Note: I'm a programmer, not a mathematician - please be gentle. I'm not even really sure how to tag this question; feel free to re-tag as appropriate.
I'm using the Douglas-Peucker algorithm to reduce the number of points in polygons (in a mapping application). The algorithm takes a tolerance parameter that indicates how far I'm willing to deviate from the original polygon.
For practical reasons, I sometimes need to ensure that the reduced polygon doesn't exceed a predetermined number of points. Is there a way to predict in advance the tolerance value that will reduce a polygon with N points to one with N' points?