computeLinesDistance

Computes the closest points and shortest distance between two 3D line primitives (segments, rays, or infinite lines).

Overview

Supports Segment3D, Ray3D, and Line3D. Each type must expose P1 and P2 members of type Eigen::RowVector3d, representing its endpoints.

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Function Signatures

template<typename LineT>
std::tuple<Eigen::RowVector3d, Eigen::RowVector3d, double> computeLinesDistance(
    const LineT& geoAB, const LineT& geoCD)；

Parameters

• geoAB (LineT): The first 3D line primitive (e.g., Segment3D, Ray3D, Line3D). Must provide members P1 and P2 of type Eigen::RowVector3d.

• geoCD (LineT): The second 3D line primitive, with the same requirements as geoAB.

Return Value

A std::tuple containing:

1. Closest point on geoAB (Eigen::RowVector3d).
2. Closest point on geoCD (Eigen::RowVector3d).
3. Shortest distance between the two line primitives (double).

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Example Usage

#include "LiteGeometry.h"

int main() {
    {
        Eigen::RowVector3d A(1, 1, 0);
        Eigen::RowVector3d B(0, -1, 0.4);
        Eigen::RowVector3d C(1, -1, 0);
        Eigen::RowVector3d D(0, 0, 0.5);
        Segment3D AB{ A ,B };
        Segment3D CD{ C ,D };
        const auto& [closestP1, closestP2, dist] = computeLinesDistance(AB, CD);
        std::cout << "Closest Point on Segment AB: " << closestP1.format(Eigen::FullPrecision) << "\n";
        std::cout << "Closest Point on Segment CD: " << closestP2.format(Eigen::FullPrecision) << "\n";
        std::cout << "Distance: " << dist << "\n";
    }

    {
        Eigen::RowVector3d A(1, 1, 0);
        Eigen::RowVector3d B(0, 0.5, 0.55);
        Eigen::RowVector3d C(1, -1, 0);
        Eigen::RowVector3d D(0, 0, 0.45);
        Ray3D AB{ A ,B };
        Ray3D CD{ C ,D };
        std::tuple<Eigen::RowVector3d, Eigen::RowVector3d, double> Intersection;
        const auto& [closestP1, closestP2, dist] = computeLinesDistance(AB, CD);
        std::cout << "Closest Point on Ray AB: " << closestP1.format(Eigen::FullPrecision) << "\n";
        std::cout << "Closest Point on Ray CD: " << closestP2.format(Eigen::FullPrecision) << "\n";
        std::cout << "Distance: " << dist << "\n";
    }

    return 0;
}

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