Matrix Transformations
The rules which govern how elements in matrices behave give rise to unique behvours and characteristics. In many cases these characteristics can be used to simplifiy multi-step operations in algebra by creating a predictable structure of manipulation which can be elegantly manipulated using matrix operations. With vector manipulation x and y cordinates of a object can be stored in a matrix so the matrix acts to describe the object. This matrix can then be multiplied by another matrix call and operator which will modify its perperties in a predicatble way creating a resulting matrix with a new modified description of the original object.

For example:


All the matrix does is provide the mechanism in which to calculate a set of results. However this mechanism can be used to produce a variety of effects on the properties of objects in space such as translation, reflection, rotation and distortion.

The 3D Indentity Matrix



Multiplying 3D coordomates by the identity matrix:

How to reflect a shape using matrices and actionscript

The 3D Reflection Matrix:



Reflecting an object in the y axis:


How to reflect a shape using matrices and actionscript
To learn more about matrix reflection [3D Matrix Reflection Knowledegbase].

The 3D Translation Matrix:



Translating an object in 2d space:


How to move an object in 3D using matrices and actionscript
To learn more about matrix translation [3D Matrix Translation Knowledegbase].



A 3D Rotation Matrix



Rotating a shape about the z axis:

How to rotate an object in 3D using matrices and actionscript
To learn more about matrix rotation [3D Matrix Rotation Knowledegbase].

A 3D Distortion Matrix (affline transformations)



Stretch a shape along the y axis

How to stretch an object using matrices and actionscript:
To learn more about matrix distortion [3D Matrix Skew Knowledegbase] and [3D Matrix Scale Knowledegbase].