CoreSource checked

Point-to-Segment Distance

Computes the shortest distance from a point to a finite line segment.

Explore relationships Open constellationBrowse atlas

Quick Facts

Compact metadata for implementation and discovery.

Category: Geometry
Difficulty: Intermediate
Family: Distance Queries
Tier: Core
Status: Verified
Review: Source Checked
Sources: 2
Formulas: 1
Relationships: 5
Code example: Ready
Visualization: Ready

Overview

Point-to-segment distance projects the point onto the segment's supporting line, clamps the projection parameter to the segment endpoints, and measures the resulting Euclidean distance.

Core Concepts

point distance querydistance queriesgeometric primitivesgeometry

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(1)

Average

O(1)

Worst

O(1)

Space

O(1)

When to Use

Use when the closest point must lie on a finite segment, not an infinite line.
Use in collision, snapping, simplification, or geometry query code.

When Not to Use

Avoid when the segment may be degenerate unless endpoint behavior is defined.
Avoid when a different metric than Euclidean distance is required.

What It Does

Point-to-Segment Distance uses projecting a point onto a segment and clamping the parameter for point distance query
Organizes the work around point distance query and distance queries.

Use Cases

Production and research workloads requiring distance queries via Computes the shortest distance from a point to a finite line segment.
Distance Queries pipelines where O(1) time and O(1) space fit system constraints.
Engineering comparisons against Circle-Line Intersection and Orthogonal Range Search when tuning distance queries.

Inputs

Points, segments, polygons, or geometric primitives
Query or construction parameters

Outputs

Geometric decision, measurement, or constructed structure

Key Formulas (1)

Clamped projection

t = clamp(dot(p−a, b−a) / dot(b−a, b−a), 0, 1)

t = clamp(dot(p-a, b-a) / dot(b-a, b-a), 0, 1)

Finds the closest point on a segment to the query point.

Pseudocode

1.Let AB = B - A and AP = P - A
2.If AB has zero length, return distance from P to A
3.Compute t = dot(AP, AB) / dot(AB, AB)
4.Clamp t between 0 and 1
5.Closest point is A + t * AB
6.Return distance from P to closest point

Canonical Example

Input: point P(2,1), segment A(0,0) to B(3,0)
Output: distance 1
Explanation: The projection falls inside the segment at (2,0), one unit below P.

Implementation Notes

Compute t = dot(P-A, B-A) / dot(B-A, B-A).
Clamp t to [0, 1] before computing the closest point.
Return squared distance when only comparisons are needed.

Common Pitfalls

Forgetting to clamp the projection parameter gives line distance instead of segment distance.
Zero-length segments require a point-to-point fallback.
Squared distance comparisons should not mix with unsquared distances.