Subdivision

In image processing, we often have a low resolution image that we want to display at a higher resolution. Since we only have a few samples of the original signal, we need to somehow interpolate or upsample the image. One idea would be to simply cut each pixel into four, leaving the color values unchanged, but this leads to a blocky appearance. Instead we might try a more sophisticated scheme (like bilinear or trilinear interpolation) that yields a smoother appearance.

In geometry processing, one encounters the same situation: we may have a low-resolution polygon mesh that we wish to upsample for display, simulation, etc. Simply splitting each polygon into smaller pieces doesn't help, because it does nothing to alleviate blocky silhouettes or chunky features. Instead, we need an upsampling scheme that nicely interpolates or approximates the original data. Polygon meshes are quite a bit trickier than images, however, since our sample points are generally at irregular locations, i.e., they are no longer found at regular intervals on a grid.

Three subdivision schemes are supported by Scotty3D: Linear, Catmull-Clark, and Loop. The first two can be used on any polygon mesh, and should be implemented via the global replacement strategy described above. Loop subdivision can be implemented using repeated application of local operations. See further details in the linked sections.