| Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterlzatlons |
| |
| 摘 要： | Non-uniform rational B-spline (NURBS) curves and surfaces are very important tools for modelling curves and surfaces. Several important details, such as the choice of the sample points, of the parameterization, and of the termination condition, are however not well described. These details have a great influence on the performance of the approximation algorithm, both in terms of quality as well as time and space usage. This paper described how to sample points, examining two standard parameterizations: equidistant and chordal. A new and local parameterization, namely an adaptive equidistant model, was proposed, which enhances the equidistant model, Localization can also be used to enhance the chordal parameterizatfon, For NURBS surfaces, one must choose which direction will be approximated first and must pay special attention to surfaces of degree 1 which have to be handled as a special case.
|
| 关 键 词： | NURBS曲线 NURBS表面 计算机制图 计算机辅助设计 CAD 近似值 |
| 收稿时间： | 6 June 2004. |
Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations |
| |
| Authors: | Wulamu Aziguli ¼í&#x; Marc Goetting Dirk Zeckzer |
| |
| Institution: | aSchool of Information Engineering, University of Science and Technology Beijing, Beijing 100083, China;bSchool of Information Science and Engineering, University of Xinjiang, Urumq 830046, China;cDepartment of Computer Science, University of Kaiserslautern, D-6753, Germany |
| |
| Abstract: | Non-uniform rational B-spline (NURBS) curves and surfaces are very important tools for modelling curves and surfaces. Several important details, such as the choice of the sample points, of the parameterization, and of the termination condition, are however not well described. These details have a great influence on the performance of the approximation algorithm, both in terms of quality as well as time and space usage. This paper described how to sample points, examining two standard parameterizations: equidistant and chordal. A new and local parameterization, namely an adaptive equidistant model, was proposed, which enhances the equidistant model. Localization can also be used to enhance the chordal parameterization. For NURBS surfaces, one must choose which direction will be approximated first and must pay special attention to surfaces of degree 1 which have to be handled as a special case. |
| |
| Keywords: | computer graphics computer-aided design (CAD) computer-aided geometric design (CAGD) NURBS curves NURBS surfaces approximation implementation |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
