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January 31st, 2018, 08:04 AM   #1
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Smile Ellipsoid problem...c axis calculation

Hi all,
i'm new on this forum. First of all sorry for my written english.

I'm a PhD student in Earth Science and i need help with a geometry problem.
I'm trying to determine the c axis of some ellipsoid-shape objects.
With the microscope I've measured the two axis in the xy plane and the length that i get when i rotate the object of 45°. I need to calculate the other axis in order to determine the thickness of these objects.

I think that my case could be represented by this picture:
https://www.researchgate.net/profile...-dependent.png

My Idea was to apply some trigonometry equations, as:

Cos45 = measured length when rotated of 45° / c axis, and than get the c axis. Anyway i don't really like the result that i get, so i think i'm doing something wrong.

Can you help me? any advice?
Hope you understand the problem
Thank you
Alberto
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February 3rd, 2018, 02:59 AM   #2
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Nobody can help me?
Cheers
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February 3rd, 2018, 08:50 AM   #3
SDK
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You haven't said what a "c axis" is. However, if I'm understanding your question correctly you are interested in the coordinates for an ellipse after rotating it in the plane?

The polar transformation for an ellipse gives the coordinates:
$x = A \cos (\theta)$ and $y = B \sin(\theta)$ where $A,B$ are constants related to the eccentricity of the ellipse. If you write them in this way, then applying a rotation by $\alpha$ is nothing more than multiplication by the matrix
\[ \left( \begin{array}{cc} \cos(\alpha) & -\sin(\alpha) \\ \sin(\alpha) & \cos(\alpha) \end{array} \right) \]
which can be combined with the polar coordinates for $x,y$ using standard trig identities.

If this doesn't help, then you need to clarify what exactly you are asking.
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