Nagata patch interpolation using surface normal vectors evaluated from the IGES file

Abstract

This paper presents an algorithm to accurately evaluate the surface normal vector in any vertex of a finite element mesh, in order to be able to efficiently apply the Nagata patch interpolation as surface mesh smoothing method when solving contact problems. The proposed algorithm considers that the surface geometry is also described by trimmed NURBS surfaces, with input data available in IGES file format. For each mesh vertex, the proposed approach comprises the following three steps: surface global search, local search, and normal vector evaluation. In the global search procedure, all trimmed NURBS surfaces composing the geometric model are ordered by proximity to the vertex. After that, local search is performed to find both the correct NURBS surface and the local coordinates of the vertex, which are defined by its projection on the selected surface. The vertex normal vector is them determined based on the first derivatives of the NURBS surface at the projection point. To highlight the feasibility of the developed algorithm, a mesh smoothing example is presented, emphasising the influence of the vertex normal vector approximation on the interpolation accuracy.