G^1 Continuous Condition of B-Spline Surfaces with Double Knots  

具有重结点的B-样条曲面G^1的连续条件(英文)

作　　者：赵岩[1] 施锡泉[2] 

机构地区：[1]大连民族学院应用数理系,辽宁大连116600 [2]大连理工大学应用数学系,辽宁大连116024

出　　处：《Journal of Mathematical Research and Exposition》2005年第2期211-226,共16页数学研究与评论（英文版）

基　　金：973 Foundation of China (G19980306007) National Natural Science Foundation of China (G1999014115, 60473108) Outstanding Young Teacher Foundation of Educational Department of China (60073038) Doctoral Program Foundation of Educational Department of China.

摘　　要：The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.本文得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G1光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G1光滑造型.

关 键 词：B-spline surface patches double knots geometric continuity. 

分 类 号：O186.12[理学—数学]