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Spatial planning: a configuration space approach
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Tangent, normal, and visibility cones on Be´zier surfaces
Computer Aided Geometric Design
Arbitrarily precise computation of Gauss maps and visibility sets for freeform surfaces
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
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IEEE Transactions on Pattern Analysis and Machine Intelligence
An algorithm to compute the Minkowski sum outer-face of two simple polygons
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Exact from-region visibility culling
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
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IEEE Transactions on Visualization and Computer Graphics
View planning for automated three-dimensional object reconstruction and inspection
ACM Computing Surveys (CSUR)
Cones on bezier curves and surfaces
Cones on bezier curves and surfaces
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Computer-Aided Design
Computing an exact spherical visibility map for meshed polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Exact and approximate construction of offset polygons
Computer-Aided Design
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Arrangements of geodesic arcs on the sphere
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Computer-Aided Design
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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International Journal of Robotics Research
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
Computer-Aided Design
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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A global visibility map is a spherical image built to describe the complete set of global visible view directions for a surface. In this paper, we consider the computation of global visibility maps for regions on the boundary of a polyhedron. Both the self-occlusions introduced by a region and the global occlusions introduced by the rest of the surfaces on the boundary of the polyhedron are considered for computing a global visibility map. We show that the occluded view directions introduced between a pair of polyhedral surfaces can be computed from the spherical projection of the Minkowski sum of one surface and the reflection of the other. A suitable subset of the Minkowski sum, which shares the identical spherical projection with the complete Minkowski sum, is constructed to obtain the spherical images representing global occlusions. Our method has been successfully tested on many CAD models. It extends the previous methods for computing global visibility maps using convex decomposition, and it exhibits a better performance.