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Looking for a book that covers the math of vectors and planes, and their relations with each other (such as intersections, reflecting vectors across a point on a plane, etc.)
I'm looking for something that describes these things in great detail in a math sense. If you know of a good book like this, feel free to divulge. Thanks.
Well, wait I thought you've already had some games programming books that detail this?
Also, are you looking for something in a university context or a graphical/games programming context?
Every University calculus book I've personally comes across details the math for doing vector/plane analysis (which includes projecting/rotating vectors)...same story with any university physics book. I thought you were already doing both of these at waterloo?
For a game/graphics programming book, I have several that do this math. Mathematics for 3D game programming and computer graphics is excellent in terms of the amount that it covers, but I've found that if I wasn't already somewhat familiar with the material I had a hard time picking it up with that as my source. Also, there are various versions of this, the second having recently been released. It is by eric lengyel.
From a game physics programming perspective I have 'Game Physics' by David Eberly...it has a huge math reference in the back, detailed enough that it should work for anybody (even if you weren't interested in game physics).
Engineering Mathematics is somethign else to look into (I don't remember the latest edition). It discusses pretty much anything you'd ever need to know about, with a lot on vector/plane analysis (but it comes more from physics/statics point of view, mostly with integration).
Elementary Linear Algebra by Howard Anton 0-471-66960-1
Cool.
So far, what I'm trying to do is make some simple OpenGL demos for colliding lines with planes. I've currently got it so I can shoot a line through a plane and plot the interception point. I can also determine if it's actually inside the plane (with a triangle so far).
Other stuff I'm hoping to do is reflecting on planes, sliding across planes, all that good stuff. I found some info in my calc book about vectors but it only covered the stuff I already knew (dot product, cross product).
And at bob: no, we haven't done any vector stuff at all, sadly. Just a review of high school calculus and some really crazy algebra stuff with proofs (blegh).
Everything you have described can be done with vector projections, which just requires unit vectors (typically the plane normal) and a dotproduct, and in the case of determining if a point lays inside a triangle it requires dot products and crossproducts (I can show you my implementation of that if you want).
For instance, sliding across a plane requires that you remove the component of your velocity vector in the same direction of the plane normal.
Reflecting a vector off a plane is the same thing, except you remove twice the component of the vector in the same direction of the plane normal.
Incidentally, a better source for doing these types of things can actually be found in a mechanics book, look for 'coefficient of restitution' for both reflecting and sliding across planes are really just two manifestations of the coefficient of restitution. This information can be found in probably all of the books mentioned thusfar except a calculus book.
Physics for Game Developers is a watered-down physics book which contains this information (david bourg).