|
|||||
|
|
On rationally supported surfaces |
|
| Authors: | Jens Gravesen Bert Jüttler Zbyn k &#x;ír |
| Affiliation: | aTechnical University of Denmark, Department of Mathematics, Kgs. Lyngby, Denmark bJohannes Kepler University, Institute of Applied Geometry, Linz, Austria cUniversity of West Bohemia, Faculty of Applied Sciences, Department of Mathematics, Plzeň, Czech Republic |
| Abstract: | We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions. In particular it is shown that odd rational support functions correspond to those rational surfaces which can be equipped with a linear field of normal vectors, which were discussed by Sampoli et al. (Sampoli, M.L., Peternell, M., Jüttler, B., 2006. Rational surfaces with linear normals and their convolutions with rational surfaces. Comput. Aided Geom. Design 23, 179–192). As shown recently, this class of surfaces includes non-developable quadratic triangular Bézier surface patches (Lávi?ka, M., Bastl, B., 2007. Rational hypersurfaces with rational convolutions. Comput. Aided Geom. Design 24, 410–426; Peternell, M., Odehnal, B., 2008. Convolution surfaces of quadratic triangular Bézier surfaces. Comput. Aided Geom. Design 25, 116–129). |
| Keywords: | Rational support function LN-surfaces Triangular quadratic Bézier surface patches |
| 本文献已被 ScienceDirect 等数据库收录！ | |