Reparametrization and its application in computer‐aided geometric design

Abstract The paper develops the theory of reparametrization within the context of computer‐aided geometric design. It is established that the parametrization plays a positive role in the numerical description of curves and surfaces and it is proposed that the parametrization should be controlled, independently from the shape, via reparametrization. A general approach to reparametrization is adopted in which a function to change the parametrization is modelled in addition to the basic parametric equation. Examples are given for parametric polynomial curves, probably the most commonly used curve segments in computer‐aided geometric design. Finally it is shown how reparametrization might be applied to enhance existing surface definition procedures. A surface equation is developed based on the parametric cubic segment that can define shapes virtually independent of the parametrization.