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Hy,
I need to calculate the (total) area covered by several circles of known size and position.
The problem is, these circles can overlapp.
To calculate the area of two overlapping circles is not the big problem, but whow do I calculate the areas where more then two circles overlapp?
Thanks
Just use inclusion-exclusion (count up are shared by 2- subtract shared by 3- add shared by 4 etc)
That's quite clear, but whow would you calculate the area which is common to 3 or more circles?
using geometry is hard enough already to find the area when the two circles overlap. sql_lall's method assumes you already know the area of the intersection(s), such as C1^C2,C1^C3,C1UC3, and/or... where ^ denotes intersection and U denotes Union. but apparently u don't. well, we are basically looking at finding the area of a figure which is bounded by 3 arcs. know its vertices can be figured by solving for the intersection of 2 given circles, thus you can figure out the distance between any of the 2 given vertices, they are cords of one of the circles. now the area of that is: area of the triangle formed by the cords + area of A1 + area of A2 + area of A3. where A1,A2,A3 are area between three cords and and the respective arc who shares BOTH of the cord's vertices. to find A1,A2,A3, figure out the distance from the center of the circle to the center point of the cord and figure out the angle in the middle and that area is the ratio of the angle to 360 degrees of the area of circle minus the triangle formed by two radius and that cord.