Texturing a semicircle

There are ofcourse several ways of doing this. I can't tell if this is a graphically good way or not, but one option is to imagine your texure as a plane with the semi-circle on top of it, as if the plane had cut the sphere in half. And then project each pixel on the plane through a straight vertical line to the corresponding points on the semi-sphere above that point.

Another option would be to use stereographic projection, which basically means to project each point on the plane to the point of intersection of a straight line, from a virtual southern pole (virtual since it's non-existing when you have a semi-sphere) through the point of interest on the plane, and the semi-cirle.

thanks. I will implement the first one.