The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Graphical Models
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Geometric and topological guarantees for the WRAP reconstruction algorithm
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Computing handle and tunnel loops with knot linking
Computer-Aided Design
Manifold homotopy via the flow complex
SGP '09 Proceedings of the Symposium on Geometry Processing
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
A parallel algorithm for computing the flow complex
Proceedings of the twenty-ninth annual symposium on Computational geometry
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The medial axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of Rn has the same homotopy type as its medial axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its medial axis approximation, in form of a piecewise linear cell complex, that captures the topology of the medial axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual medial axis.