Half-Space Power Diagrams and Discrete Surface Offsets
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We present a novel algorithm to compute offset surfaces of shapes discretized using a dexel data structure that is both fast and trivially parallel. We achieve this by exploiting properties of half-space power diagrams, where each seed is only visible by a half space. This allows us to develop a two-stage sweeping algorithm that is both simple to implement and efficient, and avoids computing a 3D volumetric distance field. The primary application of our method is interactive modeling for digital fabrication, where printed objects have a finite resolution. However, our method can also be used for other purposes where a fast but approximate offset solution is desirable. We present experimental timings, how they compare with previous approaches, and provide a reference implementation in the supplemental material.
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