Science China Information Sciences

, Volume 56, Issue 10, pp 1–22 | Cite as

A framework for improving uniformity of parameterizations of curves

Research Paper

Abstract

We define quasi-speed as a generalization of linear speed and angular speed for parameterizations of curves and use the uniformity of quasi-speed to measure the quality of the parameterizations. With such conceptual setting, a general framework is developed for studying uniformity behaviors under reparameterization via proper parameter transformation and for computing reparameterizations with improved uniformity of quasispeed by means of optimal single-piece, C0 piecewise, and C1 piecewise Möbius transformations. Algorithms are described for uniformity-improved reparameterization using different Möbius transformations with different optimization techniques. Examples are presented to illustrate the concepts, the framework, and the algorithms. Experimental results are provided to validate the framework and to show the efficiency of the algorithms.

Keywords

parametric curve framework quasi-speed uniform parameterization uniformity-improved reparameterization optimal Möbius transformation 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.LIP6, CNRS—Université Pierre et Marie CurieParis cedex 05France
  3. 3.LMIB-School of Mathematics and Systems ScienceBeihang UniversityBeijingChina

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