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| B样条曲面在严格约束状态下的光顺拟合 |
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王国瑾1,2, 王振武1,2, 寿华好1,2
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1.浙江大学CAD&CG国家重点实验室,杭州,310027;2.浙江大学应用数学系,杭州,310027
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| 摘要: |
| 提出一种新的B样条曲面造型方法:光顺地拟合空间型值点且同时严格地通过其中部分点.运用Lagrange乘子的条件极值法并引入光顺加权项，求出位置偏离和形状弯曲的最小二乘解，可以得到被称为B样条光顺准拟合的良好造型曲面.这一方法在包含门窗的交通工具外壳曲面设计、机械产品装配联接件制造中具有明显的实用价值. |
| 关键词: 曲线拟合，曲面拟合，插值，数据光顺，B样条，条件极值. |
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| 基金项目:本文研究得到国家自然科学基金资助. |
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| Smooth Fitting of B-Spline Surfaces with Strict Interpolation Conditions |
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WANG Guo-jin,WANG Zhen-wu,SHOU Hua-hao
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| Abstract: |
| In this paper, the authors present a new B-spline surface modelling method which fairly fits 3D data points while at the same time strictly interpolates some of them. By using Lagrange multiplier's conditional extreme method, introducing fairness weights and finding the least squares solutions of position deviation and shape curvature, some B-spline fair quasi-fitting modelling surfaces can be obtained. This method obviously has some practical applications in designing outer shell surfaces of transportation tools with windows and gates, or in manufacturing assembled/joined parts of mechanical productions. |
| Key words: Curve fitting, surface fitting, interpolation, smoothing of data, B-spline, conditional extremum. |
