Wei Li
ABSTRACT
We present a new approach for computing the voxelized Minkowski sum 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. 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 holes and support high volumetric resolution of 10243 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 for computing Minkowski sums of objects with curved surfaces at similar accuracy. It avoids complex 3D Boolean operations and is easy to implement. The voxelized Minkowski sums can be used in a variety of applications including motion planning and penetration depth computation.
- H. Barki, F. Denis, and F. Dupont. Contributing vertices-based Minkowski sum of a non-convex polyhedron without fold and a convex polyhedron. In IEEE International Conference on Shape Modeling and Applications, pages 73--80, 2009.Google Scholar
Cross Ref
- J. R. Baumgardner and P. O. Frederickson. Icosahedral discretization of the two-sphere. SIAM Journal on Numerical Analysis, 22(6):1107--1115, 1985.Google ScholarCross Ref
- S. Burtsev and Y. Kuzmin. An efficient flood-filling algorithm. Computers & Graphics, 17(5):549--561, 1993.Google ScholarCross Ref
- CGAL. Cgal, Computational Geometry Algorithms Library, 2010. http://www.cgal.org.Google Scholar
- CUDA. NVIDIA CUDA programming guide version 3.0, 2010. http://www.nvidia.com.Google Scholar
- Z. Dong, W. Chen, H. Bao, H. Zhang, and Q. Peng. Real-time voxelization for complex polygonal models. In PG '04, pages 43--50, 2004. Google ScholarDigital Library
- S. Fang and H. Chen. Hardware accelerated voxelization. Computers and Graphics, 24:433--442, 2000.Google ScholarCross Ref
- R. Fernando and M. J. Kilgard. The Cg Tutorial. 2003.Google Scholar
- E. Fogel. Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere. Ph.D. dissertation, Tel-Aviv Univ., October 2008.Google Scholar
- E. Fogel and D. Halperin. Exact and efficient construction of Minkowski sums of convex polyhedra with applications. Comput. Aided Des., 39(11):929--940, 2007. Google ScholarDigital Library
- P. K. Ghosh. A unified computational framework for Minkowski operations. Computers & Graphics, 17(4):357--378, 1993.Google ScholarCross Ref
- L. Guibas and R. Seidel. Computing convolutions by reciprocal search. In SCG '86, pages 90--99, 1986. Google ScholarDigital Library
- P. Hachenberger. Exact Minkowski sums of polyhedra and exact and efficient decomposition of polyhedra into convex pieces. Algorithmica, 55(2):329--345, 2009. Google ScholarDigital Library
- D. Halperin. Robust geometric computing in motion. Int. J. Rob. Res., 21(3):219--232, 2002.Google ScholarCross Ref
- E. E. Hartquist, J. Menon, K. Suresh, H. B. Voelcker, and J. Zagajac. A computing strategy for applications involving offsets, sweeps, and Minkowski operations. Comput. Aided Des., 31(3):175--183, 1999.Google ScholarCross Ref
- E.-A. Karabassi, G. Papaioannou, and T. Theoharis. A fast depth-buffer-based voxelization algorithm. Journal of Graphics Tools, 4(4):5--10, 1999. Google ScholarDigital Library
- A. Kaul and J. Rossignac. Solid-interpolating deformations: Construction and animation of PIPS. Computers & Graphics, 16(1):107--115, 1992.Google ScholarCross Ref
- J.-M. Lien. Covering Minkowski sum boundary using points with applications. Comput. Aided Geom. Des., 25(8):652--666, 2008. Google ScholarDigital Library
- J.-M. Lien. Hybrid motion planning using Minkowski sums. In Proceedings of Robotics: Science and Systems IV, Zurich, Switzerland, June 2008.Google ScholarCross Ref
- J.-M. Lien. A simple method for computing Minkowski sum boundary in 3D using collision detection. In The 8th Int. Workshop on the Alg. Found. of Robotics, 2008.Google Scholar
- M. Liu, Y.-S. Liu, and K. Ramani. Computing global visibility maps for regions on the boundaries of polyhedra using Minkowski sums. Comput. Aided Des., 41(9):668--680, 2009. Google ScholarDigital Library
- I. Llamas. Real-time voxelization of triangle meshes on the GPU. In SIGGRAPH '07: SIGGRAPH Sketches, page 18, 2007. Google ScholarDigital Library
- T. Lozano-Pérez. Spatial planning: a configuration space approach. IEEE Trans. Comp., C-32(2):108--120, 1983. Google ScholarDigital Library
- H. Mühlthaler and H. Pottmann. Computing the Minkowski sum of ruled surfaces. Graph. Models, 65(6):369--384, 2003. Google ScholarDigital Library
- S. Nelaturi and V. Shapiro. Configuration products in geometric modeling. In SPM '09, pages 247--258, 2009. Google ScholarDigital Library
- M. Peternell and T. Steiner. Minkowski sum boundary surfaces of 3D-objects. Graph. Models, 69(3-4):180--190, 2007. Google ScholarDigital Library
- J.-K. Seong, M.-S. Kim, and K. Sugihara. The Minkowski sum of two simple surfaces generated by slope-monotone closed curves. In Proceedings of Geometric Modeling and Processing --- Theory and Applications, page 33, 2002. Google ScholarDigital Library
- G. Varadhan, S. Krishnan, T. Sriram, and D. Manocha. A simple algorithm for complete motion planning of translating polyhedral robots. Int. J. Rob. Res., 25(11):1049--1070, 2006. Google ScholarDigital Library
- G. Varadhan and D. Manocha. Accurate Minkowski sum approximation of polyhedral models. Graph. Models, 68(4):343--355, 2006. Google ScholarDigital Library
- R. Wein. Exact and efficient construction of planar Minkowski sums using the convolution method. In ESA'06, pages 829--840, 2006. Google ScholarDigital Library
Index Terms
- A GPU-based voxelization approach to 3D Minkowski sum computation
Recommendations
Fast scene voxelization and applications
I3D '06: Proceedings of the 2006 symposium on Interactive 3D graphics and gamesThis paper presents a novel approach that uses graphics hardware to dynamically calculate a voxel-based representation of a scene. The voxelization is obtained on run-time in the order of milliseconds, even for complex and dynamic scenes containing more ...
Grid-free out-of-core voxelization to sparse voxel octrees on GPU
HPG '15: Proceedings of the 7th Conference on High-Performance GraphicsIn this paper, we present the first grid-free, out-of-core GPU voxelization method. Our method combines efficient parallel triangle voxelization on GPU with out-of-core technologies in order to allow the processing of scenes with large triangle counts ...
Voxelized Minkowski sum computation on the GPU with robust culling
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 ...
Comments