Approximating of conic sections by DP curves with endpoint interpolation

Abstract

Conic sections have many applications in industrial design, however, they cannot be exactly represented in polynomial form. Hence approximating conic sections with polynomials is a challenging problem. In this paper, we use the monomial form of Delgado and Peña (DP) curves and present a matrix representation for them. Using the matrix form and the least squares method, we propose a simple and efficient algorithm for approximating conic sections by DP curves of arbitrary degree with endpoint interpolation. Finally, we test and compare the proposed algorithm on some numerical examples which validates and confirms efficiency of it.

Keywords:

• conic sections
• DP curves
• curve approximation
• least square method
• matrix representation

2010 AMS Subject Classifications::

• 68U05
• 65D17
• 65D05

Acknowledgements

We would like to thank unknown reviewers for their three rounds reviews and valuable comments in improving this paper.