|
|
|
|
|
| Computer Graphics is a very mathematics intensive field. If you really want to get into programming graphics you’re going to have to get a hang of a little bit of the math involved. This tutorial expects that you know some calculus and trigonometry at the very least.
This tutorial is going to focus on some of the more basic principles you need to know before going into the field of computer graphics. These principles are taken from a branch of mathematics known as Linear Algebra..While most common graphics libraries (such as D3DX – which is part of DirectX) shield you from the majority of the math involved, it is still important to develop an understanding of the calculations involved. So this tutorial is your first step into some of the mathematics that you’ll probably end up needing to use at some point or the other. Keep in mind that this is not a complete reference (not even close) to the mathematics you could need during your adventures, but it’s a start.
There are 2 ways in which we can tackle the math (i.e., Linear Algebra) we need. One is to go about it abstractly which is usually how it’s done at university level. But since this is an introductory tutorial which is just going to give you enough to survive, we’re going to take a mixed formal and informal route with explanations that a 2 year old can understand (theoretically speaking). So if you scroll through, it may look math heavy, but if you read this tutorial you’ll find that the explanations are lighter than a feather (as I’ve taken the liberty of abusing the really technical definitions and explanations – I’ll leave that to your university professor or some big scary math book).
Definitions Scalar: A single valued term or a value which more or less is what is meant when most people say "number". E.g., 1, 3, 4, 2.5, etc… Set: Naively, a collection of objects e.g {mom, dad, US}, {a,b,c} , {C#, C++, BASIC, HTML}, {Everything in Existance} , {10, 0.5}, etc… Tuple: A finite collection of objects which are ordered in a certain way and having that every element contained may appear more than once. e.g. (2.7, 0.1, 300, 1024), (10, 0.5), (car, mouse, house), etc… Note also that a tuple is a set but a set is *not* a tuple. Actually, here's something to confuse you, everything is a set. n-tuple: A tuple that has ‘n’ objects in it. Pair: A 2-tuple, (doublet) Triple: A 3-tuple, (triplet) Quadtuplet: A 4-tuple Pentuplet: A 5-tuple Frustum: A pyramid with the tip cut off (i.e. flat tip instead of pointy). |
|
