Premium
Optimal constrained polynomials approximation of hyperbolas based on Lupaş q ‐Bézier curves
Author(s) -
Han Xuli,
Zhang Yali
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5104
Subject(s) - hyperbola , mathematics , bézier curve , quadratic function , quadratic equation , bernstein polynomial , polynomial , mathematical analysis , geometry
This paper presents an explicit optimal polynomial for approximating the quadratic Lupaş q ‐Bézier curve. We first prove that the quadratic Lupaş q ‐Bézier curve represents a hyperbola or a parabola. Then we research the approximation of quadratic Lupaş q ‐Bézier curves by polynomials. Since the denominator of quadratic Lupaş q ‐Bézier curves is a linear function, the explicit optimal constrained approximation is obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method.