Our method transforms the graph of the surface mesh iteratively by changing the dual cycle structure until we get the surface mesh of a single hexahedron. Starting with a single hexahedron and reversing the order of the graph transformations, each transformation step can be interpreted as adding one or more hexahedra to the so far created hex complex. Given an arbitrary solid body, we first decompose it into simpler subdomains equivalent to topological balls by adding virtual 2- manifolds. Second, we determine a compatible quadrilateral surface mesh for all created subdomains. Then, in the main part we can use the core routine to build up a hex complex for each subdomain independently.
First results obtained for complex geometries are encouraging.