Transform 2d picture of cone (x,y) to (s,phi)

Hello all,

I have a 2d image of a cone plotted in cartesian coordinates with an associated intensity value for each pixel. I wanted to reimage the picture in terms of polar coordinates (slant length, azimuthal angle). Here are the equations that I think should be using for the transformation, but I'm stuck from there.

if true
  % code
s = sqrt(x^2+y^2)   % 's' is the slant length at a particular x,y coordinate
R = s * sin(alpha)  % 'alpha' is the half angle of the cone, 'R' is the radius at that slant length
theta = phi * sin(alpha) % 'phi' is the azimuthal angle of the cone, 'theta' is the angle of the rolled out cone
phi = s * theta / R

So for each x,y pixel I can find the slant length, but how do I determine the roll-out angle? This website, page 14, helped with the equations:

http://www.mamikon.com/USArticles/RollingConesCylinders.pdf

Assuming I can find 'phi' do I use an interp function to get the intensities for the new coordinate system? Let me know if I need to be clearer on anything.

Thanks