A New Mesh Simplification Algorithm Based on Quadric Error Metrics

Abstract

This paper proposes a mesh simplification algorithm base on quadric error metric. Most of the simplification algorithms use the geometric distance as their simplification criteria, the distance metric is very efficient to measure geometric error, but it is difficult to distinguish important shape features such as a high-curvature region even though it has a small distance metric. The curvature is one of the good criteria of simplification to preserve the shape of an original model, if the curvature of the vertex is larger, it can present the geometric features of model well. Besides curvature, the size of the incident edges around the vertex can also reflect the geometric feature, if the edge lengths that adjoin the vertex are larger, it infects larger area on the surface of the model. We considered both the local curvature and the size of the incident edges around the vertex on the basis of the quadric error metrics, it can reflect changes on the model surface and still maintain many important geometric features after large scale simplified.