3D Objects Representation for Real-Time Boolean Operations - Plotnikov, I. E.; Kostyuk, D. I. (Automatic documentation and mathematical linguistics, 2025)
The paper presents a comparative analysis of methods for the representation of three-dimensional objects to perform real-time Boolean operations in the Unity game engine environment. Four main approaches are considered: polygonal representation based on constructive solid geometry (CSG), sign distance functions (SDF), voxel methods, and CAD-systems with boundary representation (B-Rep) and NURBS-surfaces. An experimental study of the performance of polygonal algorithms of Boolean operations and SDF functions based on ray-marching implementation is conducted. It is revealed that polygonal methods are characterized by high initial system construction costs, but they provide stable performance during long operations and preservation of transformation results. SDF functions demonstrate high-speed operations and flexibility in creating smooth transitions between objects but are limited in their application to long-term tasks due to the peculiarities of the computational model. The areas of effective application of each approach are identified: polygonal methods are recommended for tasks that require precise geometric control and integration with traditional graphics pipelines, while SDF functions are optimal for procedural generation, multilayer material rendering, and the creation of dynamic visual effects. The results of this study can be used in the development of interactive simulators, game applications and virtual reality systems.