@article{5715add04db545888596b939d7643b69, title = "Multi-degree reduction of B{\'e}zier curves using reparameterization", abstract = "L2-norms are often used in the multi-degree reduction problem of Bzier curves or surfaces. Conventional methods on curve cases are to minimize ∫01∥A(t)-C(t)∥2dt, where C(t) and A(t) are the given curve and the approximation curve, respectively. A much better solution is to minimize ∫01∥A(φ(t))- C(t)∥2dt, where A(φ(t)) is the closest point to point C(t), 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 Bzier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods. {\textcopyright} 2010 Elsevier Ltd. All rights reserved.", keywords = "Bzier curves, L2-norm, Multi degree reduction, Reparameterization", author = "Xiao-Diao Chen and Weiyin Ma and Jean-Claude Paul", year = "2011", month = feb, doi = "10.1016/j.cad.2010.11.001", language = "English", volume = "43", pages = "161--169", journal = "CAD Computer Aided Design", issn = "0010-4485", publisher = "Pergamon Press", number = "2", }