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AI / LUA / C++ / Game Math Library Questions

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I am currently working on a custom engine that is c++ based. For now, I am trying to do an integration of Lua into the engine. I have read the forum of the pros and cons, the logic behind Lua and c++ engine (low level scripting or high level scripting). 

I still have doubts whether should I bind game math library (GLM;vector3d etc....) into Lua as well. 

Currently, the LUA script controls how the AI reacts and the control setup for the player. (WASD for movement etc).

The game is focusing on FPS.

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To my opinion, yes. Your scripting should behave just like your engine mathematics, whether for accuracy, quickness, and also what it provides (maybe lua will lack some of your mathematical types).  The latter works also for the interface (so, same name for functions). This looks essential so that one could easily work with both the script and the sources of the engine.

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Im having the same thoughts about what I need to do in LUA for my own engine and scripting also.  Firstly, picking the right LUA library (my project is in C# also).

But I feel I will need to do as you are doing, bind my complex functions and leave the very basic scripting to LUA.  

Interested to know what your goal with the LUA scripting will be.  


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