Implementation

This is an Implementation of the Square3-Subdivision as proposed by Leif Kobbelt in his paper.

Usual Subdivision schemes that operate on triangle meshes insert a vertex for every edge of the original mesh - this results in a quadrupling of triangles in every single subdivision step:

Kobbelt takes a different approach - instead of inserting a new vertex for every edge he inserts one for every triangle and connectes it to all vertices of this triangle. After that, all the original edges are flipped (see rightmost picture in Figure2) which gives a 30 degree rotated regular mesh. If you apply this scheme twice, you will get two new vertices for every original edge, giving a 1-to-9 refinement of the original mesh.

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GUI

The GUI is pretty straightforward, when you start the test application you will get a standard windows MDI-Application, which will allow you to open and close files and to arrange windows. The open dialog let's you open 3DS files (generated with the 3DS-Max-Exporter). We included a couple of test files, which should help you estimating the improvement that can be achieved with this scheme:

You can open as many files as you like - for every file open you will get an MDI child window, that lets you select the number of subdivisions and the subdivision scheme you would like to have applied:

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Results

Here you see a direct comparison of the different subdivision schemes; as you can see in the first example, the butterfly filter expands the initial object while the loop filter shrinks it.

The second example illustrates that the loop filter performs much better at smoothing a rough mesh, while the butterfly filter still produces visible smoothing artifacts.

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Source

You can find a complete description of the new class here.

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Download

square3subdivision.zip

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References

Square3-Subdivision-Paper

Mathematische Methoden der CG

Visualization Toolkit

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