Computing rational parametrizations of canal surfaces

Martin Peternell; Helmut Pottmann

doi:10.1006/jsco.1996.0087

Computing rational parametrizations of canal surfaces

Martin Peternell^*, Helmut Pottmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

100 Scopus citations

Abstract

A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametrizations and put particular emphasis on low degree representations.

Original language	English (US)
Pages (from-to)	255-266
Number of pages	12
Journal	Journal of Symbolic Computation
Volume	23
Issue number	2-3
DOIs	https://doi.org/10.1006/jsco.1996.0087
State	Published - Feb 1997
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1006/jsco.1996.0087

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title = "Computing rational parametrizations of canal surfaces",

abstract = "A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametrizations and put particular emphasis on low degree representations.",

author = "Martin Peternell and Helmut Pottmann",

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AU - Peternell, Martin

AU - Pottmann, Helmut

PY - 1997/2

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N2 - A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametrizations and put particular emphasis on low degree representations.

AB - A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametrizations and put particular emphasis on low degree representations.

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U2 - 10.1006/jsco.1996.0087

DO - 10.1006/jsco.1996.0087

M3 - Article

AN - SCOPUS:0031073214

SN - 0747-7171

VL - 23

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EP - 266

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 2-3

ER -

Computing rational parametrizations of canal surfaces

Abstract

ASJC Scopus subject areas

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