Exact fast parallel intersection of large 3-d triangular meshes. We present 3D-EPUG-Overlay, a fast, exact, parallel, memory-efficient, algorithm for computing the intersection between two large 3-D triangular meshes with geometric degeneracies. Applications include CAD/CAM, CFD, GIS, and additive manufacturing. 3D-EPUG-Overlay combines five separate techniques: multiple precision rational numbers to eliminate roundoff errors during the computations; Simulation of Simplicity to properly handle geometric degeneracies; simple data representations and only local topological information to simplify the correct processing of the data and make the algorithm more parallelizable; a uniform grid to efficiently index the data, and accelerate testing pairs of triangles for intersection or locating points in the mesh; and parallel programming to exploit current hardware. 3D-EPUG-Overlay is up to 101 times faster than LibiGL, and comparable to QuickCSG, a parallel inexact algorithm. 3D-EPUG-Overlay is also more memory efficient. In all test cases 3D-EPUG-Overlay’s result matched the reference solution. It is freely available for nonprofit research and education at ttps://