how to make "Azimuthal Equidistant Projection" in iOS - ios

I'm thinking about creating an iOS app that transforms a 3D sphere into a 2D image using the azimuthal equidistant projection. Here is a nice sample of this type of projection.
Azimuthal Map, Anywhere
I'm new to 3D programming, so I would like to ask for advice which framework / tool is good to use in this case. These are the options that I know:
Unity (+ OpenGL?)
SceneKit (+ CoreGraphics?)
Processing + Processing.js (inside WebView)
Please tell me if there are other solutions. I'd be also glad if you could tell me if there is any sample code or an open source library for this projection.
Thanks in advance!

this can easily be done using shaders, and does not require external libraries.
See http://rogerallen.github.io/webgl/2014/01/27/azimuthal-equidistant-projection/

I would highly recommend to use the c++ 3D libraries such as GXmap and VES/VTK.
GXmap is a small virtual globe and map program. Apart from showing an ordinary globe view of the earth, it can also generate Azimuthal equidistant projection maps suitable for amateur radio use.
VES is the VTK OpenGL ES Rendering Toolkit. It is a C++ library for mobile devices using OpenGL ES 2.0

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