for Flash 3D Programming Maths

This document is a summary of my reading trying to understand the maths underpinning flash 3D Programming. Much respect to Ahab and all the rest of the flash maths gurus.

Linear Algebra

The equation of a line in 2D space has the form:

ax + by = c;

The equation of a plane in 3D space is:

ax + by + cz = d;

Linear equations have no products or roots of variables and no variables involved in trigonometric, exponential , or logarithmic functions. Variables appear only to the first power.(no squares).

Matrices

A common use of matrices is to represent a system of linear equations. The matrix derived from the coefficients and constant terms of a set of equations is called the augmented matrix. The matrix containing only the coefficients of the system is called the coefficient matrix of the system. Here is an example :

		Equations	Augmented Matrix 	Coefficient Matrix
	x  - 4y + 3z =  5	| 1 -4  3  5 |		|  1  -4   3 |
	-x + 3y - z  = -3	| -1 3 -1 -3 |		| -1   3  -1 |
	2x      - 4z =  6	| 2  0 -4  6 |   	|  2   0  -4 |

So what ? Well lines are drawn using these equations. And you can manipulate that line by changing the matrix. Multiply it by 2 to make it twice as big? Swap first and second rows. It gives you quick and easy control over the equations(lines).

Applications of Linear Equation systems

Polynomial Curve Fitting
Suppose you had a collection of points (x1,y1), (x2,y2), (x3,y3),....(xn,yn) in the x-y plane and you want to find the equation that passes through these points. (put scan of pic here..) Dont know if it works yet.. it is pure speculation on my part. LMAO .