Hermite interpolation by piecewise polynomial surfaces with rational offsets. (English) Zbl 0938.68123

Summary: 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.


68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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