关键词: 计算机辅助几何设计； 区间算法； q-Bernstein基； 区间q-Bézier曲线； 降阶

Abstract: Interval q-Bézier curves are presented using a generalized Bernstein basis and the problem of degree reduction approximation of them is studied. We propose three different methods, namely, perturbation method, best uniform approximation method and constrained best uniform approximation method based on Chebyshev polynomials. The explicit representation of bounding error of each method is derived. The advantages and disadvantages of these methods are discussed by several numerical examples. These examples show that the best uniform approximation algorithm provides much tighter approximation interval curves than the perturbation method.

Key words: computer aided geometric design; interval arithmetic; q-Bernstein basis; interval q-Bézier curves; degree reduction