Extended Quadric Error Function for Surface Simplification

Deepak Bandyopadhyay

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Mid-Semester Update (10/26/00)

STUFF DONE


RESULTS

Our premise was that since the order of merging vertices to a great extent determines the quality of the simplification, we would change this order to use our distance functiuon and see what happens to the simplification. Here are a few images demonstrating what we observed:

original cow model


original bunny model


cow, 3000 triangles, original


cow, 3000 triangles, distance function


2000 triangles, original


2000 triangles, distance function


1000 triangles, original


1000 triangles, distance function


250 triangles, original


250 triangles, distance function


250 triangles, original side on


250 triangles, distance function side on


250 triangles, original tail view


250 triangles, distance function tail view


bunny, 10000 triangles, original


bunny, 10000 triangles, distance function


1000 triangles, original


1000 triangles, distance function


250 triangles, original


250 triangles, distance function



DISCUSSION OF RESULTS

  1. Both the algorithms give similar results when not too many edges have been collapsed. However the order of edges picked is very different. Since we do not see the difference in structure of the simplified model until we come down to very coarse resolutions, we conclude that initially both algorithms are picking a reasonable set of edges to simplify. As the initial edges (before any combination/merging has taken place) correspond to direct use of our distance function on real edges, we conclude that our distance function is likely to pick edges having a low cost of merging.

  2. On trivial models (eg. a cube model made with 12 triangles), both the algorithms always pick the same pair of edges.

  3. When we get down to lower numbers of faces (where low is defined as some function of the original number of faces), our variant of the algorithm progressively messes up.
  4. It is not clearly understood why the distance function is yielding these strange artifacts. However, the encouraging sign is that the quality of simplification is not an order of magnitude worse at sufficiently high triangle counts.

  5. For my next report, I expect to plug in the distance function into a lot more than just the order of edge selection (eg. in computing the merge error of a pair merge and the resultant error of the new vertex smartly, rather than calling the distance function again on the physical location of the merged vertex and all its neighbors).