Approximation of Planar Rational Curves by Polynomial Curves

DOI

10.2991/meic-14.2014.291How to use a DOI?

Keywords

Polynomial; Polynomial interpolation;Rational curve;Conic rational curve circle; Approximation

Abstract

A Rational curve r(t) can pass through interpolation points (m+1) by a polynomial of degree m or under some circumstances, and the same is true when rational curve is restricted or the function values of r(t) are replaced by derivatives . The paper will show in these cases a rational curve r(t) of degree m tends to pass through interpolation points more than (m+1) geometric data. In a Hermite sense ,this paper studied using polynomial interpolation of rational curve to reduce polynomial degree and to increase interpolation points by showing that a large class of rational parametric curves can be interpolated ,in some certain cases, by a polynomial of degree m matching 2m-2k+4 data. This paper constructs a simple polynomial p (t) and employs quadratic planar rational curve as interpolation curve to test practicability of the method. The result shows that in test taking symmetrical points can effectively reduce computing time, improve approximation data and visual experience.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hongmei Zhang
AU  - Zhigao Zhang
AU  - Zhili Pei
PY  - 2014/11
DA  - 2014/11
TI  - Approximation of Planar Rational Curves by Polynomial Curves
BT  - Proceedings of the 2014 International Conference on Mechatronics, Electronic, Industrial and Control Engineering
PB  - Atlantis Press
SP  - 1293
EP  - 1297
SN  - 2352-5401
UR  - https://doi.org/10.2991/meic-14.2014.291
DO  - 10.2991/meic-14.2014.291
ID  - Zhang2014/11
ER  -