Convex Hulls: Surface Mapping onto a Sphere

TL;DR

This paper introduces a new iterative method for computing 2D and 3D convex hulls that addresses common technical challenges like numerical issues and degeneracies, making the algorithm more robust and scalable.

Contribution

The paper presents a novel iterative approach using support mapping and surface projection to improve convex hull computation robustness.

Findings

Addresses numerical accuracy issues in convex hull algorithms

Provides a scalable solution for 3D convex hull computation

Reduces algorithmic complexity and handling of degenerate points

Abstract

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are a number of methods available for finding the convex hull based on geometric calculations, such as, the distance between points, but do not address the technical challenges when implementing a usable solution (e.g., numerical issues and degenerate cloud points). We explain some common algorithm pitfalls and engineering modifications to overcome and solve these limitations. We present a novel iterative method using support mapping and surface projection to create an uncomplicated and robust 2d and 3d convex hull algorithm.