Half-Space Power Diagrams and Discrete Surface Offsets

TL;DR

This paper introduces a fast, parallelizable algorithm for computing surface offsets of discretized shapes using half-space power diagrams, avoiding volumetric distance fields and enabling interactive modeling and other geometry tasks.

Contribution

The paper presents a novel, efficient algorithm based on half-space power diagrams for surface offset computation, avoiding volumetric distance fields and supporting interactive applications.

Findings

Algorithm is trivially parallelizable and efficient.

Outperforms previous methods in speed and simplicity.

Applicable to various geometry processing tasks.

Abstract

We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient, entirely avoiding volumetric distance field computations typical of existing methods. Our construction is based on properties of half-space power diagrams, where each seed is only visible by a half-space, which were never used before for the computation of surface offsets. The primary application of our method is interactive modeling for digital fabrication. Our technique enables a user to interactively process high-resolution models. It is also useful in a plethora of other geometry processing tasks requiring fast, approximate offsets, such as topology optimization, collision detection, and skeleton extraction. We present experimental timings, comparisons with previous approaches, and provide a reference implementation in the supplemental material.