Visualizing orientation of a 3D coordinate system

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Dear GLBasic forum members,
I would like to create a program to visualize the orientation in 3D space of a orthogonal coordinate system.
The orientation of the coordinate system is specified using Euler angles the values of which would be controlled using slider controls.
The coordinate axis of the rotated system will be represented by arrow vectors.

Perhaps the forum could provide some hints as to how to get started on such a project using GLBasic?

The diagram contained in the Wiki article on Euler angles gives an idea of what I would like to create.

Kitty Hello

Search for euler in the forum. Also open the sample files of NewtonSDK and EntitySystem. Search for Euler in these files.