Three dimensional sphere analysis method of block theory

As one of the most useful analysis methods of block theory, stereographic projection is used to reduce the dimensions of the problem from three to two, thus analyzing and solving it with graph tools. However, the circle of the stereographic projection is not so intuitive and is hard to understand. In this paper, combined with computer graphics technology, a new method is proposed to analyze rock mass stability by three dimensional sphere pyramids of blocks directly. Furthermore, OpenGL is available to implement the rendering and human-computer interaction of the graphical analysis tools. Some examples are also provided for comparison between the new method and the traditional stereographic projection. The results indicate that the proposed method is easy to learn, and is a valuable development of block theory.