I think math.stackexchange is the right place to post this, but if not, feel free to tell me.
I have a series of points to be plotted on a sphere (Each one has a latitude and longitude value). These points are not actually spherical, but are differences from a perfect sphere at the lat/longitude. I'm trying to find out how to convert them into the absolute density.
For example, I have a sphere with a radius of 10. At latitude 10, longitude 5, the point should b extruded outward 1 unit ('Away' / on the radius). However, I do not know how to get the x,y,z coordinates (Cartesian) for the actual location of that point. In other wards, how do you map a height map to a sphere and get the exact locations of points?
Thanks!
Just look at the point $(\rho,\theta,\varphi)$ in spherical coordinates. You could locate the point you need using $\theta$ and $\varphi$ then the height variation can be done by increasing/decreasing $\rho$ by the height difference from the sphere it would normally sit on.