isCoplanar

Checks whether a set of 3D points lies on the same plane.

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Function Signatures

bool isCoplanar(const Eigen::MatrixX3d& points);

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Parameters

• points: Matrix of 3D points (Eigen::MatrixX3d, one point per row).

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Return Value

• true if all points are coplanar; otherwise, false.

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Example Usage

#include "LiteGeometry.h"

int main() {
    Eigen::Matrix<double, 5, 3> points1;
    points1 << 
        0.0,   0.0,   0.5,
        0.0,   1.0,   0.5,
        1.0,   1.0,   0.5,
        1.0,   0.0,   0.5,
        0.5,   0.5,   1.0;

    bool isCoplanar1  = isCoplanar(points1);
    std::cout << "Test Case 1 (points1): ";
    if (isCoplanar1) {
        std::cout << "coplanar" << std::endl;
    } else {
        std::cout << "not coplanar" << std::endl;
    }

    Eigen::Matrix<double, 5, 3> points2;
    points2 << 
        0.0,   0.0,   0.5,
        0.0,   1.0,   0.5,
        1.0,   1.0,   0.5,
        1.0,   0.0,   0.5,
        0.5,   0.5,   0.5;

    bool isCoplanar2 = isCoplanar(points2);
    std::cout << "Test Case 2 (points2): ";
    if (isCoplanar2) {
        std::cout << "coplanar" << std::endl;
    } else {
        std::cout << "not coplanar" << std::endl;
    }

    return 0;
}

The following illustration shows the two test cases:

• left: a non-coplanar set of points
• right: a coplanar configuration.

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