It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of curves.
Sampoli, M.L., Peternell, M., Juettler, B. (2006). Rational surfaces with linear normals and their convolutions with rational surfaces. COMPUTER AIDED GEOMETRIC DESIGN, 23(2), 179-192 [10.1016/j.cagd.2005.07.001].
Rational surfaces with linear normals and their convolutions with rational surfaces
SAMPOLI, MARIA LUCIA;
2006-01-01
Abstract
It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of curves.
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https://hdl.handle.net/11365/18776
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