Applications in computer graphics, geometric modeling, and simulation based engineering design demand highly flexible and efficient algorithms for the manipulation of large scale, complex geometry. Examples include the acquisition, processing, and transmission of finely tessellated models of real world geometry. These geometries are typically represented as very large meshes ranging into hundreds of thousands if not millions of triangles per object. Since the use of such geometries occurs typically in interactive applications, highly scalable algorithms, which are capable of allocating resources in very flexible ways, are required. Examples include the generation of level-of-detail (LOD) representations with well controlled error or compression of geometry for progressive transmission purposes.These needs have fueled an active and vibrant research area concerned with the construction and efficient manipulation of multi-resolution representations, i.e., data structures and algorithms exhibiting low time and space complexity, capable of providing fluid speed/accuracy tradeoffs. There are two distinct approaches in this area, those based on classical subdivision [35, 40] and those based on more recent mesh simplification techniques [16].