MULTI-DEGREE REDUCTION OF BEZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 29, No. 2
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2016.05267 - 281 (15 pages)
- 2
In this paper, we consider multi-degree reduction of B´ezier curves with continuity of any (r, s) order with respect to 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.
1. Introduction
2. Preliminaries
3. Some properties of generalized inverse
4. Matrix representation of constraints
5. Degree reduction using Lagrange multipliers
6. Error analysis
7. Conclusions
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