Fast and memory efficient polygonal simplification

Conventional wisdom says that in order to produce high-quality simplified polygonal models, one must retain and use information about the original model during the simplification process. We demonstrate that excellent simplified models can be produced with-out the need to compare against information from the original ge-ometry while performing local changes to the model. We use edge collapses to perform simplification, as do a number of other meth-ods. We select the position of the new vertex so that the original vol-ume of the model is maintained and we minimize the per-triangle change in volume of the tetrahedra swept out by those triangles that are moved. We also maintain surface area near boundaries and min-imize the per-triangle area changes. Calculating the edge collapse priorities and the positions of the new vertices requires only the face connectivity and the the vertex locations in the intermediate model. This approach is memory efficient, allowing the simplification of very large polygonal models, and it is also fast. Moreover, sim-plified models created using this technique compare favorably to a number of other published simplification methods in terms of mean geometric error.