We introduce the feature rejection algorithm for meshing (FRAM) to generate a high quality conforming Delaunay triangulation of a three-dimensional discrete fracture network (DFN). The geometric features (fractures, fracture intersections, spaces between fracture intersections, etc.) that must be resolved in a stochastically generated DFN typically span a wide range of spatial scales and make the efficient automated generation of high-quality meshes a challenge. To deal with these challenges, many previous approaches often deformed the DFN to align its features with a mesh through various techniques including redefining lines of intersection as stair step functions and distorting the fracture edges. In contrast, FRAM generates networks on which high-quality meshes occur automatically by constraining the generation of the network. The cornerstone of FRAM is prescribing a minimum length scale and then restricting the generation of the network to only create features of that size and larger. The process is f...