A method and apparatus for the smoothing of a mesh surface is disclosed whereby neighboring vertices of a target vertex are identified, for example, by identifying the neighboring vertices within a desired distance from the target vertex. A normal of the target vertex is determined as a function of, for example, the features of a set of neighbor triangles corresponding to the set of neighboring vertices. A local coordinate system is then established. Unknowns in a quadratic surface function are then solved as a function of the position of the neighboring vertices with respect to the local coordinate system and new x and y coordinates in the local coordinate system are determined for the target vertex. These new x and y coordinates are entered into the quadratic surface function to obtain a new smoothed z coordinate for the target vertex.