Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL B$\acute{e}$zier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES

  • Received : 2011.01.18
  • Accepted : 2011.04.05
  • Published : 2011.06.25
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Abstract

In this paper, we present arc-length estimations for quadratic rational B$\acute{e}$zier 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$\acute{e}$zier curve exactly when the weight ${\omega}$ is 0, 1 and ${\infty}$. We show that for all ${\omega}$ > 0 our estimations are strictly increasing with respect to ${\omega}$. Moreover, we find the parameter ${\mu}^*$ which makes our estimation coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve when it is a circular arc too. We also show that ${\mu}^*$ 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 ${\mu}^*$ is an optimal estimation.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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