Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases
SIAM Journal on Discrete Mathematics
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Octree-based decimation of marching cubes surfaces
Proceedings of the 7th conference on Visualization '96
A random sampling scheme for path planning
International Journal of Robotics Research
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
OBPRM: an obstacle-based PRM for 3D workspaces
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral processing of point-sampled geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Point-Based Minkowski Sum Boundary
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Configuration products in geometric modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Group morphology with convolution algebras
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Robust Minkowski sums of polyhedra via controlled linear perturbation
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
Configuration products and quotients in geometric modeling
Computer-Aided Design
Non-commutative morphology: Shapes, filters, and convolutions
Computer Aided Geometric Design
Algorithm to calculate the Minkowski sums of 3-polytopes based on normal fans
Computer-Aided Design
PolyDepth: Real-time penetration depth computation using iterative contact-space projection
ACM Transactions on Graphics (TOG)
Controlled linear perturbation
Computer-Aided Design
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
City-scale urban transport and dispersion simulation using geographic information system footprints
Proceedings of the 3rd International Conference on Computing for Geospatial Research and Applications
GPU-based offset surface computation using point samples
Computer-Aided Design
ACM Transactions on Graphics (TOG)
Computer-Aided Design
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
Surface embedding narrow volume reconstruction from unorganized points
Computer Vision and Image Understanding
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Minkowski sum is a fundamental operation in many geometric applications, including robotic motion planning, penetration depth estimation, solid modeling, and virtual prototyping. However, due to its high computational complexity and several non-trivial implementation issues, computing the exact boundary of the Minkowski sum of two arbitrary polyhedra is generally a difficult task. In this work, we propose to represent the boundary of the Minkowski sum approximately using only points. Our results show that this point-based representation can be generated efficiently. An important feature of our method is its straightforward implementation and parallelization. We demonstrate that the point-based representation of the Minkowski sum boundary can indeed provide similar functionality as the mesh-based representations can. We show several applications in motion planning, penetration depth approximation and geometric modeling. An implementation of the proposed method can be obtained from our project webpage.