Fast and Robust Method for Boolean Operations on Triangulated Solids Based on Signed Octree

In this paper, a fast and robust method for Boolean operations on triangulated solids is presented. It is applied to regularized Boolean operations including union, difference, and intersection. This approach is less time costing because a signed Octree and several optimizations are introduced in the algorithm. The operation starts with the minimum bounding box of the models to form the root node of the Octree, which is then continuously divided into sub-nodes, until triangles in each sub-node only have a number of triangles from both meshes, or the sub-node reaches a certain depth. After the Octree division, we run a traverse of the Octree to calculate intersection points between two meshes. This only occurs with triangles from each mesh in the very bottom sub-node of the Octree. With an in/out sign addicted to triangle’s data structure, the final facet selection process is greatly simplified. The computational complexity is highly reduced through this method with the accuracy remains to the same level. This hierarchical Octree based method enables us to do Boolean calculation on very complex models. In the end, we give some sample results and some comparisons with other algorithms and commercial software.