- The topology of polygonal meshes has a large impact on the performance of various geometric processing algorithms, such as rendering and collision detection algorithms. Several approaches for simplifying topology have been discussed in the literature. These methods operate locally on models, which makes their effect on topology hard to predict and analyze. Most existing methods also tend to exhibit various disturbing artifacts, such as shrinking of the input and splitting of its components. We propose a novel top-down method for topology simplification that avoids the problems common in existing methods. The method starts with a simple, genus-zero mesh that bounds the input and gradually introduces topological features by a series of carving operations. Through this process a multiresolution stream of meshes is created with increasing topologic level of detail. Following the proposed approach, we present a practical carving algorithm that is based on the Constrained Delaunay Tetrahedralization (CDT). The algorithm pretetrahedralizes the complement of the input with respect to its convex hull and then eliminates tetrahedra in a prioritized manner. We present quality results for two families of meshes that are difficult to simplify by all existing methods known to us - topologically complex and highly clustered meshes.