isPointInPolyhedron

Determines whether a 3D point is located inside (or on the boundary of) a given polyhedron.

---

Function Signatures

bool isPointInPolyhedron(
    const Eigen::MatrixX3d& polyhedronVertices,
    const Eigen::RowVector3d& point,
    bool checkBoundary = true
);

---

Parameters

Parameter	Type	Description
polyhedronVertices	Eigen::MatrixX3d	A matrix of size N×3, each row representing a polyhedron vertex.
point	Eigen::RowVector3d	The 3D point to test for containment in the polyhedron.
checkBoundary	bool (default = true)	If true, points lying on the polyhedron’s boundary (faces or edges) are considered inside.

---

Return Value

• true if the point is inside the polyhedron, or on its boundary if checkBoundary is enabled.
• false if the point lies strictly outside the polyhedron.

---

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 testPoint1(20.785733063246152, 76.974749045767595, 55.56473456);
    Eigen::RowVector3d testPoint2(65.50742704979844, 77.06750108447973, 65.0984928161587);


    bool insideWithBoundary1 = isPointInPolyhedron(polyhedronVertices, testPoint1);
    bool insideStrict1   = isPointInPolyhedron(polyhedronVertices, testPoint1, false);

    bool insideWithBoundary2 = isPointInPolyhedron(polyhedronVertices, testPoint2);
    bool insideStrict2   = isPointInPolyhedron(polyhedronVertices, testPoint2, false);

    std::cout << "TestPoint1 (on face/edge):\n"
              << "  Including boundary: " << insideWithBoundary1 << "\n"
              << "  Strict only:       " << insideStrict1   << "\n\n";

    std::cout << "TestPoint2 (interior):\n"
              << "  Including boundary: " << insideWithBoundary2 << "\n"
              << "  Strict only:       " << insideStrict2   << "\n";

    return 0;
}

These examples demonstrate how the checkBoundary flag affects the classification of two test points:

• When checkBoundary = false (left image)，both points are considered outside the polyhedron
• When checkBoundary = true (right image)，both points are considered inside the polyhedron.

×