1. A method of simplifying a surface represented as a height field, having a two-dimensional grid of vertices and a corresponding height value at each vertex location wherein for certain vertices the height value is undefined, into a simplified triangular mesh, such that the topology of the surface is maintained in the simplified surface representation, comprising: a. assigning error values to each vertex not having a missing value; b. identifying as required vertices those vertices that may not be removed without altering the topology of the surface; c. removing u-n vertices where where u is the number of vertices that do not have missing values in the original height field and n is greater than or equal to the number of required vertices and less than or equal to u.