Finding Planar Regions in a Terrain

We onsider the problem of omputing large onne ted regions in a triangulated terrain of size n for whi h the normals of the triangles deviate by at most some small xed angle. In previous work an exa t near-quadrati algorithm was presented, but only a heuristi implementation with no guarantee was pra ti able. We present a new approximation algorithm for the problem whi h runs in O(n= 2 ) time and|apart from giving a guarantee on the quality of the produ ed solution|has been implemented and shows good performan e on real data sets representing fra ture surfa es with around half a million triangles.