Application of vector sum operator
Computer-Aided Design
The complexity of robot motion planning
The complexity of robot motion planning
Three-dimensional rotations by three shears
Graphical Models and Image Processing
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
On finding narrow passages with probabilistic roadmap planners
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Robot Motion Planning
Geometric Fundamentals of Robotics (Monographs in Computer Science)
Geometric Fundamentals of Robotics (Monographs in Computer Science)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Rotation of 3D volumes by Fourier-interpolated shears
Graphical Models - Special issue on PG2004
Planning Algorithms
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration
International Journal of Robotics Research
Group morphology with convolution algebras
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Configuration products and quotients in geometric modeling
Computer-Aided Design
Two- and three-dimensional image rotation using the FFT
IEEE Transactions on Image Processing
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Given two shapes in relative motion, an important class of inverse configuration problems are solved by determining relative configurations that maintain set-inclusion relationships (non-interference, containment, or contact) between the shapes. This class of inverse problems includes the well-known problem of constructing a configuration space obstacle, as well as many other problems in computational design such as sweep decomposition, accessibility analysis, and dynamic packaging. We show that solutions to such problems may be efficiently approximated directly in the 6D configuration space SE(3) of relative motions by adaptive sampling. The proposed method relies on a well-known fact that the manifold of the group SE(3) is a Cartesian product of two manifold subgroups: the group of rotations SO(3) and the group of translations R^3. This property allows generating desired configurations by combining samples that are generated in these subgroups independently and adaptively. We demonstrate the effectiveness of the proposed approach on several inverse problems including the problem of sweep decomposition that arises in reverse engineering applications.