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Math. Comput. Appl. 2017, 22(3), 39; doi:10.3390/mca22030039

A Novel Method of Offset Approximation along the Normal Direction with High Precision

1
College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China
2
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
*
Author to whom correspondence should be addressed.
Received: 3 July 2017 / Revised: 17 August 2017 / Accepted: 21 August 2017 / Published: 4 September 2017
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Abstract

A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of normal, and thus could reflect the approximate performance more properly. The approximation is completely independent of the original curve parameterization, and thus could ensure the stability of the approximation result. Experimental results show that the proposed algorithm is reasonable and effective. View Full-Text
Keywords: Computer Aided Geometric Design (CAGD); offset curve; rational approximation Computer Aided Geometric Design (CAGD); offset curve; rational approximation
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Zhao, H.; Zhou, L. A Novel Method of Offset Approximation along the Normal Direction with High Precision. Math. Comput. Appl. 2017, 22, 39.

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