I think in class you mentioned we could create a 3D version of "mip-map". I could imagine it being useful for bi-linear like model choosing based on distance to save rendering time, but how would you do a tri-linear interpolation between meshes of different number of vertices if that is a thing?
@harveybia You would use different techniques depending on how your mesh hierarchy is constructed. With subdivision surfaces, the strategy is really quite similar to MIP mapping: find two adjacent subdivision levels and interpolate between the finer level and a linear subdivision of the coarser level (i.e., imagine splitting the mesh elements but keeping the vertices on the original surface). The first video here shows how this kind of strategy can be applied adaptively in Pixar’s OpenSubDiv library (closer to the end of the video): http://graphics.pixar.com/opensubdiv/docs/additional_resources.html#videos
Triangle meshes don’t get used as much these days for adaptive rendering (AFAIK), but there are some classic techniques for working with “progressive meshes” that may resurface now that we are seeing more and more scanned geometry, and wanting to do more things with geometry over the web, in VR, etc. Search for “progressive meahes” on Hugues Hoppe’s page: http://hhoppe.com
Can we perform the reverse process to improve the quality of rendering?
@tpan496 This process isn't reversible in the sense that you destroy information when you do an edge collapse (there are multiple vertex pairs that could result in the same collapsed vertex location). But you can do things like subdivision to upsample a low-res surface.
Are there any other commonly used error metrics? Or is this method currently state-of-the-art?
@kc1 There is very little discussion in new research about "mesh simplification"; instead, people are thinking a lot more about "remeshing," which involves both the quality of the geometric approximation as well as the element quality, and trying to balance the two. Take a look for instance at this paper, which tries to balance generating nice quadrilateral elements with adapting to the scale and curvature of the geometry. Of course, these methods are far more expensive than iterative edge collapses.