I have a flat rectangular plane representing an area of the earth. I am trying to bend this plane on all three axes to fit the surface of a sphere (in this case I am modeling the earth as a perfect sphere).
My work so far, assuming the Z axis is above, Y is north/south, and X is east/west, I have computed that need to bend it 34.1 degrees on the Y axis to correct for the latitude differences in the width of this plane. I have also computed the Z and Y bends.
However, the software I am using (Blender) applies these bends one after the other. That is, once I bend the Y axis, it will then bend the Z axis. This means the order I apply these bends affects the final shape.
I am having trouble with the math of bending an already curved surface along a different axis to match a sphere.
I suspect there is something simple I am missing here. I am using elements of 3D software, GIS software, and math, and I'm not sure where is most appropriate to post this question. Since I am modeling the earth as a perfect sphere I am hoping someone can point me in the right direction in determining the correct angles to apply to this plane.
If it is relevant, the plane represents an area defined by the following coordinates:
Upper left corner: 53.898 degrees north, 125.359 degrees west
Lower right corner: 24.218 degrees north, 60.906 degrees west
To this plane I have applied an equirectangular projected map image.
I have attached a screenshot of Blender. You can see the rectangle does not touch the sphere at the edges based on the computation on bending the flat plane, how close it is depends on the order I apply the transforms (on the lower right of the screenshot). I am not sure if the angles are correct, but whatever the values, I don't believe they would ever work as the order of the transform matters.
