Does anyone know any free/shareware pack for fitting a cloud of points in space to a surface?
The idea is, I have a number of (say, about half a dozen) experimental points that should be theoretically distributed on the surface of an ellipsoid:
z = Sqr(1 - (x/a)2 -(y/b)2)
The problem is determining a and b so the error (or the sum of the squared errors) is a minimum. The error would be the distance from each point to the surface (measured along a direction which is perpendicular to the tangent plane to the surface).
Now, the above equation corresponds to an ellipsoid with its center at the coordinate origin and its main (symmetry) axes coincident with the corrdinate axes x,y & z.
However, the points are not necessarily distributed around my coordinate origin so you've got to make a translation. And secondly, the ellipsoid's main axes could be arbitrarily oriented in space. Therefore you have to somehow determine what the most probable orientation would be and rotate the coordinate axes accordingly.
I kind of solved the problem using Excel but the whole thing was very messy and I wouldn't waste any more time on it. That's why I'd like to use someone else's (better!?) software. :confused:
