Approximate implicitization of space curves and of surfaces of revolution

Mohamed Shalaby; Bert Jüttler

doi:10.1007/978-3-540-72185-7_12

Approximate implicitization of space curves and of surfaces of revolution

Mohamed Shalaby, Bert Jüttler

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

11 Scopus citations

Abstract

We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space curves, which are described as the intersection of two implicitly defined surfaces, we show how to generate an approximately orthogonalized implicit representation. In the case of surfaces of revolution, we address the problem of avoiding unwanted branches and singular points in the region of interest.

Original language	English (US)
Title of host publication	Geometric Modeling and Algebraic Geometry
Publisher	Springer Berlin Heidelberg
Pages	215-227
Number of pages	13
ISBN (Print)	9783540721840
DOIs	https://doi.org/10.1007/978-3-540-72185-7_12
State	Published - 2008
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-540-72185-7_12

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title = "Approximate implicitization of space curves and of surfaces of revolution",

abstract = "We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space curves, which are described as the intersection of two implicitly defined surfaces, we show how to generate an approximately orthogonalized implicit representation. In the case of surfaces of revolution, we address the problem of avoiding unwanted branches and singular points in the region of interest.",

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N2 - We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space curves, which are described as the intersection of two implicitly defined surfaces, we show how to generate an approximately orthogonalized implicit representation. In the case of surfaces of revolution, we address the problem of avoiding unwanted branches and singular points in the region of interest.

AB - We present techniques for creating an approximate implicit representation of space curves and of surfaces of revolution. In both cases, the proposed techniques reduce the problem to that of implicitization of planar curves. For space curves, which are described as the intersection of two implicitly defined surfaces, we show how to generate an approximately orthogonalized implicit representation. In the case of surfaces of revolution, we address the problem of avoiding unwanted branches and singular points in the region of interest.

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DO - 10.1007/978-3-540-72185-7_12

M3 - Chapter

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SN - 9783540721840

SP - 215

EP - 227

BT - Geometric Modeling and Algebraic Geometry

PB - Springer Berlin Heidelberg

ER -

Approximate implicitization of space curves and of surfaces of revolution

Abstract

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