双三次B-样条曲面的G^1连续条件

G^1 Continuous Conditions of Bicubic B-spline Surfaces

非均匀有理 B-样条曲面 ( NURBS)是曲面构造的常用工具 ,是目前工业界曲面曲线表示的数学标准 .B-样条曲面尽管是一种特殊 NURBS,但在实际应用中是首选形式 .本文得到了关于两个双三次 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-样条曲面控制向量表示 .

NURBS is the industrial standard to represent curves and surfaces. B spline as a special of NURBS is the most often used method in the industrial world. In this paper, the necessary and sufficient conditions of G 1 continuity between two bicubic B spline surfaces patches are obtained, and the instrinsic conditions of control vectors of common boundary curves and presented. These conditions are directly represented by the control vectors of the two non uniform B spline patches.