Computing convolutions by reciprocal search
SCG '86 Proceedings of the second annual symposium on Computational geometry
Geometric representation of swept volumes with application to polyhedral objects
International Journal of Robotics Research
Strategies for polyhedral surface decomposition: an experimental study
Proceedings of the eleventh annual symposium on Computational geometry
The Union of Convex Polyhedra in Three Dimensions
SIAM Journal on Computing
Fast volumetric CSG modeling using standard graphics system
Proceedings of the seventh ACM symposium on Solid modeling and applications
The Minkowski Sum of Two Simple Surfaces Generated by Slope-Monotone Closed Curves
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Convex decompositions of polyhedra
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Computing the Minkowski sum of ruled surfaces
Graphical Models
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Real-time Voxelization for Complex Polygonal Models
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Approximate convex decomposition of polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots
International Journal of Robotics Research
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Real-time voxelization of triangle meshes on the GPU
ACM SIGGRAPH 2007 sketches
The Visual Computer: International Journal of Computer Graphics
Minkowski sum boundary surfaces of 3D-objects
Graphical Models
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Single-pass GPU solid voxelization for real-time applications
GI '08 Proceedings of graphics interface 2008
Minkowski sums of rotating convex polyhedra
Proceedings of the twenty-fourth annual symposium on Computational geometry
Covering Minkowski sum boundary using points with applications
Computer Aided Geometric Design
GPU-accelerated multi-valued solid voxelization by slice functions in real time
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Group morphology with convolution algebras
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Non-commutative morphology: Shapes, filters, and convolutions
Computer Aided Geometric Design
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Computing the Minkowski sum of two arbitrary polyhedra in R^3 is difficult because of high combinatorial complexity. We present an algorithm for directly computing a voxelization of the Minkowski sum of two closed watertight input polyhedra for applications such as path planning that do not require a boundary representation as output. We introduce a new decomposition formula for computing the Minkowski sum and prove its correctness. We describe an efficient Graphics Processing Unit (GPU) implementation of the algorithm using stencil shadow volumes to create a solid voxelization of the Minkowski sum.