generateClosedPolygon

Generates a closed polygon from an unordered set of 2D points or coplanar 3D points.

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Function Signature

Eigen::MatrixXd generateClosedPolygon(
    const Eigen::MatrixXd& polygonVertices
);

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Parameters

• polygonVertices: An Eigen::MatrixXd of size N×2 (for 2D) or N×3 (for coplanar 3D), representing the unordered vertices of the polygon.

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Return Value

• An Eigen::MatrixXd containing the input vertices reordered in counter-clockwise sequence, with the first vertex repeated at the end to close the loop.

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Example Usage

1. Define Unordered Points

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;

If you connect these points in their given order, you obtain an open, zig-zag path rather than a closed polygon.

×

2. Executing the Function

Call the function to compute the centroid, sort the points, and close the polygon:

Eigen::MatrixX3d polygon = generateClosedPolygon(unorderedVertices);

After the call, polygon contains the vertices in counter-clockwise order, with the first point repeated at the end to form a closed loop:

×

Complete Implementation

#include "LiteGeometry.h"

int main() {

    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::MatrixX3d polygon = generateClosedPolygon(unorderedVertices);
    std::cout << "[Input] Original unordered vertices (n x 3):\n";
    std::cout << unorderedVertices.format(Eigen::FullPrecision) << "\n\n";

    std::cout << "[Output] Generated closed polygon (n x 3):\n";
    std::cout << polygon.format(Eigen::FullPrecision) << "\n";

    return 0;
}