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Voxelized Minkowski sum computation on the GPU with robust culling

Wei Li, Sara McMains
University of California, Berkeley, United States
Computer-Aided Design, Volume 43, Issue 10, Pages 1270-1283, 2011

@article{li2011voxelized,

   title={Voxelized Minkowski sum computation on the GPU with robust culling},

   author={Li, W. and McMains, S.},

   journal={Computer-Aided Design},

   year={2011},

   publisher={Elsevier}

}

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We present a new approach for computing the voxelized Minkowski sum (excluding any enclosed voids) of two polyhedral objects using programmable Graphics Processing Units (GPUs). We first cull out surface primitives that will not contribute to the final boundary of the Minkowski sum, analyzing and adaptively bounding the rounding errors of the culling algorithm to solve the floating point error problem. The remaining surface primitives are then rendered to depth textures along six orthogonal directions to generate an initial solid voxelization of the Minkowski sum. Finally we employ fast flood fill to find all the outside voxels. We generate both solid and surface voxelizations of Minkowski sums without enclosed voids and support high volumetric resolution of 1024^3 with low video memory cost. The whole algorithm runs on the GPU and is at least one order of magnitude faster than existing boundary representation (B-rep) based algorithms. It avoids the large number of 3D Boolean operations needed in most existing algorithms and is easy to implement. The voxelized Minkowski sums can be used in a variety of applications including motion planning and penetration depth computation.
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