Improving angular speed uniformity by reparameterization

Jing Yang; Dongming Wang; Hoon Hong

doi:10.1016/j.cagd.2013.04.001

Improving angular speed uniformity by reparameterization

Jing Yang^*
, Dongming Wang
, Hoon Hong

^*Corresponding author for this work

Beihang University
North Carolina State University
CNRS

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

11 Scopus citations

Abstract

We introduce the notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and propose an algorithm to compute uniform reparameterizations for quadratic and cubic curves. We prove that only straight lines have uniform rational parameterizations. For any plane curve other than lines, we show how to find a rational reparameterization that has the maximum uniformity among all the rational parameterizations of the same degree. We also establish specific results for quadratic and certain cubic Bézier curves.

Original language	English
Pages (from-to)	636-652
Number of pages	17
Journal	Computer Aided Geometric Design
Volume	30
Issue number	7
DOIs	https://doi.org/10.1016/j.cagd.2013.04.001
State	Published - 2013
Externally published	Yes

Keywords

Angular speed uniformity
Optimal Möbius transformation
Optimally uniform rational parameterization
Parametric plane curve
Uniform parameterization

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10.1016/j.cagd.2013.04.001

Cite this

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abstract = "We introduce the notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and propose an algorithm to compute uniform reparameterizations for quadratic and cubic curves. We prove that only straight lines have uniform rational parameterizations. For any plane curve other than lines, we show how to find a rational reparameterization that has the maximum uniformity among all the rational parameterizations of the same degree. We also establish specific results for quadratic and certain cubic B{\'e}zier curves.",

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AU - Hong, Hoon

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AB - We introduce the notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and propose an algorithm to compute uniform reparameterizations for quadratic and cubic curves. We prove that only straight lines have uniform rational parameterizations. For any plane curve other than lines, we show how to find a rational reparameterization that has the maximum uniformity among all the rational parameterizations of the same degree. We also establish specific results for quadratic and certain cubic Bézier curves.

KW - Angular speed uniformity

KW - Optimal Möbius transformation

KW - Optimally uniform rational parameterization

KW - Parametric plane curve

KW - Uniform parameterization

UR - https://www.scopus.com/pages/publications/84878001124

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DO - 10.1016/j.cagd.2013.04.001

M3 - 文章

AN - SCOPUS:84878001124

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EP - 652

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JF - Computer Aided Geometric Design

IS - 7

ER -

Improving angular speed uniformity by reparameterization

Abstract

Keywords

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