Computation of topological and geometric properties of iso-surfaces .1. Theory and numerical method

A numerical method for the computation of topological and geometric properties of iso-surfaces with and without boundaries is developed. It is based on triangulation and provides the Euler characteristic, the number of disjoint surface parts and geometric properties such as surface area and integrals of vector and tensor fluxes over the surface. A quantitative measure for the intrinsic topology of level surfaces is constructed using the Euler number, that is suitable for solutions of the Navier-Stokes equations. The numerical accuracy of the method is shown to be satisfactory.