The complexity of robot motion planning
The complexity of robot motion planning
Computer algebra (2nd ed.): systems and algorithms for algebraic computation
Computer algebra (2nd ed.): systems and algorithms for algebraic computation
The Euclidean distance transform
The Euclidean distance transform
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
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Shape Description By Medial Surface Construction
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Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Computing the medial axis of a polyhedron reliably and efficiently
Computing the medial axis of a polyhedron reliably and efficiently
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Simultaneous shape decomposition and skeletonization
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Defining and computing curve-skeletons with medial geodesic function
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MOS surfaces: medial surface transforms with rational domain boundaries
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Computer Graphics Forum
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We present an accurate algorithm to compute the internal Voronoi diagram and medial axis of a 3-D polyhedron. It uses exact arithmetic and exact representations for accurate computation of the medial axis. The algorithm works by recursively finding neighboring junctions along the seam curves. To speed up the computation, we have designed specialized algorithms for fast computation with algebraic curves and surfaces. These algorithms include lazy evaluation based on multivariate Sturm sequences, fast resultant computation, culling operations, and floating-point filters. The algorithm has been implemented and we highlight its performance on a number of examples.