An algebraic framework for computing the topology of offsets to rational curves

Caravantes, Jorge; Diaz–Toca, Gema M.; Fioravanti, Mario; González-Vega, Laureano; Necula, Ioana

doi:10.1016/j.cagd.2017.03.007

Cited by 1 publication

(3 citation statements)

References 37 publications

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“…the local singularities and the self-intersections, except perhaps for P ±∞ , are solutions of Eq. (10). The proof of this result in given in Appendix I, so as not to stop the flow of the paper.…”

Section: Computing the Points Of G Giving Rise To Critical Points Of Cmentioning

confidence: 99%

“…Suppose that x has no base points lying on G. Then every singularity of C, except perhaps for P ±∞ , is a solution of Eq. (10).…”

Section: Computing the Points Of G Giving Rise To Critical Points Of Cmentioning

confidence: 99%

“…In [3] the curve is seen as the image of the real line under a planar or space birational mapping, so somehow the germ of the idea in this paper is already in [3]. In [10], a method to compute the topology of a (non-necessarily rational) offset curve of a rational planar curve is provided. The method exploits similar ideas to [3], but focuses on offset curves, which have special properties.…”

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confidence: 99%

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Computing the topology of a plane or space hyperelliptic curve

Alcázar¹,

Caravantes²,

Diaz–Toca³

et al. 2020

Computer Aided Geometric Design

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We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Maple implementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.

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Section: Computing the Points Of G Giving Rise To Critical Points Of Cmentioning

confidence: 99%

“…Suppose that x has no base points lying on G. Then every singularity of C, except perhaps for P ±∞ , is a solution of Eq. (10).…”

Section: Computing the Points Of G Giving Rise To Critical Points Of Cmentioning

confidence: 99%

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confidence: 99%

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