ZSamuels, if I understand your question correctly, you're trying to write a g-code simulator in C++ to be used with your laser. Is that correct?
If so, there's quite a lot for you to consider. I've got a simulator in Beta Test called G-Wizard Editor:
GWizard Editor: A G-Code Editor and Simulator
Something you may find useful about GWE is it has a facility called "Hints" for folks that are not dyed in the wool g-code experts (actually it is helpful to many experts too, LOL). It pumps out a lot of information about each line of g-code in easy to understand English.
Here is a typical hint with information on an arc, for example:
You might find it useful just because it provides a lot of information about the arc that is not immediately obvious just looking at the raw g-code.
As for the other considerations of a g-code simulator, the language has all sorts of ways to modify what's going on that you'll need to be aware of depending on which dialect your laser's controller plans to support.
For example, you'll need to be prepared to plot the arc when scaling, work offsets, coordinate rotation, and various other factors are in play. Quite a bit of work required to build a general purpose simulator, LOL.
Probably the best place to drill down and see at least one way things are done is to go check out the source code for EMC2.
Best,
BW
Try G-Wizard Machinist's Calculator for free:
http://www.cnccookbook.com/CCGWizard.html