Offsetting operations in solid modelling
Computer Aided Geometric Design
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Minkowski operations for satellite antenna layout
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The Union of Convex Polyhedra in Three Dimensions
SIAM Journal on Computing
Strategies for polyhedral surface decomposition: an experimental study
Computational Geometry: Theory and Applications
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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
Efficient max-norm distance computation and reliable voxelization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
Configuration products in geometric modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Discrete critical values: a general framework for silhouettes computation
SGP '09 Proceedings of the Symposium on Geometry Processing
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
Uniform offsetting of polygonal model based on Layered Depth-Normal Images
Computer-Aided Design
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedra
ACM Transactions on Graphics (TOG)
Configuration products and quotients in geometric modeling
Computer-Aided Design
GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces
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
Controlled linear perturbation
Computer-Aided Design
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
GPU-based offset surface computation using point samples
Computer-Aided Design
Dynamic Minkowski sums under scaling
Computer-Aided Design
On soft predicates in subdivision motion planning
Proceedings of the twenty-ninth annual symposium on Computational geometry
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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We present an algorithm to approximate the 3D Minkowski sum of polyhedral objects. Our algorithm decomposes the polyhedral objects into convex pieces, generates pairwise convex Minkowski sums, and computes their union. We approximate the union by generating a voxel grid, computing signed distance on the grid points, and performing isosurface extraction from the distance field. The accuracy of the algorithm is mainly governed by the resolution of the underlying volumetric grid. Insufficient resolution can result in unwanted handles or disconnected components in the approximation. We use an adaptive subdivision algorithm that overcomes these problems by generating a volumetric grid at an appropriate resolution. We guarantee that our approximation has the same topology as the exact Minkowski sum. We also provide a two-sided Hausdorff distance bound on the approximation. Our algorithm is relatively simple to implement and works well on complex models. We have used it for exact 3D translation motion planning, offset computation, mathematical morphological operations, and bounded-error penetration depth estimation.