Boolean operations between triangle meshes

Boolean operations between triangle meshes is an important and common operation in computer graphics and computational geometry. The purpose of this operation is to compute the intersection, union or difference of two given triangle meshes. These operations are widely used in various applications, such as computer-aided design, geometric modeling, virtual reality, and computer gaming.

To perform Boolean operations between triangle meshes, several algorithms have been proposed in the literature. The most popular approaches are the boundary representation (B-rep) based methods and the constructive solid geometry (CSG) based methods. In the B-rep based methods, the triangle meshes are represented as a set of faces, edges and vertices, and the Boolean operation is performed by manipulating the topology of these elements. In the CSG based methods, the Boolean operation is performed by combining the geometric primitives that are used to construct the meshes, such as planes, spheres, cones, cylinders and tori.

One of the challenges in performing Boolean operations between triangle meshes is the robustness and efficiency of the algorithms. The input meshes may contain topological and geometric degeneracies like self-intersections, degenerate triangles, holes, and concavities, which may cause numerical instabilities and even infinite loops in the algorithms. Moreover, the output meshes may also have topological and geometric redundancies like isolated vertices, edges, and faces, which need to be removed to obtain a valid and clean mesh.

To address these challenges, many researchers have proposed different techniques for improving the robustness and efficiency of Boolean operations between triangle meshes. Some of these techniques include using adaptive floating-point precision, mesh simplification and regularization, topological healing and repair, and error control and tolerance techniques.

In conclusion, Boolean operations between triangle meshes is a fundamental task in computer graphics and computational geometry. The B-Rep based and CSG based methods are the most popular techniques for performing these operations. However, due to the complexity and variability of the input meshes, the algorithms require careful attention to robustness and efficiency.