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The dataset I am using only has 200 degrees of the ellipse. The ellipse is not centered at (0,0). The data in this case ranges from 110 degrees to 310 degrees. I need to determine the center of the partial ellipse so that I can calculate the x and y radius to complete the ellipse.

I have tried using the Max and Min values of the dataset to determine the center, but that does not work correctly; (Max + Min)/2

The main focus is to complete the ellipse, so if someone has a better approach please let me know. I know if I obtain the center of the ellipse I can complete the ellipse, so that is the approach I have taken.

KSdev
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1 Answers1

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You could represent your ellipse as a general conic: $$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$$ with unknown $A$, $B$, $C$, $D$, $E$, $F$. Plug in five points $(x,y)$, and you have enough equation to compute the coefficients, up to the obvious homegeneity. If you have more than five points, and there is some measurement uncertainty, you could solve the overdetermined system as a least squares problem instead.

Harald Hanche-Olsen
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  • I think this will be a valid approach. I am just trying to remember how to solve for a system of equations, it has been a while. Although your last sentence, you could solve the overdetermined system as a least squares problem instead seems to be what I should aim at doing. Any hints/links on this approach? – KSdev Jan 14 '14 at 19:00
  • You could look at the Wikipedia article on linear least squares, in particular this section. You set up and solve the normal equations, as explained (very briefly) in that article. – Harald Hanche-Olsen Jan 14 '14 at 19:35
  • Thank you for the input. I will work through this and if successful mark this as answered. – KSdev Jan 14 '14 at 22:18
  • Found a Good site that had MatLab code for this here – KSdev Jan 15 '14 at 13:31