Polygon reduction : edge collapsing


I have been reading about algorithms for reducing the polygon count. I came across the edge collapsing technique. It seems easy enough,
the only thing I do not understand is the metric used to to choose an edge to collapse to a point.

Can someone please explain this



Can anyone please help, it’s said that an edge is chosen using a metric and collapsed to a point. Does anyone know exactly how an edge is chosen?

All i know is that if you want to reduce polies, using the decimator modifier gives some okay, but often messy, results.
you could alsoo selct individual edges and hit alt-m.

as far as the algorithms, i fail miserably with math above basic algebra and probably am not the best candidate to ask.

As far as I recall, the easiest method is via edge-threshold

The smaller the absolute value of 3 edges intersecting in a vertex, the less it contributes to the overall shape -> remove vertex/merge into closest vertex.
Requires lot’s of vector math and possibly delaunay triangulation.

But there are a gazillion papers out there on that topic, another idea is to look in the sourcecode of meshlab.

There are various metrics around for choosing which edges to collapse (and in what order), and usually involve some approximation of the local curvature of the mesh around each edge. Examples range from simple dihedral angle checks, to the more advanced quadrics method. However, these are just a few simple examples of the many papers which have been published out there.

Blender’s decimate modifier for many years only used an edge-collapse technique, using a quadrics-based cost function.

An alternative to choosing edges to collapse is to find vertices to remove (i.e. vertex decimation).