Multi-degree reduction of Bézier curves for fixed endpoints using Lagrange multipliers

In this paper, we consider multi-degree reduction of Bézier curves with respect to $$L_2$$ norm for fixed endpoints. The optimal control points of a degree-reduced curve can be obtained using the least squares method with help of Lagrange multipliers and some properties of generalized inverses. From this result, the degree-reduced control points with fixed endpoints can be represented in terms of the least squares degree-reduced control points without endpoints continuity and the original control points.

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