Surface description accuracy is of paramount importance when modelling contact problems. However, most FEM researchers still resort to polyhedral models to describe contact surfaces, which can oversimplify the original system by neglecting the curvature. To try to bridge this gap between CAD and CAE models, Nagata (2005) proposed a simple algorithm for interpolating discretized surfaces and recover the original geometry. In this work the Nagata patches algorithms are applied to interpolate polyhedral meshes of simple geometries (cylinder, sphere and torus), using the normal vector...