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Improving Angular Speed Uniformity by Reparameterization

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Jing Yang (University of Beihang, China), 13 September 2012, 10:00 am, RICAM seminar room S2 416
When Sep 13, 2012
from 10:00 AM to 11:30 AM
Where RICAM seminar room S2 416
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Improving Angular Speed Uniformity by Reparameterization

In this talk, we introduce the notion of angular speed uniformity as a quality measure for parameterizations of plane curves and give the definition of arc-angle parameterization whose angular speed is uniform. Then we propose an algorithm to compute arc-angle reparameterizations for quadratic and cubic curves. We prove that only straight lines have rational arc-angle 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 by Möbius transformation. Considering the single piece rational function cannot produce a reparameterization good enough, we adapt the C0 piecewise Möbius transformation to compute a C0 piecewise-rational reparameterization that approximates closely to the arc-angle parameterization of the curve. We also explore a C1 piecewise-rational reparameterization that approximates closely to the arc-angle parameterization but with a better geometric property than the C0one. Experimental results are reported to show the effectiveness and efficiency of the reparameterization methods.

 

This work is done in cooperation with Professors Dongming Wang and Hoon Hong.