For grid terrain data, we propose a Lepp-surface triangulation method that starts with a coarse initial triangulation of the input data, and incrementally adds data points that reduce the worst edge approximation error in the mesh. The method generalizes a previous Lepp-centroid method in two dimensions as follows: for the edge E, having highest error in the mesh, one or two points close to (one or two) terminal edges associated to E, are inserted in the mesh. The edge error is computed by adding the triangle approximation errors of the two triangles that share E, while each triangle error in L-2-norm is computed by using a curvature tensor (good approximation of the surface) at a representative point associated to both triangles. The method produces triangular approximations that capture well the relevant features of the terrain surface by naturally producing well-shaped triangles.