We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [RB93] by using error quadric information for the placement of each cluster's representative vertex, which better preserves fine details and results in a low mean geometric error. The use of quadrics instead of the vertex grading approach in [RB93] has the additional benefits of requiring less disk space and only a single pass over the model rather than two. The resulting linear time algorithm allows simplification of datasets of arbitrary complexity.

In order to handle degenerate quadrics associated with (near) flat regions and regions with zero Gaussian curvature, we present a robust method for solving the corresponding underconstrained least-squares problem. The algorithm is able to detect these degeneracies and handle them gracefully. Key features of the simplification method include a bounded Hausdorff error, low mean geometric error, high simplification speed (up to 100,000 triangles/second reduction), output (but not input) sensitive memory requirements, no disk space overhead, and a running time that is independent of the order in which vertices and triangles occur in the mesh.