I've spent a lot of time working on a bunch of classes (point, vector, ray, triangle, plane) etc to work with these objects and their intersections in c++. However, now that I am ready to do a full scale project with them, I am finding they are terribly slow! I've look around online and found a handful of things like this, but I was wondering if there was kind of an "industry standard" one that I should use so that if I share code with other people they will already have the libraries installed and be familiar with the notations/function names.
There isn't any standard I'm aware of, but there are good libraries for different purposes - like LEDA, the "Library of Efficient Data types and Algorithms" or CGAL, the "Computational Geometry Algorithms Library" if you are interested in efficient exact or robust computations, but they are not suitable for real-time purposes (I am not aware of any exact and real-time capable library). For real-time purposes you most likely want a subset of a game engine (they are, usually, rather expensive, but you may want to have a look at free engines like OGRE. You most likely will find some interesting "basic" geometry algorithms/implementations in the collision detection and adjacent code of these engines). Furthermore, some fast geometric algorithms are discussed in "Real-Time Rendering" by Möller&Haines.