isPointOnLine (2D & 3D)

Determine whether a query point lies on a specified line primitive in 2D or 3D space.

Supported types include:

• 2D: Segment2D, Ray2D, or Line2D
• 3D: Segment3D, Ray3D, or Line3D

Overview

A query point P is considered on the primitive AB when both conditions hold:

Criterion	Meaning
Collinearity	P, A, and B are collinear (within numerical tolerance).
Parametric bounds	P falls within the parameter range that defines the primitive:   • Segment – between (or at) the endpoints.   • Ray – on or beyond the origin, in the ray’s direction.   • Line – unbounded; any collinear point qualifies.

---

2D Version

Function Signatures

template<typename LineT>
bool isPointOnLine2D(
    const LineT& geoAB,
    const Eigen::RowVector2d& point
);

Parameters

• geoAB (LineT): 2D line primitive (Segment2D, Ray2D, Line2D).
• point (Eigen::RowVector2d): The point to be tested.

Return Value

• true: point satisfies both Collinearity and Parametric bounds.

• false: Otherwise.

---

3D Version

Function Signatures

template<typename LineT>
bool isPointOnLine3D(
    const LineT& geoAB,
    const Eigen::RowVector3d& point
);

Parameters

• geoAB (LineT): 3D line primitive (Segment3D, Ray3D, Line3D).
• point (Eigen::RowVector3d): The point to be tested.

Return Value

Same as the 2D version.

---

Example Usage

#include "LiteGeometry.h"
int main() {

    Eigen::RowVector3d A(0, 0, 0);
    Eigen::RowVector3d B(1, 1, 1);
    Eigen::RowVector3d C(0.5, 0.5, 0.5);
    Eigen::RowVector3d D(2, 2, 2);
    Eigen::RowVector3d E(-1, -1, -1);
    Segment3D segAB = Segment3D{ A,B };
    Ray3D rayAB = Ray3D{ A,B };
    Line3D lineAB = Line3D{ A,B };

    std::cout << "--- On Segment AB ---\n";
    std::cout << "  C on Segment AB: " << isPointOnLine3D(segAB, C) << "\n";
    std::cout << "  D on Segment AB: " << isPointOnLine3D(segAB, D) << "\n";
    std::cout << "  E on Segment AB: " << isPointOnLine3D(segAB, E) << "\n\n";

    std::cout << "--- On Ray AB ---\n";
    std::cout << "  C on Ray AB: " << isPointOnLine3D(rayAB, C) << "\n";
    std::cout << "  D on Ray AB: " << isPointOnLine3D(rayAB, D) << "\n";
    std::cout << "  E on Ray AB: " << isPointOnLine3D(rayAB, E) << "\n\n";

    std::cout << "--- On Line AB ---\n";
    std::cout << "  C on Line AB: " << isPointOnLine3D(lineAB, C) << "\n";
    std::cout << "  D on Line AB: " << isPointOnLine3D(lineAB, D) << "\n";
    std::cout << "  E on Line AB: " << isPointOnLine3D(lineAB, E) << "\n";

    return 0;
}

The figure below visualises the test results for points C, D, and E with respect to the segment, the ray, and the infinite line defined by A and B.

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