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

Title & Authors
MULTI-DEGREE REDUCTION OF BÉZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS
Sunwoo, Hasik;

Abstract
In this paper, we consider multi-degree reduction of $\small{B{\acute{e}}zier}$ curves with continuity of any (r, s) order with respect to $\small{L_2}$ 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
$\small{B{\acute{e}}zier}$ curve;degree reduction;Lagrange multipliers;generalized inverse;
Language
English
Cited by
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