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Line Intersection Visualizer — Orientation Tests

Animated line segment intersection — cross-product orientation tests plus the exact crossing point, with step controls. Runs in your browser.

Free No signup Client-side Privacy friendly Updated

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Pseudocode

Press Run to animate the algorithm.

How to use

  1. 1 Press Run to test whether the two segments cross.
  2. 2 Watch the four orientation (cross-product) tests decide the outcome.
  3. 3 If they cross, the intersection point is marked in green; if not, the segments turn red.
  4. 4 Use Shuffle for a new random pair of segments.

Why use this tool

  • See how four cross-product orientation tests detect a segment crossing without division.
  • Understand the rule: each segment must straddle the line through the other.
  • Watch the exact intersection point computed when the segments cross.
  • Runs entirely in your browser. No signup, no uploads.

Frequently asked questions

How do you tell if two line segments intersect?

Use orientation (cross-product) tests: two segments properly cross when each segment has its endpoints on opposite sides of the line through the other segment.

What is the cross-product orientation test?

The sign of (b−a) × (c−a) tells whether point c is to the left (positive), right (negative), or on (zero) the directed line from a to b.

What is the time complexity?

O(1) — a fixed number of arithmetic operations for two segments. Finding intersections among n segments efficiently uses a sweep-line algorithm in O((n+k) log n).

How is the intersection point computed?

By solving the two line equations with a determinant (Cramer’s rule), which gives the exact crossing point once the segments are known to intersect.

What is Line Segment Intersection Visualizer?

A Line Segment Intersection Visualizer animates the orientation (cross-product) tests that decide whether two segments cross: each segment must straddle the line through the other. When they cross, it computes the exact intersection point.

Features

Orientation tests

Watch the cross-product turn tests decide whether the segments cross.

Complexity

Two segments: O(1). n segments (sweep-line): O((n + k) log n). Space: O(n).

100% private

Runs entirely in your browser — nothing is uploaded.

Example

Input

segments (0,0)-(4,4) and (0,4)-(4,0)

Output

intersect: yes, at (2, 2)

Common use cases

  1. 1

    Geometry & graphics

    Detect crossing edges in polygons, maps, or collision checks.

  2. 2

    Learn orientation math

    See how signed cross products classify turns and crossings.

  3. 3

    Sweep-line intuition

    Understand how the sweep-line finds all intersections efficiently.

Summary

Zerethon's line segment intersection visualizer animates whether two segments cross and where, in your browser, using orientation (cross-product) tests. Testing two segments is O(1); detecting all intersections among n segments takes O((n + k) log n) with a sweep-line (Bentley–Ottmann, k = intersections). Space is O(n).

Category
Algorithm
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Line Segment Intersection Visualizer runs entirely client-side — no server upload, no logging, no tracking of your input.

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