Overview

Computational geometry plays a crucial role in various fields, from computer graphics to robotics and geographic mapping. One fundamental concept within this domain is the convex hull—the smallest convex shape that can enclose a given set of points. In this post, we explore a dynamic convex hull visualization that allows users to see this concept in action.

What is a Convex Hull?

A convex hull is the minimal boundary that encloses a set of points in a plane. Imagine stretching a rubber band around a group of nails on a board; once released, the band forms the convex hull of those points. This structure has applications in collision detection, image processing, and data analysis.

How Does the Visualization Work?

This project provides an interactive convex hull visualization, dynamically computing and displaying the convex boundary as points are generated. The implementation consists of:

Algorithm Implementation

The visualization relies on a computational geometry approach to construct the convex hull efficiently. A commonly used method is the Graham’s scan algorithm, which sorts points by their polar angle and constructs the hull iteratively using a stack-based approach. Alternatively, the Jarvis March (Gift Wrapping) algorithm may be employed for simplicity, iteratively selecting the next hull point by checking orientations.

Technology Stack