问题陈述
问题的实质
找到两个圆相交的重叠区域。
The whole picture shown in the blow:
The matlab plot code:
The way to solving this problem :Part I
Rotate the figure 2 and draw the subline to help us to solve this question, then we will get:
Starting from the top left, clockwise, define the four triangles and fan-shaped as t1, t2, t3, t4 and f1, f2, f3, f4.
Then, the overlap area will be:
which can be convert as:
Bring this method back to the origin plot, we can get
Calculate the VIP: Part II
First, we need write the two different circle function:
and
Calculate the cross point,
Calculate the overlap area: Part III