| Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations |
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| 引用本文： | 阿孜古丽·吾拉木,GOETTING Marc,ZECKZER Dirk. Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations[J]. 清华大学学报, 2005, 10(3) |
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| 作者姓名： | 阿孜古丽·吾拉木 GOETTING Marc ZECKZER Dirk |
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| 作者单位： | School of Information Engineering，University of Science and Technology Beijing，Beijing 100083，China，School of Information Science and Engineering，University of Xinjiang，Urumq 830046，China，Department of Computer Science，University of Kaiserslautern，D-6753，Germany，Department of Computer Science，University of Kaiserslautern，D-6753，Germany |
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| 基金项目： | Supported by the Company ProCAEss GmbH, Landau in der Pfalz, Germany |
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| 摘 要： | Introduction Curves and surfaces can be represented using coefficients and a set of basis functions[1]. In the following, only curves are considered, but all statements apply equally to surfaces. Different representations use different sets of basis functions. These basis functions can be, for example, polynomials for polynomial curves, Bernstein-polynomials for Bézier curves, or B-spline basis functions for B-spline curves. As long as the general representation is of the form: 0( ) ( )ni i…
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Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations |
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| Aziguli Wulamu ,,GOETTING Marc,ZECKZER Dirk . School of Information Engineering,University of Science and Technology Beijing,Beijing ,China, . School of Information Science and Engineering,University of Xinjiang,Urumq ,China. Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations[J]. Tsinghua Science and Technology, 2005, 10(3) |
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| Authors: | Aziguli Wulamu GOETTING Marc ZECKZER Dirk . School of Information Engineering University of Science Technology Beijing Beijing China . School of Information Science Engineering University of Xinjiang Urumq China |
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| Affiliation: | Aziguli Wulamu 1,2,GOETTING Marc3,ZECKZER Dirk3 1. School of Information Engineering,University of Science and Technology Beijing,Beijing 100083,China, 2. School of Information Science and Engineering,University of Xinjiang,Urumq 830046,China, 3. Department of Computer Science,University of Kaiserslautern,D-6753,Germany |
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| Abstract: | Non-uniform rational B-spline (NURBS) curves and surfaces are very important tools for model- ling curves and surfaces. Several important details, such as the choice of the sample points, of the parame- terization, and of the termination condition, are however not well described. These details have a great in- fluence 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: equi- distant and chordal. A new and local parameterization, namely an adaptive equidistant model, was pro- posed, 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. |
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| Keywords: | computer graphics computer-aided design (CAD) computer-aided geometric design (CAGD) NURBS curves NURBS surfaces approximation implementation |
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