algorithm - Combined area of overlapping circles

Question

I recently came across a problem where I had four circles (midpoints and radius) and had to calculate the area of the union of these circles.

Example image:

For two circles it's quite easy,

I can just calculate the fraction of the each circles area that is not within the triangles and then calculate the area of the triangles.

But is there a clever algorithm I can use when there is more than two circles?

Answer 1

Find all circle intersections on the outer perimeter (e.g. B,D,F,H on the following diagram). Connect them together with the centres of the corresponding circles to form a polygon. The area of the union of the circles is the area of the polygon + the area of the circle slices defined by consecutive intersection points and the circle center in between them. You'll need to also account for any holes.