The management of spatial data in applications such as graphics and image processing, geography as well as computer aided design (CAD) imposes stringent new requirements on spatial database systems, in particular on efficient query processing of complex spatial objects. In this paper, we propose a two-level, multi-representation query processing technique which consists of a filter and a refinement level. The efficiency of spatial query processing is improved considerably using the following two design paradigms: first, divide and conquer, i.e. decomposition of complex spatial objects into more simple spatial components such as convex polygons, triangles or trapezoids, and second, application of efficient and robust spatial access methods for simple spatial objects. The most powerful ingredient in our approach is the concept of object decomposition. Applied to the refinement level of spatial query processing, it substitutes complex computational geometry algorithms by simple and fast algorithms for simple components. In this paper, we present four different decomposition techniques for polygonal shaped objects. The second part of the paper consists of an empirical performance comparison of those techniques using real and synthetic data sets. The four types of decomposition techniques are compared to each other and to the traditional approach with respect to the performance of spatial query processing. This comparison points out that our approach using object decomposition is superior to traditional query processing strategies.