Multi-degree reduction of Bézier curves using reparameterization

L₂-norms are often used in the multi-degree reduction problem of Bézier curves or surfaces. Conventional methods on curve cases are to minimize , where and are the given curve and the approximation curve, respectively. A much better solution is to minimize , where is the closest point to point , that produces a similar effect as that of the Hausdorff distance. This paper uses a piecewise linear function L(t) instead of t to approximate the function φ(t) for a constrained multi-degree reduction of Bézier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods.