It sounds like you're trying to do too many things at once. First focus on zooming.
I don't see any problem using glOrtho to implement zooming/panning for 2d as it works fine for me.



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How have you implemented the drawing of lines? Do you have a geometry/vector math class to generate lines created from two points with an x,y coordinate. That's where you want start.

So your...

I'm developing a small charting control that displays time series data using OpenGL. I'm programming in C++ in Visual Studio.
My control works great. I can zoom, and scroll data using glOrtho. ...