Theory of constructing closed parametric curves based on manifolds
| Autor: | YU Xiao-li, Gao Bin, HU Shu-gen, Song Xiao-wen |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Sharp angle
Mathematical analysis Cad system Manifold Mathematics::Numerical Analysis Electronic Optical and Magnetic Materials Unit circle Base function Electrical and Electronic Engineering Parametric equation ComputingMethodologies_COMPUTERGRAPHICS Parametric statistics Mathematics Knot (mathematics) |
| Zdroj: | Frontiers of Electrical and Electronic Engineering in China. 1:451-454 |
| ISSN: | 1673-3584 1673-3460 |
| DOI: | 10.1007/s11460-006-0086-0 |
| Popis: | A parametric curve based on a manifold is designed for constructing an accurate closed curve. A circle was defined as the parametric space and a non-uniform B-splines defined on the unit circle were used as base functions. A method to construct knot vectors, control points and corresponding parameters were proposed. A method to determine the coordinates for any point on a curve was also proposed. Some non-uniform rational B-splines (NURBS) control techniques, such as curves with an embedded line, a sharp angle, and so on, were used to verify the proposed method’s compatibility with NURBS. Some examples were used to compare the arithmetic with that of NURBS. The results show that the method is not only simple, feasible and reliable but also compatible with a CAD system using NURBS. |
| Databáze: | OpenAIRE |
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