Least squares degree reduction of Bézier curves

Abstract In this paper we investigate the problem of reducing the degree of Bezier curves approximately from n to a prescribed target degree m whereby (parametric) continuity of any order ≤ m−1 2 can be preserved at the two endpoints. The computations are carried out by minimizing the (constrained) L2-norm between the two curves. In addition, a complete algorithm is given for performing the degree reduction within a prescribed error tolerance by help of subdivision. This work is an evident improvement on a previous paper (Eck M Comput.-Aided Geom. Des. Vol 10 (1993) pp 237–251) about degree reduction in the sense that the algorithm presented is faster and much easier to implement, while still producing very good results.

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