Local refinement of ERBS curves

Abstract

Expo-rational B-splines (ERBS) provide a blending type construction where local functions at each knot are blended together by infinitely smooth basis functions. In this work we consider some specific ERBS curves that are approximations of parametric curves. We study local refinement to increase flexibility by inserting local control curves at points of interest on the ERBS curve. Inserting knots into an existing B-spline knot vector results in a new spline space which contains the original spline space as a sub-space. In contrast to B-splines, knot insertion with ERBS results in a rational local function. We investigate methods to generate local curves of different brands. Using this, we blend extra local curves with the original ERBS curve, by knot insertion, and compare the differences with respect to geometric shape and approximation errors.