A Balanced Surface Parameterization Method and Its Application to Spline Fitting

Surface parameterization refers to the process of mapping a surface into a canonical domain. The goal of parameterization is to minimize geometric distortions, which can be classified as angle and area distortions. Unfortunately, in general it is impossible to achieve both angle-preserving and area-preserving parameterization. This work proposes a novel balanced parameterization method which could produce results with good balancing between the two distortions. This method is rigorous in theory and moderate in computation. Surface parameterization is a fundamental step of spline fitting. This work in further studies the spline fitting results which are respectively based on angle-preserving, area-preserving and different balanced parameterization. The experiment shows that by using balanced parameterization one could improve the spline fitting quality, and demonstrates the efficiency and efficacy of the proposed method.