Topology simplification for polygonal virtual environments

We present a topology simplifying approach that can be used for genus reductions, removal of protuberances, and repair of cracks in polygonal models in a unified framework. Our work is complementary to the existing work on geometry simplification of polygonal datasets and we demonstrate that using topology and geometry simplifications together yields superior multiresolution hierarchies than is possible by using either of them alone. Our approach can also address the important issue of repair of cracks in polygonal models, as well as for rapid identification and removal of protuberances based on internal accessibility in polygonal models. Our approach is based on identifying holes and cracks by extending the concept of α-shapes to polygonal meshes under the L_∞ distance metric. We then generate valid triangulations to fill them using the intuitive notion of sweeping an L_∞ cube over the identified regions