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# 3D Meshes: how to minimize error during reduction of order?

a set of vertices defined by the following code:

```
int xMax; // this is the size of the mesh in the x dimension
int zMax; // this is the size of the mesh in the z dimension
Vector3[] vertices = new Vector3[xMax * zMax];
int i;
for (int z = 0; z < zMax; z++){
for (int x = 0; x < xMax; x++){
i = z + zMax * x; // this is just the index in the vertices array
vertices[i] = new Vector3(x, f(x,y), y); // f(x,y) might perhaps return a value from a heightmap
}
}
```

how do i find a subset with n of these vertices and then triangulate it in such a way that either the standard deviation of the area of the triangles is minimal, or the three-dimensional correlation coefficient is as close to 1 as possible? (preferably the latter) EDIT: any way that keeps as much detail as possible is fine

This is an extremely challenging problem and any help would be appreciated.

Minimizing error during reductions of order is a fair question. This paper presents a poly-count reduction scheme that might be what you're looking for.

Thank you for your fast response. I don't know if it is anything i can work with yet but i will have a look.

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