DEGREE REDUCTION OF BEZIER CURVES

被引：83

作者：

ECK, M

机构：

[1] Fachbereich Mathematik, Technische Hochschule Darmstadt

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1993年 / 10卷 / 3-4期

关键词：

DEGREE REDUCTION; BEZIER CURVE; TENSOR PRODUCT BEZIER SURFACE; CONSTRAINED CHEBYSHEV POLYNOMIALS; CONSTRAINED BEST APPROXIMATION; SUBDIVISION;

D O I：

10.1016/0167-8396(93)90039-6

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We provide an simple algorithm for constructing an polynomial Bezier approximation of degree n - 1 to an nth degree Bezier curve. This algorithm makes previous work of Lachance more transparent as formulas are given which express the geometric relationship between the control points. The two curves agree at the two endpoints up to a preselected differentiation order since the method is based on constrained Chebyshev polynomials in order to obtain best constrained approximations. These polynomials then allow a detailed error analysis providing apriori bounds of the pointwise approximation error. The extension to tensor product surfaces is also briefly discussed.

引用

页码：237 / 251

页数：15

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