Hermite interpolation by piecewise polynomial surfaces with rational offsets

Abstract

We present a construction for polynomial spline surfaces with a piecewise linear field of normal vectors. As main advantageous feature these surfaces possess exact rational offsets. The spline surface is composed of quartic Clough–Tocher-type macro elements. Each element is capable of matching boundary data consisting of three points with associated normal vectors. The collection of the macro elements forms a G 1 continuous spline surface. With the help of a reparamaterization technique we obtain an exact rational representation of the offset surfaces by rational triangular spline surfaces of degree 10.