Fast, Exact and Robust Set Operations on Polyhedrons Using Localized Constructive Solid Geometry Trees

• Published in: 中兴通讯技术（英文版） Vol. 13; no. 3; pp. 57 - 66
• Main Author: Ping Lu Xudong Jiang Wei Lu Ran Wei Bin Sheng
• Format: Journal Article
• Language: English
• Published: ZTE Corporation, Nanjing 210012, China%Autodesk China Research & Development Center, Shanghai 200061, China%Shanghai Jiao Tong University, Shanghai 200240, China 2015
• Subjects: CSG树; 几何树; 分而治之算法; 多面体; 局部构造; 布尔运算; 构造实体几何; 集合运算; Boolean operations; constructive solid geometry; binary space partitioning tree; polyhedrons
• ISSN: 1673-5188
• DOI: 10.3969/j.issn.1673??5188.2015.03.007

Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel and unified technique is proposed in this paper for computing single and iterated set operations efficiently, robustly and exactly. An adaptive octree is combined with a nested constructive solid geometry （CSG） tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actually occurs. Within those cells, a CSG tree template is instanced by the surfaces and the tree is converted to planebased binary space partitioning （BSP） for set evaluation; Moreover, the surface classification is restricted to the ceils in the octree where the surfaces only come from a model and are within the bounding-boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the operations, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are classified as a whole. Robustness and exactness are achieved by integrating plane-based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide-and-conquer arithmetic on surface classification. Experimental results demonstrate that the proposed approach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.