Abstract: This paper presents a novel selective refinement scheme of progressive meshes. In previous schemes, topology information in the neighborhood of a collapsed edge is stored in the analysis phase. A vertex split or edge collapse transformation is possible in the synthesis phase only if the configuration of neighborhood vertices in the current mesh corresponds to the stored topology information. In contrast, the proposed scheme makes it possible to apply a vertex split or an edge collapse to any selected vertex or edge in the current mesh without a precondition. Our main observation is that the concept of a dual piece can be used to clearly enumerate and visualize the set of all possible selectively refined meshes for a given mesh. Our refinement scheme is truly selective in the sense that each vertex split or edge collapse can be performed without incurring additional vertex split and/or edge collapse transformations.