Abstract
In this paper we present a novel algorithm for the multi-degree reduction of Bézier curves with geometric constraints. Based on the given constraints, we construct an objective function which is abstracted from the approximation error in L2-norm. Two types of geometric constraints are tackled. With the constraints of G2-continuity at one endpoint and G1-continuity (or Cr-continuity) at the other endpoint, we derive the optimal degree-reduced curves in explicit form. With the constraints of G2-continuity at two endpoints, the problem of degree reduction is equivalent to minimizing a bivariate polynomial function of degree 4. Compared with the traditional methods, we derive the optimal degree-reduced curves more effectively. Finally, evaluation results demonstrate the effectiveness of our method.
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