinates.
template<typename LineT>
bool isLinePolyhedronIntersection(
    const Eigen::MatrixX3d& polyhedronVertices,
    const LineT& geoAB
)

---

Parameters

• polyhedronVertices (Eigen::MatrixX3d): Matrix of size N×3; each row represents a vertex of the polyhedron. Vertices may be unordered or unclosed.
• geoAB (LineT): The 3D line primitive (e.g., Segment3D, Ray3D, Line3D) to check for intersection with the polyhedron.
• intersections (std::vector<Eigen::RowVector3d>&): If provided, receives all computed intersection points..

---

Return Value

• true if there is at least one intersection; otherwise returns false.

---

Example Usage

#include "LiteGeometry.h"

int main() {

    Eigen::Matrix<double, 8, 3> polyhedronVertices;
    polyhedronVertices << 748674.4539194419, 2564739.5306861168, 49,
           748694.4635618832, 2564739.3775614789, 49,
           748694.42507040221, 2564734.3476669602, 49,
           748674.41542796092, 2564734.5007915981, 49,
           748674.4539194419, 2564739.5306861168, 81,
           748694.4635618832, 2564739.3775614789, 81,
           748694.42507040221, 2564734.3476669602, 81,
           748674.41542796092, 2564734.5007915981, 81;
    {
        Eigen::RowVector3d A(748674.6211, 2564712.4947, 64.5593);
        Eigen::RowVector3d B(748708.8839, 2564753.8769, 59.6075);
        Segment3D AB{ A ,B };
        std::vector<Eigen::RowVector3d> intersections;
        bool isIntersection = isLinePolyhedronIntersection(testPolyhedron, AB, intersections);
        std::cout << "\n-- Segment AB Intersection with Polyhedron --\n";
        if (isIntersection) {
            std::cout << "Intersection Points:\n";
            for (const auto& point : intersections) {
                std::cout << point.format(Eigen::FullPrecision) << "\n";
            }
        }
    }
    std::cout << "\n--------------------------------\n";
    {
        Eigen::RowVector3d A(748674.6211, 2564712.4947, 64.5593);
        Eigen::RowVector3d B(748680.9715683657, 2564720.1647197301, 63.641504336681471);
        Ray3D AB{ A, B };
        std::vector<Eigen::RowVector3d> intersections;
        std::cout << "\n-- Ray AB Intersection with Polyhedron --\n";
        bool isIntersection = isLinePolyhedronIntersection(testPolyhedron, AB, intersections);
        if (isIntersection) {
            std::cout << "Intersection Points:\n";
            for (const auto& point : intersections) {
                std::cout << point.format(Eigen::FullPrecision) << "\n";
            }
        }
    }

    return 0;
}

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