基于Sylvester结式消元低次拼接条件的研究

Research of lower degree condition for blending surface based on Sylvester resultant

根据拼接中的主曲面和辅助曲面方程,利用同伦映射方法构造出含有单位区间变元的代数方程,应用Sylvester结式方法消去变元得到拼接曲面表达式。然后,假设该曲面表达式能够进行因式分解,分析G0和G1次光滑拼接中拼接曲面的次数最低时辅助曲面S(hi)应满足的条件。最后,运用Grobner基理论判断分解因式后各因式是否在主曲面和辅助曲面生成的理想中,从而得出符合条件的低次拼接曲面。

According to the algebraic surihces and their auxiliary surface in blending, by using the homotopy mapping method to get the unit interval variables, the variable with the Sylvester resultant method is used to get the blending surface expression. The Sylvester elimination method of reverse assuming the expressions is assumed to have factorization, the condition that auxiliary surface S（hi） should satisfy the conditions of the minimum number of surfaces is analyzed when G0 and G1 smooth connection has shortest times in blending. Then by using Grobner theory to judge whether or not the the ideal factored polynomial is produced, thus the low degree blending surface meeting the eonditionsis.