Block collapse or sliding is one of the main failure modes of rock slope engineering. Namely, block stability analysis plays a key role in rock slope engineering. Taking the Shenxianju rock slope in Xianju County, Zhejiang Province as the research background, this paper mainly conducts the stability analysis and visualization of rock blocks. A new method for fitting structural planes and free faces is proposed based on the linear regression method and the non-uniform rational B-spline method. Then, based on the coordinate projection method, the method for calculating the stability coefficients of the single sliding surface and double sliding surface blocks is proposed. Finally, the unmanned aerial vehicle (UAV) measurement technology combined with the coordinate projection method is used to develop a CPG program using MATLAB, which can be adopted in the stability analysis of planar polyhedron blocks and curved blocks in rock slope engineering. This program enables the spatial representation and visualization of structural planes, free faces and unstable blocks. Engineering practice shows that the new proposed method is effectively applicable to engineering geological disasters, such as rockfall and collapse. The results of the program calculation are basically consistent with those of the coordinate projection block theory, demonstrating that this method is reliable and the developed CPG program is feasible. This method is of vital significance in practical engineering since it can greatly improve the efficiency of block stability analysis.