Optimal constrained polynomials approximation of hyperbolas based on Lupaş q‐Bézier curves

Abstract

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.