Progressive Meshes with Controlled Topology Modifications

Due to the rapid evolution of 3D acquisition and modeling methods highly complex and detailed models became ubiquitous. In order to be able to cope with the complexity, concentrated efforts were dedicated to the development of new mesh decimation methods in the recent years. In works of Garland and Heckbert [Garland and Heckbert 1997] and Popović and Hoppe [Popović and Hoppe 1997], the traditional edge contraction operator was generalized to vertex contraction, which allowed for topology modification during the decimation. The vertex contraction facilitates the joining of originally disconnected regions of the mesh by contracting vertices lying in different connected components of the model. While this operation provides considerable topological flexibility during the mesh simplification, in some cases joining of disconnected regions might be desirable only along the boundaries of the model. As a combination of two already available techniques, we present a mesh decimation technique allowing for increased control over topology changes induced by the decimation process. Our method proceeds in essence by applying two types of operators: the well known edge contraction and the vertex-edge contraction introduced recently by Borodin et al [Borodin et al. n. d.]. This facilitates efficient mesh simplification and gradual closing of gaps along the boundaries of the model. The process is controlled by a geometric error and since inverse operations may be implemented for both of the operators, it is conducted in a progressive manner.