Subdivision Methods for the Topology of 2d and 3d Implicit Curves

Chen Liang, Bernard Mourrain () and Jean-Pascal Pavone ()
Additional contact information
Chen Liang: GALAAD, INRIA
Bernard Mourrain: GALAAD, INRIA
Jean-Pascal Pavone: GALAAD, INRIA

Chapter 11 in Geometric Modeling and Algebraic Geometry, 2008, pp 199-214 from Springer

Abstract: In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and 3d. We use the representation of polynomials in the Bernstein basis associated with a given box, to check if the topology of the curve is determined inside this box, from its points on the border of the box. Subdivision solvers are used for computing these points on the faces of the box, and segments joining these points are deduced to get a graph isotopic to the curve. Using envelop of polynomials, we show how this method allow to handle efficiently and accurately implicit curves with large coefficients.We report on implementation aspects and experimentations on 2d curves such as ridge curves or self intersection curves of parameterized surfaces, and on silhouette curves of implicit surfaces, showing the interesting practical behavior of this approach.

Keywords: Algebraic Surface; Topological Graph; Implicit Surface; Regularity Criterion; Bernstein Basis (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-72185-7_11

Ordering information: This item can be ordered from
http://www.springer.com/9783540721857

DOI: 10.1007/978-3-540-72185-7_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().