This talk will describe the application of numerical algebraic geometry to decompose an almost smooth real algebraic surface into a cell structure consisting of faces, edges, and vertices. The algorithm starts with a witness set for a complex surface and returns a decomposition of the real surface contained therein. Noncompact surfaces are treated by casting them into projective space. The method has applications in robot workspace studies and mechanism design. This is joint work with G.-M. Besana, S. Di Rocco, J. Hauenstein, and A. Sommese.