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Non-linear computational geometry for planar algebraic curves

Luis Peñaranda 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We tackle in this thesis the problem of computing the topology of plane algebraic curves. We present an algorithm that avoids special treatment of degenerate cases, based on algebraic tools such as Gröbner bases and rational univariate representations. We implemented this algorithm and showed its performance by comparing to similar existing programs. We also present an output-sensitive complexity analysis of this algorithm. We then discuss the tools that are necessary for the implementation of non-linear geometric algorithms in CGAL, the reference library in the computational geometry community. We present an univariate algebraic kernel for CGAL, a set of functions aimed to handle curved objects defined by univariate polynomials. We validated our approach by comparing it to other similar implementations.
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Contributor : Luis Peñaranda <>
Submitted on : Friday, December 17, 2010 - 2:43:34 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Friday, December 2, 2016 - 6:03:44 PM


  • HAL Id : tel-00547829, version 1



Luis Peñaranda. Non-linear computational geometry for planar algebraic curves. Other [cs.OH]. Université Nancy II, 2010. English. ⟨tel-00547829⟩



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