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- Homework Statement
- I am trying to figure out the area on the surface of a sphere as a result of the sphere intersecting a much smaller rectangular prism.

- Relevant Equations
- N/A

Think of a 3D rectilinear grid made of these rectangular cells, some of the cells will intersect with the sphere. I am trying to compute each intersecting area and the total sum. Ideally the total sum of the intersecting area should be close to ##4 \pi r^2##. I have not found any literature discussing this problem. Part of the problem is that the polygon on the sphere as a result of the intersection is not necessarily made of geodesics. Moreover, part of the rectangular prism can embed inside the sphere causing irregular intersecting shape. I am looking for ideas how to get this done correctly. Has anyone seen any problem. I would imagine this might be useful in computer science, but obviously people there are not too concerned with accuracy of the result. Thanks!