Abstract: We introduce the permission grid, a spatial occupancy grid which can be used to guide almost any standard polygonal surface simplification algorithm into generating an approximation with a guaranteed geometric error bound. In particular, all points on the approximation are guaranteed to be within some user-specified distance from the original surface. Such bounds are notably absent from many current simplification methods, and are becoming increasingly important for applications in scientific computing and adaptive level of detail control. Conceptually simple, the permission grid defines a volume in which the approximation must lie, and does not permit the underlying simplification algorithm to generate approximations outside the volume.The permission grid makes three important, practical improvements over current error-bounded simplification methods. First, it works on arbitrary triangular models, handling all manners of mesh degeneracies gracefully. Further, the error tolerance may be easily expanded as simplification proceeds, allowing the construction of an error-bounded level of detail hierarchy with vertex correspondences among all levels of detail. And finally, the permission grid has a representation complexity independent of the size of the input model, and a small running time overhead, making it more practical and efficient than current methods with similar guarantees.