3D Coordinate Reflection Using Matrices
As we have seen in matrix multiplication any* matrix when multiplied by the unit matrix remains unchanged.

The Unit Matrix






The unit matrix can be modified to change the resulting matrix in predictable way. Each non zero term in the unit matrix acts on a single specific column of elements in the matrix it is multiplied with. This can be very usefull if you wish to perform a transformation on a sepcific set of data within a matrix. For example if you create a matrix with the x,y,z coordinates of a point in 3D and then multiply it with this modified unit matrix:



The resulting matrix is identicle accept for the fact that the value of the x coordinate is now negative.


This has the effect of reflecting that point on the y axis. Modifying other values in the unit matrix can create reflection about other axis:

Reflection about the x axis



Resulting in the value of the y coordinate becoming negative.


Reflection of z coordinates:



Resulting in the value of the z coordinate becoming negative.

3D Reflection Using Matrices In Actionscript (points)

To learn more about matrices in flash see the [3D Matrices Knowledgebase].

*Note: This is true only if the matrix meets the basic condition that the number of rows of columns of the first matrix match the number of rows of the unit matrix.