4
votes
0answers
49 views

How I cut my orange - spherical volume integral

I cut my orange in six eatable pieces, following some rules. My orange is a perfect sphere, and there is a cylindrical volume down through my orange, that is not eatable. In the diagram, the orange ...
0
votes
0answers
138 views

Spherical Coordinates Integral to Great Circle

I need the function $\cos^n(\phi)$ integrated over the unit hemisphere cut with a great circle path. The following diagram shows the area to be integrated and the coordinate system used: The great ...
3
votes
1answer
123 views

Integration on a sphere

I have an integral at hand which has the form of $$I = \int_{u\in \mathbb{S}^2} f(\mathbf{u}\cdot \mathbf{s}_1) f(\mathbf{u}\cdot \mathbf{s}_2) d\mathbf{u}$$ where $\mathbb{S}^2$ is the unit sphere ...
0
votes
1answer
321 views

Integrate linear function over spherical triangle

In the plane I can integrate a linear function over a triangle as the average of the corner values times the area of the triangle. Then if I subdivide the triangle into 4 triangles by introducing a ...