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Idea
1. Impose a voxel grid on the input mesh.
2. For each cell containing vertices, compute a cell representative.
3. Create a new mesh which only has cell representatives as vertices. Three cell representatives are connected with a triangle if there was a triangle in the original mesh wich had one vertex in each of the three cells.

Quality Control
The approximation error is bounded by the voxel resolution : Vertices are shifted by at most .

Cell Representative

• Cell Center: Requires no computation but leads to bad approximation error and produces stair artifacts.
• Center of Gravity: Slightly better approximation. Introduces low-pass filter.
• Median: i.e. closest point to center of gravity. Less pronounced low pass.
• Error Quadric: Find least-squares closest point to all triangle planes in the cell. Produces best sampling of sharp features.

Advantages
Out-of-core implementation possible
Works on arbitrary geometry (no manifold required)

Disadvantages
Output mesh not guaranteed to be manifold
Loss of detail due to uniform sampling

Out-Of-Core Implementation
Required storage: One error quadric for every cell. Connectivity information (list of cells which need to be connected).
Processing: Read one triangle at a time. If the vertices fall into three different cells, keep a record on the connectivity list. Add the fundamental error quadric of the triangle to the cells of the vertices. After all triangles have been read, compute cell representatives and connect them.