This paper deals with four processes for constructing mathematical models based on measurement data. The first process is smoothing measurement data based on the hypothesis that a small area of a curved surface can be approximated to an ellipsoid. The second process is fitting the measurement data into the cross points between a 3D lattice and filling points by approximating the ellipse surface. As information on the positions of data is converted from coordinate value into integral code, it is easier to find neighboring points and clear neighboring relations between surfaces help prevent the gap between neighboring surfaces when constructing the surfaces. The third process is recognizing surfaces and boundary lines composing a physical model from the curvature of the points located on the 3D lattice and variance of the coordinate values of the points. The last process is approximately defining NURBS surfaces by the minimum square method to average positional errors. Experiments on surface construction were conducted to show the usefulness of the proposed methods.