Math
You should know enough linear algebra to know how the various linear transformations in 3D graphics work – translation, scaling, change of coordinate basis, view transformation etc.
You should also know how to render curves and surfaces using splines, Bezier curves, Bezier patches, subdivision methods (e.g., Catmull-Clark) etc.
Mathematics for 3D Game Programming and Computer Graphics is a good place to start if you are unfamiliar with the math.
GUI
After that, you need to pick the libraries for building the application. For building the GUI, if you want to make it easy to port it across platforms, go with Qt. If you only want to target Windows, then go with the native .NET library.
3D Engine
For representing, manipulating, and rendering 3D objects, you could go with the Unity engine. There are a lot of tutorials and books around to teach you how it works.
If you want to go deeper and build your own engine, you can either work with DirectX or OpenGL/Khronos.
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solved Resources for a 3D animation program [closed]