Subdivision is a natural extension of the existing patch-based surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for mesh manipulation. Combination of subdivision and smoothing algorithms of Taubin allows us to construct a set of algorithms for interactive multiresolution editing of complex meshes of arbitrary topology. Simplicity of the essential algorithms for refinement and coarsification allows to make them local and adaptive, considerably improving their efficiency. We have built a scalable interactive multiresolution editing system based on such algorithms.
The images below show an example of an edited mesh obtained using our system: The original is on the right (courtesy Venkat Krischnamurthy). The edited version on the left illustrates large scale edits, such as armodillo's belly, and smaller scale edits such as his double chin; all edits were performed at about 5 frames per second on an Indigo R10000 Solid Impact.
The general structure of the editor is shown on this diagram:
Analysis propagates the changes on finer levels to coarser levels, keeping the magnitude of details under control. Left: The initial mesh. Center: A simple edit on level 3. Right: The effect of the edit on level 2. A significant part of the change was absorbed by higher level details.
To achieve performance rates that are necessary for interactive manipulation, we use adaptive and local versions of these algorithms. In addition, a significant fraction of rendering is done adaptively.
On the left is the mesh which is uniformly subdivided and consist of 11k triangles. On another meshes mesh with approximately the same numbers of triangles. Upper and lower meshes are generated from the same original data but the right meshes were optimized through suitable choice of epsilon. Click on the images to view them at a higher resolution. Another example:
It is easy to change epsilon locally. Here a lens was applied to the right eye of the mannequin head with decreasing epsilon to force very fine resolution of the mesh around the eye.
|Coarse-level edit, ears:||MPEG (1.3 MB)|
|Coarse-level edit, hand||MPEG (742 KB)|
|Fine-level edit: eye||MPEG (1.4 MB)|
Denis Zorin, Peter Schröder and Wim Sweldens, ``Interactive Multiresolution
Mesh Editing'', CS-TR-97-06, Department of Computer Science, Caltech, January
Compressed PostScript with images (7.8MB) (will uncompress to 70MB),
Compressed PostScript without images (72KB),