Origin Ver. and Service Release: OriginPro 9.1 OG (64-bit) Operating System: Windows 7 Enterprise
Hello dear Origin-Community!
Actually I'm working on an implicit fitting function for a sphere.
(f = (x-x0)^2+(y-y0)^2+(z-z0)^2-R^2)
I wrote a very simple "Parameter Init" in form of
x0 = max(x_data); y0 = max(y_data); R = 5000; z0= 5000; Due to the implicit form I have to use the orthogonal distance regression. The value 5000 is a result of already observed measurement values and also the problem I'll need help with. The max data for x and y works quite fine as a result of the Situation in the coordinate Systems.
Depending on what value I choose (3000-7000) for R and z0 (same as R due to surface conditions) the result of the fit shows very different results. None of the variables is allowed to be fixed and so this might be the first problem. Also the surface of the measurement values could be a reason for the instability of the results. Compared to a radius of about 7 meters (for the fitted sphere) the measurement surface is just 15 mm x 15 mm....
Hopefully someone has the idea to solve my problem and bring some stability to the resulting parameters of the implicit fitting function.
The fitting result of User Defined Function heavily depends on the initial values you give. And orthogonal distance regression method has more affect than Levenberg Marquardt. So you must provide a good initial value, based on your background knowledge. And you can check Adj. R-Square to judge if the fitting result is good or not.
Instability of implicit sphere fitting function
Posted - 10/09/2017 : 11:00:48 AM
