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 G1 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.
B., J., Sampoli, M.L. (2000). Hermite interpolation by piecewise polynomial surfaces with rational offsets. COMPUTER AIDED GEOMETRIC DESIGN, 17(4), 361-385 [10.1016/S0167-8396(00)00002-9].
Hermite interpolation by piecewise polynomial surfaces with rational offsets
SAMPOLI, MARIA LUCIA
2000-01-01
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 G1 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.
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https://hdl.handle.net/11365/38029
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