Design And Implementation Of Algorithms For Curve Reparameterization

Curves and surfaces are the main objects studied heavily in computer-aided geometric design.Curve parameterization theory is driven by the demand in practice and industry.In order to make the parametric curve applied in practice,researchers design many algorithms for parameterizing the curve using the theory of high-reliability computation.This paper focuses on how to find an optimal linear transformation to reparameterize a given rational curve so that the parametric curve after reparameterization can meet the actual demand.And a related software package was designed to analyze the technical problems encountered in the design and implementation process,and the corresponding solutions were given.The algorithm framework of this paper is based on the uniform quasi-speed reparameterization algorithm and discusses the spatial parameter curve.The core of algorithms is to find the reparameterization of a given curve by using M?bius transformation and piecewise M?bius transformation.Furthermore,based on the algorithm framework,a software package ImUp+ can be implemented to calculate the spatial parameter curve uniform quasi-speed reparameterization(including the curve linear velocity,angular velocity,torsion speed reparameterization).Finally,experiment results show that ImUp+ can be used to reparameterize plane/space curves upon different optimization standard and the reparameterized curve shows better property than the original curves.The plottings generated with these reparameterizations are smoother than those generated by the original curves.