As I googled for some sites about the approximation method of least squares, I noticed that this method is a very powerful tool in computer graphics.  I also came across a variation of the method called Moving Least Squares (MLS).  According to Wikipedia, moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure. 

The MLS method was created with the goal of interpolating data.  It is similar to the least squares approach, but you use a weighted least squares form:  Min of the SUM(Theta(||x_bar – x_i||) * ||f(x_i) – f_i||^2).  The error that we are trying to minimize is weighted by Theta(d), where di is the distance between x_bar and the positions of the data points x_i.  MLS starts with this weighted least squares for a random point in R^d, but instead of just calculating each point individually, you move this point over the entire parameter domain.   

In computer graphics, linear MLS is utilized when performing smooth image deformations and morphing.  The method presented in the article (second link) utilizes the Moving Least Squares approach and gives the user the ability to manipulate the object as if the user was handling it in real life.  The image is given a set of handles in which the user can intuitively control its position and orientation.  In terms of applications of this technique of deforming and morphing images, not only is it applied to computer graphics and animation, but it is also used in things such as medical imaging. 

Links:

http://en.wikipedia.org/wiki/Moving_least_squares

http://faculty.cs.tamu.edu/schaefer/research/mls.pdf

http://www.ams.org/mcom/1998-67-224/S0025-5718-98-00974-0/S0025-5718-98-00974-0.pdf