Matlab program for simulating measured points on ellipsoid with two options of
adding the random error.
In the first step, n points are randomly sampled from the interval (-a,a) on the x axis.
In the second step, for each of this coordinates the y coordinate is sampled from the
appropriate range given by the first axis length of the ellipse in the corresponding cuts.
In the third step, the z coordinate is calculated from the x and y coordinates, with a
positive/negative sign given by a realization of a bivariate random variable with probability 0.5.
Lastly, the random error is added.
For the first option (opt.I), a realization of a three-dimensional random vector of independent
normal variables with zero mean and sigma2 variance. In the second option (opt.II), an u-
multiplication of a normalized normal vector in the chosen point on the ellipsoid is added.
Here, u is a realization of a normal random variable with zero mean and sigma2 variance.
Ahn. Least squares Orthogonal Distance Fitting. Springer. 2004
by method: Orthogonal distance fitting of implicit curves (coordinate based,
variable separation method = Algoritmus 3, chapter 3)
The programs were written under support of the project from MSMT of the
Czech Republic no. 1M06047 “Center of Quality and Reliability of Production”.
The program is available up on request by email at hrdlickova.z@fme.vutbr.cz .