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January 31st, 2018, 08:04 AM  #1 
Newbie Joined: Jan 2018 From: iceland Posts: 2 Thanks: 0  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 ellipsoidshape 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 
February 3rd, 2018, 02:59 AM  #2 
Newbie Joined: Jan 2018 From: iceland Posts: 2 Thanks: 0 
Nobody can help me? Cheers 
February 3rd, 2018, 08:50 AM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 472 Thanks: 262 Math Focus: Dynamical systems, analytic function theory, numerics 
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. 

Tags 
axis, calculation, ellipsoid, problemc 
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