Modelling of curves and surfaces in polarand

A new class of spline curves in polar coordinates has been presented in (SS anchez-Reyes, 1992) and independently considered in (de Casteljau, 1994). These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been provided. In particular an ad hoc algorithm of degree elevation for splines in polar coordinates is presented. On the basis of these results we propose a modelling system for NURBS curves and surfaces supplied with a modelling environment for spline curves and surfaces in polar, spherical, and mixed polar-Cartesian coordinates .