极射赤平投影中的数学方法

本文提供了严格依据赤平投影原理并利用空间解析几何知识推导出的公式计算方法，可以写出已知产状的线或面的赤平投影方程，也能计算两线所共的面，两面的交线，线或面之间的夹角以及它们的平分线或平分面，可以进行真倾斜和视倾斜的换算，倾斜和侧伏的换算；模拟线面绕轴的旋转以及恢复节理的原始产状；最后阐述用计算机进行节理统计和绘制极点等密图的原理。所用的向量表示方法直观表达了相关构造要素之间的空间关系，可用于计算机辅助教学，也能用于生产实践，精度可达0.01°。

ARITHMETIC METHOD IN POLAR STEREOGRAPHIC PROJECTION

According to basic principles of polar stereographic projection, a formula calculation method is introduced in this paper by using spatial analytical geometry knowledge. It can take the place of hand-operation and get more accurate results. For instance, it can draw projection curve on computer screen while its equation had been referred from its attitude; it can get the attitude of the co-plane between two lines or the intersect line of two planes; it can calculate the interangle and the bisectrix of two lines or two planes; it can perform the transition between apparent dip and true dip or between dip and pitch; it can model the rotation of a line or plane around 8n axis, so the original attitude of a joint can be recovered. The last part of the paper is about the computer algorithm of joint intensity statistics and the iso-intensity diagramming. This method directly shows the relationship between structural factors so that it can be used for computer Aided Instruction(CAI). It also makes satisfactory application in practice because its accuracy reaches 0.0l℃.