Abstract : We define quasi-speed as a generalization of linear speed and angular speed for parameterizations of curves and use the uniformity of quasi-speed to measure the quality of the parameterizations. With such conceptual setting, a general framework is developed for studying uniformity behaviors under reparameterization via proper parameter transformation and for computing reparameterizations with improved uniformity of quasispeed by means of optimal single-piece, C 0 piecewise, and C 1 piecewise Möbius transformations. Algorithms are described for uniformity-improved reparameterization using different Möbius transformations with different optimization techniques. Examples are presented to illustrate the concepts, the framework, and the algorithms. Experimental results are provided to validate the framework and to show the efficiency of the algorithms.