A simple and robust approach to computation of meshes intersection

Triangular meshes are important in many fields in both basic and applied research that rely on their correctness and accuracy. Many operations with meshes can lead to undesirable situations and the resulting models can be damaged and further unusable. Self-intersection and mesh-to-mesh intersection are types of operations that are often present and can cause such problems. We propose an accurate geometry-based method for local repair of intersecting meshes. The state-of-the-art methods either solve the problem inaccurately, or use methods such as arbitrary precision arithmetic or virtual perturbation to deal with the troublesome boundary cases. Our method represents a robust way to repair intersecting meshes accurately without the need to manipulate with the input data or to employ arbitrary precision arithmetic. The correct solution is obtained through a careful classification of the cases that could result from a numerical imprecision of the floating point arithmetic.