UVMAP is a library that can be used to generate a U,V coordinate map for an unstructured tria-face surface mesh with bounding curves in X,Y,Z physical space. It uses a coupled bi-harmonic method with pseudo-orthogonal boundary-conditions to generate the U,V map. AFLR4 unstructured surface mesh generation uses the UVMAP library. A stand-alone testing executable for UVMAP is available.