构造代数Blending曲面的Grobner基方法.pdf

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1、第25卷第6期计算机学报VOl.25NO.62002年6月CINESEJ.COMPUTE'SJune2002构造代数Blending曲面的Gr6bner基方法娄文平冯玉瑜陈发来邓建松(中国科学技术大学数学系合肥230026)摘要利用代数几何中关于理想的Grbner基的理论~结合CAGD中的研究方法~对代数Blending曲面做了较为细致的研究~给出了用Grbner基构造代数Blending曲面的新方法.该方法能够求出所有满足要求的代数Blending曲面~并能给出其中次数最低的曲面.文中还讨论了如何利用代数曲面插值~

2、最小平方逼近的方法来选取合适的自由参数~以达到对代数Blending曲面进行形状控制的目的.最后给出了一个茶壶表面造型示例~以说明方法的有效性.关键词代数Blending曲面~Grbner基~自由参数~形状控制中图法分类号:TP391TheMethodofGr6bnerBasisforConstructingalgebraicBlendingsurfacesLOUWen-PingFENGYu-YuCENFa-LaiDENGJian-SOng(DePC7HenofMCheHCicS~UniUeSiyofScienceC

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