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arXiv · 2304.04079

Convex Hulls: Surface Mapping onto a Sphere

Ben Kenwright
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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.

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Ben Kenwright. 2023-04-08. Convex Hulls: Surface Mapping onto a Sphere. https://arxiv.org/abs/2304.04079

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