曲面的GC^k拼接条件

The Condition for Blending Algebraic Surfaces with GC k Continuity

在一定的基本假设下，若Ｓ（ｈ１）≠Ｓ（ｈ２）≠Ｓ（ｈ３），得到了存在一个ｐ次多项式ｆ，使曲面Ｓ（ｆ）分别与Ｓ（ｇｉ）在Ｓ（ｇｉ，ｈｉ）（ｉ＝１，２，３）处ＧＣｋ光滑拼接的充要条件为存在ｐ－ｍ次多项式ｗ１，ｐ－ｎ次多项式ｗ２，ｐ－ｌ次多项式ｗ３，以及多项式ａｉ（ｉ＝１，２，３）使得ｗ１ｇ１－ｗ２ｇ２＝ａ２ｈｋ＋１２－ａ１ｈｋ＋１１∈〈ｈｋ＋１１，ｈｋ＋１２〉ｗ２ｇ２－ｗ３ｇ３＝ａ３ｈｋ＋１３－ａ２ｈｋ＋１２∈〈ｈｋ＋１２，ｈｋ＋１３〉｛从而将ＧＣｋ拼接问题的复杂运算化简成了一个简单的线性方程组。

Under a basic hypothesis, a condition for blending algebraic surfaces with GC k continuity is given. Assume that S(h 1)≠S(h 2)≠S(h 3) , then there exists polynomial f with degree p if and only if there exists polynomials w 1 of degree p-m,w 2 of degree p-n and w 3 of degree p-l , sush thatw 1g 1-w 2g 2=a 2h k+1 2-a 1h k+1 1∈〈h k+1 1,h k+1 2〉 w 2g 2-w 3g 3=a 3h k+1 3-a 2h k+1 2∈〈h k+1 2,h k+1 3〉wlere a i (i=1,2,3) is also polynomials. It reduces complicated symbol computation for GC k blending to a very simple liner system.