Optimization of set operations on triangulated polyhedrons using adaptive lazy splitting

Regularized Boolean operations have been widely used in 3D modeling systems. In recent years, Boolean algorithms based on triangular polyhedron show the distinct advantages aligning with the development of graphic hardware, as their outputs can be processed by graphic hardware directly. But most existing methods rely on localized evaluation strategy over constructive solid geometry (CSG) tree perform regularized set operations. As a result, these methods cannot guarantee robustness while synchronously keeping high efficiency, because a facet may repeatedly split up in the splitting phase and the facets classification is carried out between the split polyhedrons by triangulation. In this paper, a novel algorithm is presented to realize robust, exact and fast regularized Boolean operations through global evaluation of CSG tree. The algorithm is comprised of two steps: adaptive lazy splitting and globalized facets classification. The two steps aim to optimize splitting and facets classification phases of the regularized Boolean algorithms on triangulated polyhedrons respectively. In the adaptive lazy splitting phase, a lazy splitting strategy is applied to the whole CSG tree by coping with all intersection cases of triangular facets in order to eliminate the accumulation of number errors. In the meantime, an adaptive octree is employed to speed up the intersection test process. In the globalized facets classification phase, to ensure the accuracy of classification, the classification method is always executed between the split facet and the original input polyhedrons by divide and conquer algorithm. The performance of classification is further optimized by combining the grouping classification strategy and the octree. Experimental results demonstrate that the proposed approach cannot only guarantee the robustness of Boolean computations but also achieve better performance than existing approaches. Thus, the algorithm offers wide-ranging usage in for interactive modeling systems, such as digital sculpture, and CAD/CAM.