| GC^1约束的三角Bézier曲面降阶逼近研究 |
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| 引用本文： | 黄俊英,王相海.GC^1约束的三角Bézier曲面降阶逼近研究[J].计算机工程与应用,2009,45(11):196-198. |
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| 作者姓名： | 黄俊英 王相海 |
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| 作者单位： | 1.辽宁师范大学 计算机与信息技术学院，辽宁 大连 116029 ;2.浙江大学 CAD&CG国家重点实验室，杭州 310027 |
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| 基金项目： | 辽宁省自然科学基金（the Natural Science Foundation of Liaoning Province of China under Grant No.20072156）;辽宁省高等学校优秀人才支持计划（ No.RC-04-11 ）; 辽宁省教育厅科学技术研究项目（ No.20060486 ） |
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| 摘 要： | 研究给定的n次三角Bézier曲面在L2范数下的一次降多阶的逼近问题，给出了在无约束条件下的三角Bézier曲面降阶求解的详细过程，将降阶问题转化为非线性最优化问题求解，并将降阶过程与曲面的几何连续拼接结合在一起，给出了降阶同时满足GC^1拼接的实现过程。实验结果表明，该方法简单实用，降阶逼近效果好。
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| 关 键 词： | 三角Bézier曲面 降阶 GC1拼接 几何连续 |
| 收稿时间： | 2008-2-28 |
| 修稿时间： | 2008-4-24
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Investigation of approximate multi-degree reduction of triangular Bézier surfaces based on GC1 constraint |
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| HUANG Jun-ying,WANG Xiang-hai.Investigation of approximate multi-degree reduction of triangular Bézier surfaces based on GC1 constraint[J].Computer Engineering and Applications,2009,45(11):196-198. |
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| Authors: | HUANG Jun-ying WANG Xiang-hai |
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| Affiliation: | 1.College of Computer and Information Technology，Liaoning Normal University，Dalian，Liaoning 116029，China 2.State Key of CAD&;CG，Zhejiang University，Hangzhou 310027，China |
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| Abstract: | The approximate multi-degree reduction problem of triangular Bézier surface of degree n is researched by minimizing the defined distance function.A detailed process of the degree reduction for triangular Bézier surfaces is presented based on unconstraint，then the problem of multi-degree reduction is transformed into computational methods for nonlinear optimization.Through combining multi-degree reduction with geometric continuity of surfaces，a realized process of the degree reduction is presented based on GC1 constraint.Experimental results show that this algorithm is very efficient. |
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| Keywords: | triangular Bézier surfaces multi-degree reduction GC1 joining geometric continuity |
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