Iterative mesh generation for FE‐computations on free form surfaces

Abstract

Presents an interpolatory subdivision scheme to generate adaptively refined quadrilateral meshes which approximate a smooth surface of arbitrary topology. The described method differs significantly from classical mesh generation techniques based on spline surfaces or implicit representations since no explicit description of the limit surface is used. Instead, simple affine combinations are applied to compute new vertices if a face of the net is split. These rules are designed to guarantee asymptotic smoothness, i.e. the sequence of refined nets converges to a smooth limit surface. Subdivision techniques are useful mainly in applications where a given quadrilateral net is a coarse approximation of a surface and points on a refined grid have to be estimated. To evaluate the proposed approach, shows examples for FE‐computations on surfaces generated by this algorithm.

Citation

Kobbelt, L., Hesse, T., Prautzsch, H. and Schweizerhof, K. (1997), "Iterative mesh generation for FE‐computations on free form surfaces", Engineering Computations, Vol. 14 No. 7, pp. 806-820. https://doi.org/10.1108/02644409710188736