# Reconstructing a ring from a stack of 2D images (radially aligned)

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Gary Tsui on 6 Jul 2011
Hi there,
I have a stack of images (about 180 of them) and there are 2 black dots on every single image. Hence, the position(x,y) of the two stars are provided initially. The dimensions of all these images are fixed and constant.
The radial 'distance' between the image is about 1o with the origin to be the center of every single 2D image. Since the images are radially aligned, the output would be a possible ring shape in 3D.
the dotted red circle and dotted purple circle are there to give a stronger scent of a 3D space and the arrangement of the 2D images(like a fan). It also indicates that each slice is about 1o apart and a legend that'd give you an idea where the z-axis should be.
Now my questions:
*1) With the provided (x,y) that appeared in the 2D image, how do you get the corresponding (x,y,z) in the 3d space knowing that each image is about 1o apart?
2) I know that Matlab had 3D plotting capabilities, how should i go about implement the solution to the above scenario? (unfortunately, i have very little exp plotting 3D with matlab)
I know that every point on a sphere can be approximated by the following equations:*
x = r sin (theta) cos (phi)
y = r sin (theta) sin (phi)
z = r cos (theta)
However, i don't know how to connect those equations to my problem as i am rather weak in math as you can see by now. :(
Thanks!! Gary