Creating an arced image with imagemagick

Question

I am trying to use imagemagick to arc an image and have it fit into a predefined arc space. For that predefined arc I know the circumference of the top and bottom segments along with the width of the space between the two circumferences. I need to get the arc angle along with the top and bottom radius values so that I can feed those into imagemagick. Any ideas on how I can calculate those values?

Answer 1

TopLength = (r0 + Width) * Alpha
BottomLength  = r0 * Alpha
Alpha = (TopLength - BottomLength) / Width  

(angle in radians)