So, I decided to write a small naive 3D engine of my own, just to understand how it works.
I studied about the subject, and wrote this engine, which is basically a camera matrix: (no textures or anything)
The only external graphics function I used is the Graphics.DrawLine() function.
What is a Camera Matrix anyway?
It's something that can be used to display 3D objects on our 2D screen.
Think about a real camera like in a 2D movie (not Avatar) - you place it somewhere in the room (translation), it looks towards the scene (rotation), it can zoom in and out (scaling), and it converts the 3D scene to 2D (projection).
From now on we say "translation" instead of "position". Mathematicians are to blame for that.
It's easy to do operations on vectors, why complicate things with Matrices?
One of the main reasons is that matrices can be easily concatenated.
From DirectX MSDN:
One advantage of using matrices is that you can combine the effects of two or more matrices by multiplying them. This means that, to rotate a model and then translate it to some location, you do not need to apply two matrices. Instead, you multiply the rotation and translation matrices to produce a composite matrix that contains all of their effects.Let me put it this way:
"Using" a 4x4 matrix requires 16 multiplications and 9 additions.
So rotating, which is "using" a rotation matrix, requires 16 multiplications and 9 additions.
And scaling also requires 16 multiplications and 9 additions.
If we do rotating and then scaling it would take 32 multiplications and 18 additions. Translation would takes us up to 48 multiplications and 27 additions, and so on...
BUT, if we concatenate the rotation and scaling matrices, we will get a third matrix that does both operations in half the time (16 multiplications and 9 additions).
In fact, we could concatenate any number of matrices, so the resulting matrix will do all the operations we want in only 16 multiplications and 9 additions.
You might have noticed that we still need to do the concatenation operation which takes a long time, but it's worth it when you design a 3D game with thousands and thousands of objects to scale rotate translate etc. but only a few matrices to concatenate.
Why a Camera Matrix is not 3x3?
In short, because then we can't use it for translation (moving the vectors).
For more details read this fantastic article: