Bidirectional Adaptive √3-Subdivision

Abstract

Starting with small, rough, and low-detailed base models, √3- subdivision is able to produce smooth and highly accurate models by adaptive subdivision. However, current smoothing methods are only unidirectional, i.e., a mesh can be smoothed locally, but it is not possible to adaptively coarsen the mesh again. As a consequence, for view-dependent display, a change of the viewing parameters requires a complete restart at the base level. In this paper, a framework for bidirectional adaptive subdivision is presented, which allows us to adapt the current triangulation in both directions locally, i.e., add detail where required and remove detail whenever possible. It operates on the current triangulation only, i.e., there is no need to restore any previous states. Our smoothing process allows us to keep a constant frame rate within every single step in the refinement loop. To avoid popping artifacts, inserted and removed vertices are "geomorphed." Basic key-frame animation support is provided by moving positions of vertices of the base mesh. The framework is suitable for various applications, e.g., as part of a graphics engine for computer games or for character modeling. As a proof of concept, we implemented a view-dependent application, rendering a large number of arbitrary meshes at interactive frame rates with sufficient detail.