Which parameters defines a polar plot?
Some examples would be the null to null bandwidth(s) as well as the sidelobe levels of the first/second sidelobes. 

Example vector of 5 numbers:
[mainlobe gain, first null location, 1st sidelobe gain, second null, 2nd sidelobe gain]

From this you could produce an estimate for the 3 dB points of each lobe using some "reasonable" formula, i.e. halfway between the peak and the null.