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.
Pseudocode
Press Run to animate the algorithm.
Time · Space
How to use
- 1 Press Run to test whether the two segments cross.
- 2 Watch the four orientation (cross-product) tests decide the outcome.
- 3 If they cross, the intersection point is marked in green; if not, the segments turn red.
- 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
Geometry & graphics
Detect crossing edges in polygons, maps, or collision checks.
-
2
Learn orientation math
See how signed cross products classify turns and crossings.
-
3
Sweep-line intuition
Understand how the sweep-line finds all intersections efficiently.
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
- Line segment intersection — Wikipedia
- MIT OCW 6.006 — Introduction to Algorithms (CLRS) — MIT OpenCourseWare
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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