LP fitting approach for reconstructing parametric surfaces from points clouds

We present a method to reconstruct a surface from a group of points, each provided with two parameters. The kind of reconstructed surface can be a Bezier surface, a B-spline surface or any surface generated by a basis of functions. The usual method involved in such a reconstruction is the least squares approach. Our original fitting method called LP-fitting uses a linear program for minimizing the uniform error instead of the quadratic error considered in least squares. Experimental results comparing both approaches show that the surface obtained by LP-fitting is usually closer (from a uniform point of view) to the initial points cloud than the surface obtained by least squares.