线面体布尔运算的模糊逻辑方法

Fuzzy Logic Method of Boolean Operations Between Lines,Faces and Solids

本文推广第二作者建立色觉机制数学模型时发明的一种连续值逻辑方法──模糊开关准布尔代数，得到了线面体混合布尔函数──若干个互不相交的子区域──边界的求解方法；这种方法用布尔代数公式和ｍａｘ、ｍｉｎ运算代替复杂的条件判断，具有可靠性、通用性和简洁性。文中介绍了求解的一般方法，讨论了立体布尔函数的体积计算和截面显示等问题。

Extending a fuzzy logic method-fuzzy switching quasi-Boolean algebra-in vented for building a mathematical model of colour vision by the second author, this paper provides the solution of boundaries of a Boolean function, which includes severaldisjoint sub-fields, of lines, faces and, solids mixed together. This solution replacescomplicated conditional judgments with Boolean algebra formulas and operations:maximum and minimum. It has reliability, generality, and simplicity. This paper introducesthe general methods of the solution, discusses the problems of volume calculation andsectional drawing of the Boolean function of solids and the others.