Compute the area of intersection between a circle and a triangle?

Question

How does one compute the area of intersection between a triangle (specified as three (X,Y) pairs) and a circle (X,Y,R)? I\'ve done some searching to no avail. This is for

Answer 1

If just one of the triangle's line segments intersects the circle, the pure math solution isn't too hard. Once you know when the two points of intersection are, you can use the distance formula to find the chord length.

According to these equations:

ϑ = 2 sin⁻¹(0.5 c / r)
A = 0.5 r² (ϑ - sin(ϑ))

where c is the chord length, r is the radius, ϑ becomes the angle through the center, and A is the area. Note that this solution breaks if more than half the circle is cut off.

It's probably not worth the effort if you just need an approximation, since it makes several assumptions about what the actual intersection looks like.