I like to distinguish between game code and low level code. In game code I also use longer names like e.g. a descriptive player_position over just 'p'. For my low level collision or physics routines I prefer short names as I derived them on paper. I usually check in theses paper with the code and add a reference in the code. Then those can be used for debugging. E.g. a function to compute the intersection between a ray and a triangle would look like this:
float IntersectRayTriangle( Vector A, Vector B, Vector C, Vector P, Vector Q ).
If you need functions that take a triangle or ray structure you just overload the function and delegate to the leaf code function. Personally I found this very convenient to work, but YMMV.
As the point came up here I personally recommend against using a special point class. I have to use this lately a lot inside the Maya SDK and find this more confusing than helpful. E.g. you get the translation from a transformation matrix as vector and pass this as position (a point) for e.g. a manipulator you have to convert between types for this. Also the overloading of a multiplication operator between vectors and points which ignores the translation in the first place is very error prone. In this case I prefer explicit functions of the form TransformVector( Matrix m, Vector v ) and TransformPoint( Matrix m, Vector p ). This is my personal preference and it worked well for me, but again YMMV.
In general I find most most libraries that are available as open source these days way over-engineered for such a simple problem like a math library. E.g. using templates and extra point classes and what not else.
Edited by Dirk Gregorius, 27 January 2014 - 07:07 PM.