EDIT: what I am looking for is called a "spherical zone", as pointed out by user Jean Marie.
I need to calculate the area of a "crown", or "strip" of a sphere. Being new to the domain, I didn't find a better name for this. I think it corresponds to the surface area for two different, concentric steradians, but I could be wrong.
Basically, I have a sphere with a phi and a theta angle. Let's slice the sphere by θ. From θ = 0 to a max value, I need to calculate in MATLAB the area of the "crown" between these two values. I can't find a way to do it...
A pseudocode approach would be this:
kmax = 120;
r = 50;
areas = []
for k=0 -> k=kmax
{
areas[k] = calculate_area(k, k+1);
}
# Calculates the area of the strip on a sphere between two theta values
def calculate_area(k, k+1):
{
area = r * sin(k) * (phi(k+1)-phi(k)) * (k+1-k)); # Just a guess
return area;
}
I based my guess on this that I found, but it could be very wrong.
The final aim is to have a table of areas for every "strip" between k and k+1 for each angle in my theta range. I hope this makes sense.