Question

I have a 2d array (lat*long) containing height information. I want to map this cylindrical projection to a actual sphere with radius r and plot it.

How would I do that? Sorry it so little info, but I’m completely lost right now …

Answer 1

Longitude and latitude are not cylindrical coordinates; rather, they are equivalent to azimuth and elevation in spherical coordinates. At each latitude and longitude, you have a height (which may need to have the mean radius of the sphere added to it if it isn’t the true height from the center already).

Check out the sph2cart function, which converts from spherical to cartesian coordinates. You’ll have to convert from degrees to radians first.

Steps to take:

1. Create matrix (same size as original) with just longitudes.
2. Do the same for just latitudes (after this you should have 3 matrices of the same size as your original – latitude, longitude, height).
3. Make sure those latitude and longitude matrices are in
   radians, not degrees
4. Make sure your height info is from the
   center of the sphere
5. Use sph2cart to get x,y,z matrices.
6. Use surf(x,y,z) to plot the results

Notes on sph2cart from the documentation:

[x,y,z] = sph2cart(azimuth,elevation,r) transforms the corresponding
elements of spherical coordinate arrays to Cartesian, or xyz,
coordinates. azimuth, elevation, and r must all be the same size (or
any of them can be scalar). azimuth and elevation are angular
displacements in radians from the positive x-axis and from the x-y
plane, respectively.