MULTI-DEGREE REDUCTION OF BÉZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS

- Journal title : Journal of the Chungcheong Mathematical Society
- Volume 29, Issue 2, 2016, pp.267-281
- Publisher : Chungcheong Mathematical Society
- DOI : 10.14403/jcms.2016.29.2.267

Title & Authors

MULTI-DEGREE REDUCTION OF BÉZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS

Sunwoo, Hasik;

Sunwoo, Hasik;

Abstract

In this paper, we consider multi-degree reduction of curves with continuity of any (r, s) order with respect to norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

Keywords

curve;degree reduction;Lagrange multipliers;generalized inverse;

Language

English

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