This more of a musing (and perhaps amusing) than an answer. I find it worthy of cogitation.

If you have a bounding box (sheet of paper), you could try dividing it by hyperplanes (cutting off pieces with a straight blade) and measuring the area of the pieces cut off. One interesting aspect is to arrange the cuts so that the pieces obtained have very few sides, making the computation of the discards easier. Looking for an optimal such order of cutting is likely NP-hard, but even a suboptimal order may help with the computation, especially if the hyperplanes are fed to the algorithm one at a time.

If you do find this worthy, some credit should go to Robert (sp?) Fulghum.

Gerhard "Yes, I Do Kindergarten Math" Paseman, 2012.01.24