Skip to main content
Z

Convex Hull Visualizer — Monotone Chain

Animated convex hull (Andrew’s monotone chain) on a plane of points — push/pop construction with step controls. Runs in your browser.

Free No signup Client-side Privacy friendly Updated

/

Pseudocode

Press Run to animate the algorithm.

How to use

  1. 1 Press Run to build the convex hull of the scattered points.
  2. 2 Watch the monotone chain push points and pop them when a turn is not left.
  3. 3 Use Shuffle for a new random point set, or step through one operation at a time.
  4. 4 The green outline is the final convex hull.

Why use this tool

  • See Andrew’s monotone-chain algorithm build the lower and upper hull.
  • Understand why points causing a right turn get popped off the chain.
  • Watch the O(n log n) construction — sorting dominates the cost.
  • Runs entirely in your browser. No signup, no uploads.

Frequently asked questions

What is a convex hull?

The smallest convex polygon that contains a set of points — imagine stretching a rubber band around all the points and letting it snap tight.

What algorithm does this visualizer use?

Andrew’s monotone chain: sort the points, then build the lower and upper hulls by pushing points and popping any that would create a non-left (clockwise) turn.

What is the time complexity of the convex hull?

O(n log n), dominated by the initial sort; the chain construction itself is linear. Graham scan and QuickHull have the same average bound.

What are convex hulls used for?

Collision detection, shape analysis, pathfinding, GIS, and as a preprocessing step for many other geometric algorithms.

What is Convex Hull Visualizer?

A Convex Hull Visualizer animates how the smallest convex polygon enclosing a set of points is found. Using Andrew’s monotone-chain algorithm, it sorts the points and builds the lower and upper hulls, popping any point that makes a non-left turn.

Features

Step-by-step animation

Watch the hull get built as points are sorted and turns are tested.

Complexity

Time: O(n log n) (sort-dominated). Space: O(n).

100% private

Runs entirely in your browser — nothing is uploaded.

Example

Input

points incl. one interior point

Output

hull = outer points only; interior point excluded

Common use cases

  1. 1

    Computational geometry

    See the foundational hull used by many geometry algorithms.

  2. 2

    Collision & bounds

    Compute a tight convex boundary around a point cloud.

  3. 3

    Learn orientation tests

    Understand left/right turn tests that build the hull.

Summary

Zerethon's convex hull visualizer animates finding the smallest convex polygon that encloses a set of points in your browser, using an O(n log n) algorithm (such as Graham scan or Andrew's monotone chain — dominated by the initial sort). Interior points are excluded from the hull; 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. Convex Hull Visualizer runs entirely client-side — no server upload, no logging, no tracking of your input.

Related tools

Bubble Sort Visualizer

Animated bubble sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs entirely in your browser.

Open tool

Insertion Sort Visualizer

Animated insertion sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.

Open tool

Selection Sort Visualizer

Animated selection sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs in your browser.

Open tool

Merge Sort Visualizer

Animated merge sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.

Open tool

Build, share, and grow on Zerethon Social

Free signup. Earn points, collect achievements, and connect with creators worldwide.

Sign up free