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CAGD
2008

Topology and arrangement computation of semi-algebraic planar curves

13 years 3 months ago
Topology and arrangement computation of semi-algebraic planar curves
We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be correct. Although we focus on the implicit case, the algorithm can also treat parametric or piecewise linear curves without much additional work and no theoretical difficulties. The method isolates singular points from regular parts and deals with them independently. The topology near singular points is guaranteed through topological degree computation. In either case the topology inside regions is recovered from information on the boundary of a cell of the subdivision. Obtained regions are segmented to provide an efficient insertion operation while dynamically maintaining an arrangement structure. We use enveloping techniques of the polynomial represented in the Bernstein basis to achieve both efficiency and certification. It is finally shown on examples that this algorithm is able to handle ...
Lionel Alberti, Bernard Mourrain, Julien Wintz
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CAGD
Authors Lionel Alberti, Bernard Mourrain, Julien Wintz
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