Data Fitting and Surface Design
Example 1: I got a data set of car panel from Prof. Gerald Farin of Computer Science Dept. Arizona State Univ.. C1 cubic splines were used to find a surface which interpolates the data. The interpolatory spline gives the surface of a side panel of a car. One can see that the spline surface interpolates the given data as shown in the second surface (blue stars are given data points in 3D).
Example 2: I got a set of scattered data which were sampled from a part of an airplane from Dr. Tom Grandine of Boeing Co.
C1 spherical splines were used to find a surface which interpolates the data. (The detailed computation was done by my former Ph.D. student Victoria Baramidze). The interpolatory spline gives surface shown below. One can see that it fits the data very well.
Example 3: I got a penny image from MATLAB (load penny) and use C^1 qunitic spline to fit thepenny data (128x128) based on domain decomposition method (a joint work with L. L. Schumaker). I show two angles of the fitting surfaces below. This realizes a 3D visualization of 2D images.
Example 4: I got a set of scattered data of geo-potential around Earth sampled by a satellite called CHAMP from Geoscientist C.K. Shum and his team, we used a spherical spline to fitting the data set. Let me first show the data locations around the Earth and a uniform triangulation of the Earth.
