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Robust polyhedral Minkowski sums with GPU implementation
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DOI：10.1016/j.cad.2015.04.012.png)
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Abstract
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We present a Minkowski sum algorithm for polyhedra based on convolution. We develop robust CPU and GPU implementations, using our ACP strategy to eliminate degeneracy and to enforce a user-specified backward error bound. We test the programs on 45 inputs with an error bound of 10(-8). The CPU program outperforms prior work, including non-robust programs. The GPU program using 2688 CUDA cores exhibits a median speedup factor of 36, which increases to 68 on the 6 hardest tests. For example, it computes a Minkowski sum with a million features in 20 seconds. (C) 2015 Elsevier Ltd. All rights reserved.
Keywords:
Minkowski sums
Robust computational geometry
GPU algorithms
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