3个二次曲面沿平面截口的光滑拼接

为了扩大现有曲面拼接计算方法的应用范围，在不考虑二次控制曲面存在条件的情况下，将3个二次曲面沿平面接口的拼接曲面的存在性转化为求相应的齐次线性方程组非零解的存在性问题．给出了三次和四次拼接曲面存在的条件，即它们的线性方程组的系数矩阵的秩分别小于24和60，证明了五次拼接曲面一定存在，并且给出了拼接曲面的计算方法。

Smoothly Blending of Three Quadratic Algebraic Surfaces along Planar Sections

To expand the suitable conditions of the present blending methods, the problem of blending three quadratic algebraic surfaces along planar sections was transformed into a problem of ascertaining the existence of nonzero solution of homogeneous linear equations corresponding to these three quadratic algebraic surfaces under the condition without considering the existence of quadratic control surfaces. The existence conditions of cubic and quartic blending surfaces were given, i. e. , the ranks of the coefficient matrixes of their linear equations are less than 24 and 60 respectively, and the unconditioned existence of quintic blending surfaces was proved. Finally, the corresponding blending algorithm was presented.