圆与矩形的相交面积

Question

I want to find the area of a given circle that comes under the region of a given rectangle. I searched many posts on stackoverflow but they are not satisfying. I followed this post
http://www.eex-dev.net/index.php?id=100
But it doesn't seem accurate. I'd appreciate if someone provides me a good accurate solution atleast upto 10^-6 precision. Thanks.

Answer 1

Linked article uses integration method of left rectangle rule that suffers from precision loss (here value is underestimated because envelope is convex or straight).

You can use more precise approaches such as Simpson's rule or Gaussian quadrature .

Moreover, every configuration might be subdivided into simple parts - rectangle, triangle, circle segment with known exact area formula!