Progressive Convex Hull Simplification

Alec Jacobson

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arXiv · 2604.14468

Progressive Convex Hull Simplification

Alec Jacobson

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Abstract

Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We consider the problem of conservatively simplifying a convex hull to a specified number of half-spaces while minimizing added volume or surface area. By working in the dual representation, we propose an efficient $O(n \log n)$ greedy optimization. In comparisons, we show that existing methods either exhibit poor efficiency, tightness or safety. We demonstrate the success of our method on a variety of input shapes and downstream application domains.

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BibTeX RIS

Alec Jacobson. 2026-04-15. Progressive Convex Hull Simplification. https://arxiv.org/abs/2604.14468

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