Combining 3D shapes using operations like union, subtraction, and intersection can sometimes create geometrically invalid objects. These objects might have edges shared by more than two faces, vertices belonging to faces that don’t share an edge, or internal faces within a seemingly solid volume. For instance, subtracting a slightly smaller cube from a larger one, with a slight misalignment, could create thin, almost invisible internal faces or edges connected in unexpected ways.
The generation of these flawed shapes poses significant challenges in various 3D modeling applications. They can cause issues with rendering, mesh simplification, 3D printing, and other downstream processes that expect consistent, well-defined geometry. Understanding the potential for these problematic results is essential for robust 3D model creation and manipulation, dating back to the earliest days of solid modeling research.
