Accurate and robust geometric modeling for simulation of IC and MEMS fabrication processes
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Mason: morphological simplification
Graphical Models
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Minkowski sum boundary surfaces of 3D-objects
Graphical Models
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Optimal Accurate Minkowski Sum Approximation of Polyhedral Models
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Duplex fitting of zero-level and offset surfaces
Computer-Aided Design
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Digital geometry processing with topological guarantees
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Computer-Aided Design
Surface embedding narrow volume reconstruction from unorganized points
Computer Vision and Image Understanding
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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 underlyingvolumetric grid. Insufficient resolution can result in unwanted handles or disconnected components in the approximation. We use an adaptive sub-division algorithm that overcomes these problems by generating a volumetric grid at an appropriate resolution. We guaranteethat 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 translationmotion planning, offset computation, mathematical morphological operations andbounded-error penetration depth estimation.