Hermite interpolation by piecewise polynomial surfaces with rational offsets

We present a construction for polynomial spline surfaces with a piecewise l inear field of normal vectors. As main advantageous feature these surfaces possess exact rational offsets. The spline surface is composed of quartic C lough-Tocher-type macro elements. Each element is capable of matching bound ary data consisting of three points with associated normal vectors. The col lection of the macro elements forms a G(1) continuous spline surface. With the help of a reparamaterization technique we obtain an exact rational repr esentation of the offset surfaces by rational triangular spline surfaces of degree 10. (C) 2000 Elsevier Science B.V. All rights reserved.