/3/ - 3DCG

How can I shrinkwrap a mesh to a sphere without distorting its proportions? Here's my attempted workflow, and pic related is the result.

>add a UV sphere
>draw a curve that matches the outer edge of the shape to shrinkwrap
>draw a curve that matches the inner edge of the shape
>convert both curves to meshes, and join those meshes so that they form the outline of the shape
>without creating any additional edges, faces or extrusions, add the shrinkwrap modifier
>set the target to the UV sphere and the mode to target normal project (otherwise the shape becomes badly distorted)

As you can see, the shape is basically intact but the X and Y axes are off. The parts near the pole are shrunk, but the parts near the equator are grown.