Modern database applications including computeraided design (CAD), medical imaging, or molecular biology impose new requirements on spatial query processing. Particular problems arise from the need of high resolutions for very large spatial objects, including cars, space stations, planes and industrial plants, and from the design goal to use general purpose database management systems in order to guarantee industrial-strength. In the past two decades, various stand-alone spatial index structures have been proposed but their integration into fully-fledged database systems is problematic. Most of these approaches are based on decomposition of spatial objects leading to replicating index structures. In contrast to common black-and-white decompositions which suffer from the lack of intermediate solutions, we introduce grey approximations as a new and general concept. We demonstrate the benefits of grey approximations in the context of encoding spatial objects by space filling curves resul...