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ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL B´ezier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES

Authors
김선홍안영준
Issue Date
Jun-2011
Publisher
한국산업응용수학회
Keywords
Quadratic rational B´ezier curve; arc-length; estimation; weight; parameter; coincident
Citation
Journal of the Korean Society for Industrial and Applied Mathematics, v.15, no.2, pp.123 - 135
Journal Title
Journal of the Korean Society for Industrial and Applied Mathematics
Volume
15
Number
2
Start Page
123
End Page
135
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/12951
ISSN
1226-9433
Abstract
In this paper, we present arc-length estimations for quadratic rational B´ezier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational B´ezier curve exactly when the weight w is 0, 1 and ∞. We show that for all w > 0 our estimations are strictly increasing with respect to w. Moreover, we find the parameter μ^* which makes our estimation coincide with the arc-length of the quadratic rational B´ezier curve when it is a circular arc too. We also show that μ^* has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of μ^* is an optimal estimation.
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