*Marco Tarini, Nico Pietroni, Paolo Cignoni, Daniele Panozzo, Enrico Puppo*

**Practical Quad Mesh Simplification**

Computer Graphics Forum, Volume 29, Number 2, EuroGraphics 2010

In our community it is well know the old religious war between quad vs. triangle meshes, each approach has its own merits and I not discuss them here.

Moving back and forth between the two approaches is often useful but the issue of getting a good quad mesh from a highly irregular tri mesh is a tough one.

In the above paper we present a novel approach to the problem of quad mesh simplification, striving to use practical local operations, while maintaining the same goal to maximize tessellation quality. We aim to progressively generate a mesh made of convex, right-angled, flat, equally sided quads, with a uniform distribution of vertices (or, depending on the application, a controlled/adaptive sample density) having regular valency wherever appropriate.

In simple words we start from a tri mesh, we convert into a dense quad mesh using a new Triangle-to-Quad conversion algorithm and then we simplify it using a new progressive quad simplification algorithm. The nice side is that the quad simplification algorithm actually improves the quality of the quad mesh. Below a small example.

We are currently adding this stuff inside MeshLab. The first things that will appear are the triangle to quad conversion algorithms and some functions for measuring the quality of a quad mesh according to some metrics. More info in the next posts....

*(2/1/10 edit: if the above link for the paper does not work try this:*

**)****Practical Quad Mesh Simplification**