# How to test whether spherical caps intersect?

I have a unit sphere, on the surface of which are defined spherical caps. I typically characterize the caps by the unit vector $n$ from the center of the sphere to the top of the cap, and the angle $\theta$.

My question is: given a pair of spherical caps, how can I determine whether they intersect?

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– J. M. Nov 18 '10 at 10:11
To add to that previous comment: you will also have to check if the line made by the intersection of the two planes goes through the sphere. – J. M. Nov 18 '10 at 10:35

## 1 Answer

The angle between $n_1$ and $n_2$ is the analogue of the "distance" between the centres of the two caps. The caps intersect if this angle is less than the sum of $\theta_1$ and $\theta_2$, assuming the $\theta_i$ play the role of "radius" and not "diameter" in your notation.

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