Implicitization and Offsetting via Regular Systems

Dongming Wang 1, 2
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Given a geometric object defined by rational parametric equations, we show how to compute a disjunction of implicit equations and inequations that define exactly the same object by means of regular systems. The same technique is applied to the computation of quasi-offsets to algebraic curves and surfaces. Regular systems possess the projection property, are relatively easy to compute, and often have a compact form. Several examples are given to illustrate our approach based on the decomposition of polynomial systems into regular systems. A heuristic method is presented to simplify the output disjunction of polynomial equations and inequations.
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https://hal.inria.fr/inria-00099542
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Submitted on : Tuesday, September 26, 2006 - 9:38:27 AM
Last modification on : Thursday, March 21, 2019 - 12:59:17 PM

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Dongming Wang. Implicitization and Offsetting via Regular Systems. Chen, Falai; Wang, Dongming. Geometric Computation, 11, World Scientific, pp.156-176, 2004, Lecture Notes Series on Computing, ⟨10.1142/9789812794833_0005⟩. ⟨inria-00099542⟩

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