Plotting weather radar vertical sections - Philosophy of the procedure

Hello,

I would like to plot radar vertical section (range-height). It seems to be an easy situtation, but it isn't.

Radar's beams are shown in this image as a function of range and height. Actually, a beam of a specific angle of emission goes away from the earth gradually.
http://www.wdtb.noaa.gov/courses/dloc/topic3/lesson1/Figures/rangeVShei…

Even if We know the equations in order to convert this polar representation of the radar data into a cartesian (in order to have a correct and user-friendly representation of radar data), what could be the general procedure to do it?

We have a matrix with radar data (e.g. reflectivity) in polar co-ordinates and we want to produce a matrix of the same data but in cartesian co-ordinates. My main problem is how to create the right dimensions of the second matrix.

Perhaps, I didn't make it so clear, so if anyone need more explanation just ask me.

Any ideas?

Thank you.