A framework for improving uniformity of parameterizations of curves

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.

Improving Angular Speed Uniformity by Piecewise Radical Reparameterization

“…By [13,Theorem 2], one can construct a uniform reparameterization from p, but such a reparameterization is irrational in most cases. Therefore, we proposed several methods in [4] to improve the angular speed uniformity by computing piecewise rational reparameterizations. However, those methods are not applicable to curves whose angular speed may vanish over [0, 1].…”

“…Uniform parameterization has been studied in a series of papers (see [4,6,8,11,14,13,12] and references therein). The authors have defined a function of angular speed uniformity to measure the quality of any given parameterization of a plane curve and proposed a method to compute its uniform reparameterization.…”

“…However, the computed reparameterization is irrational in most cases (with straight lines as exceptions). For the sake of efficiency, a framework has been proposed for the computation of rational approximations of uniform parameterizations [4]. Four different methods of reparameterization (i.e., optimal reparameterization with fixed degree, C 0 and C 1 optimal piecewise reparameterization, and nearly optimal C 1 piecewise reparameterization) have been integrated into this framework.…”

QoE-driven resource allocation for mobile IP services in wireless network

“…Therefore, it can be inferred that all VoIP users' MOS requirements would meet first if our goal is to maximize the system MOS value, FD users are the second to be considered, and IPTV users are usually the least thought out. To guarantee all the users' MOS at a relatively high level, we propose a multi-objective optimization problem in Subsection 2.2 [15,16], which aims at maximizing each user's MOS utility.…”

“…Procedures in [21] can be referred. Thus, by finding the maximum λ in (16), the optimal MOS utilities f k (p), k = 1, . .…”