isPointInPolygon (2D & 3D)

These functions determine whether a point lies inside or on the boundary of a polygon in 2D or 3D space.

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Function Signatures

2D Version

bool isPointInPolygon2D(
    const Eigen::MatrixX2d& polygonVertices,
    const Eigen::RowVector2d& point,
    bool checkBoundary = true,
    bool needClosePolygon = true
);

3D Version

bool isPointInPolygon3D(
    const Eigen::MatrixX3d& polygonVertices,
    const Eigen::RowVector3d& point,
    bool checkBoundary = true,
    bool needClosePolygon = true
);

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Parameters

Parameter	Type	Description
polygonVertices	Eigen::MatrixX2d / Eigen::MatrixX3d	Each row is a vertex. If needClosePolygon is true, the vertices may be unordered or open; the function will sort them counter-clockwise and append the first vertex to close the loop.
point	Eigen::RowVector2d / Eigen::RowVector3d	Point to test.
checkBoundary	bool (default = true)	true → points on edges/vertices count as inside; false → only strictly interior points count.
needClosePolygon	bool (default = true)	true → auto-order & close polygonVertices; false → assume vertices are already counter-clockwise and closed.

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Return Value

• true if the point lies inside or on the boundary (when checkBoundary=true).
• false if the point lies outside, or if the polygon is degenerate/invalid.

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Notes

• The polygon must be simple (no self-intersections) and planar.

• When needClosePolygon = true, the function will:

  1. Sort vertices counter-clockwise.
  2. Append the first vertex to the end to close the loop.

  Disable automatic closing (needClosePolygon = false) when reusing an already-processed polygon for better performance.

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Example Usage

#include "LiteGeometry.h"

int main() {
    // Unordered, unclosed 3D polygon vertices
    Eigen::Matrix<double,4,3> unorderedVertices;
    unorderedVertices << 748694.4250704022, 2564734.3476669602, 49.5,
        748674.4539194419, 2564739.5306861168, 81.5,
        748674.4154279609, 2564734.5007915981, 49.5,
        748694.4635618832, 2564739.3775614789, 81.5;

    Eigen::RowVector3d testPoint(748674.435, 2564737.016, 65.5);    

    // Test point located on one edge of the polygon
    bool isInsideWithEdge = isPointInPolygon3D(unorderedVertices, testPoint);

    // Strict: boundary does NOT count
    bool isInsideStrict = isPointInPolygon3D(unorderedVertices, testPoint, /*checkBoundary=*/false);


    std::cout << "Including boundary: " << insideWithEdge << "\n";
    std::cout << "Strict interior only: " << strictInside << "\n";

    return 0;
}

This example evaluates a point that lies on the polygon edge.

Left: with checkBoundary = true, the point is considered inside (true).

Right: with checkBoundary = false, the same point is considered outside (false).

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