Fast and Accurate Hausdorff Distance Calculation between Meshes

Complex models generated e.g. with a laser range scanner often consist of several thousand or million triangles. For efficient rendering this high number of primitives has to be reduced. An important property of mesh reduction – or simplification – algorithms used for rendering is the control over the introduced geometric error. In general, the better this control is, the slower the simplification algorithm becomes. This is especially a problem for out-of-core simplification, since the processing time quickly reaches several hours for high-quality simplification. In this paper we present a new efficient algorithm to measure the Hausdorff distance between two meshes by sampling the meshes only in regions of high distance. In addition to comparing two arbitrary meshes, this algorithm can also be applied to check the Hausdorff error between the simplified and original meshes during simplification. By using this information to accept or reject a simplification operation, this method allows fast simplification while guaranteeing a user-specified geometric error.