# PGPRemesh

### From K-3D

## Notes

Triangulated Torus

Quadrangulated without Smoothing

With Smoothing
(In this case smoothing decreases the quality of the curvature)

Increasing divisions

Triangulating faces on the inner part of the torus

### Smoothing

The smoothing properties determine how the principal curvature directions calculated on the mesh will be smoothed. Smoothing will smooth out the curvature calculated on a noisy mesh, and will generate a more regular quadrangulation. Each smoothing step will take a long time for meshes with a large number of vertices, while the timestep increases the amount of smoothing in each step. Setting the timestep too large will wash out the details in the curvature, and you will lose these details in the final mesh.

### Remeshing

The omega parameter controls the period of the iso-lines on the mesh. The plugin will not create a coherent mesh if you provide it with a bad omega. You will need to tweak the property until you find the useable range for your mesh.

Once an omega has been found, the divisions property can be used to increase the quality of the quadrangulation.

### Triangulation

Most meshes will not be able to be completely quadrangulated, and there will be a few faces with more than four vertices. If triangulation is enabled, then these faces will be triangulated. In most cases you will want to do this, as some of the faces will not be planar.

## Future Work

Future work to improve the plugin:

- Hide omega parameter from user control, and use the input mesh to determine the value. Then the user will just use the division parameter to increase the number of quads.
- Add curl correction step, as described in the PGP paper. This will reduce the number of non-quad elements.
- Use alternative newton optimization for high quality input meshes, as described in the PGP paper.
- When the user only changes the divisions parameter, the entire plugin doesn't need to be restarted, only the final mesh creation step needs to be redone.

## References

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds - Used for calculating principal curvature directions for input into PGP algorithm

Rotational Symmetry Field Design on Surfaces - Used for globally smoothing the principal curvature field

Periodic Global Parameterization - Quad Remeshing algorithm