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Exact medial axis of quadratic NURBS curves

George Tzoumas 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We study the problem of the exact computation of the medial axis of planar shapes the boundary of which is defined by piecewise conic arcs. The algorithm used is a tracing algorithm, similar to existing numeric algorithms. We trace the medial axis edge by edge. Instead of keeping track of points on the medial axis, we are keeping track of the corresponding footpoints on the boundary curves, thus dealing with bisector curves in parametric space. We exploit some algebraic and geometric properties of the bisector curves that allow for efficient trimming and we represent bifurcation points via their associated footpoints on the boundary, as algebraic numbers. The algorithm computes the correct topology of the medial axis identifying bifurcation points of arbitrary degree.
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https://hal.inria.fr/inria-00581588
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Submitted on : Thursday, March 31, 2011 - 11:16:27 AM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
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George Tzoumas. Exact medial axis of quadratic NURBS curves. 27th European Workshop on Computational Geometry, Mar 2011, Morschach, Switzerland. ⟨inria-00581588⟩

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