A kind of Boolean operational method based on a three-dimensional grid model was proposed. Firstly, through collision detection algorithm based on hierarchical bounding box tree of Oriented Bounding Box (ORB), the intersecting triangles could be got. Through the intersection test of the triangles, the intersecting lines could be obtained and the intersecting lines topology relations with the triangles could be established. Secondly, a regional division for the intersecting triangles was made through processing the three types of intersecting lines, so as to get a series of polygons, and carry out Delaunay triangulations for polygon to get the result area. Lastly, relation adjacency list was constructed based on solid containing relations, the polygons internal relation and external relation with other entities were judged, and the triangles were located according to the mesh model topology relations. Simultaneously, according to such Boolean operations as the intersection, union, and differences, according to the grid model topology relations were judged, the position of the triangles were judged and then the final results could be obtained. Experimental results show that this algorithm can achieve better results. Experimental results show that the lithology of intersecting parts is consistent with the entities and can verify the correctness and feasibility of the algorithm.

Petri net is an effective mathematical tool for formally analyzing and verifying protocols. On the basis of the analysis of Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol, a Generalized Stochastic Petri Nets (GSPN) model of performance for LEACH protocol was proposed. With the help of SPNP tools for analyzing the performance model of protocol, the validity of the model was verified. Finally, the significance of the performance model to the protocol's low-energy improvement was discussed.