Construction and optimization of CSG representations
Computer-Aided Design - Beyond solid modelling
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Motion planning for a rigid body using random networks on the medial axis of the free space
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Journal of Computational and Applied Mathematics
Shock Graphs and Shape Matching
International Journal of Computer Vision
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
Constraint-based motion planning for virtual prototyping
Proceedings of the seventh ACM symposium on Solid modeling and applications
Coverage of Known Spaces: The Boustrophedon Cellular Decomposition
Autonomous Robots
A Shortest Path Based Path Planning Algorithm for Nonholonomic Mobile Robots
Journal of Intelligent and Robotic Systems
International Journal of Computer Vision
Visualizing 3D Configuration Spaces for Mechanical Design
IEEE Computer Graphics and Applications
The Role of Propagation and Medial Geometry in Human Vision
BMCV '02 Proceedings of the Second International Workshop on Biologically Motivated Computer Vision
Any open bounded subset of Rn has the same homotopy type than its medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Automating the CAD/CAE dimensional reduction process
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Sensor-based Planning for a Rod-shaped Robot in Three Dimensions: Piecewise Retracts of R3 X S2
International Journal of Robotics Research
Canonical Skeletons for Shape Matching
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Algorithms
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Planning Algorithms
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis based solid representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Two-dimensional motion-planning for nonholonomic robots using the bump-surfaces concept
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Creating High-quality Paths for Motion Planning
International Journal of Robotics Research
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
Finding paths through the world's photos
ACM SIGGRAPH 2008 papers
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
Strategies for shape matching using skeletons
Computer Vision and Image Understanding
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
An O(n3loglogn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
Roadmap-based motion planning in dynamic environments
IEEE Transactions on Robotics
Automatic path planning for a mobile robot among obstacles ofarbitrary shape
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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The task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in practically all geometrically intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes place. We present a strategy to construct a family of paths, or roadmaps, for two-and three-dimensional solids moving in an evolving environment that can undergo drastic topological changes. Our approach is based on a potent paradigm for constructing geometric skeletons that relies on constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations. We describe a family of skeletons that have the same homotopy as that of the environment and contains the medial axis as a special case. Of importance, our skeletons can be designed so that they are "attracted to" or "repulsed by" prescribed spatial sites of the environment. Moreover, the R-function formulation suggests the new concept of a medial zone, which can be thought of as a "thick" skeleton with significant applications for motion planning and other geometric reasoning applications. Our approach can handle problems in which the environment is not fully known a priori, and intrinsically supports local and parallel skeleton computations for domains with rigid or evolving boundaries. Furthermore, our path planning algorithm can be implemented in any commercial geometric kernel, and has attractive computational properties. The capability of the proposed technique are explored through several examples designed to simulate highly dynamic environments.