| Global subdivision is the refinement of all the faces of a polygon mesh to produce a high quality smooth surface. While the resulting surface can be used in applications, the exponential increase in the number of faces makes global subdivision memory and computation intensive. Adaptive subdivision can address this issue by refining only selected areas of the mesh to produce a surface. Adaptive subdivision results in inconsistencies in the mesh that can be avoided by insertion of new edges. However, these edges change the connectivity of the mesh, and therefore modify the shape of the resulting surface. Other approaches, such as red-green rules and mesh restriction, achieve correct results, but are inefficient and difficult to implement. Incremental subdivision is introduced in this work as a new adaptive subdivision method that produces desirable surfaces. The incremental method expands each selected area to create a buffer region that is subdivided along with the selected area. This buffer protects the connectivity and geometry of the selected region and the shape of the produced surface from being affected by the adaptive process. In addition, as the selected area is subdivided, the resolution of the mesh is increased within the buffer regions of different levels, so the resulting surface gradually varies from coarse to fine. The incremental method is efficient and easy to implement using a vertex-vertex data structure that allows fast access to vertex neighbourhood. We compare the incremental subdivision with other adaptive methods that produce inconsistencies in the mesh. Finally, some applications of incremental subdivision in modeling and rendering are presented. |
