Matrix Transforms

In applications that work with 3D graphics, you can use geometrical transforms to do the following:

• Express the location of an object relative to another object.
• Rotate and size objects.
• Change viewing positions, directions, and perspectives.

You can transform any point (x,y,z) into another point (x', y', z') by using a 4x4 matrix, as shown in the following equation.

Equation of transforming any point into another point

Perform the following equations on (x, y, z)

and the matrix to produce the point (x', y', z').

Equations for the new point

The most common transforms are translation, rotation, and scaling. You can combine the matrices that produce these effects into a single matrix to calculate several transforms at once. For example, you can build a single matrix to translate and rotate a series of points. Matrices are written in row-column order. A matrix that evenly scales vertices along each axis, known as uniform scaling, is represented by the following matrix using mathematical notation.

Liliane El Boueiz

Source: http://msdn.microsoft.com/en-us/library/bb206269(v=vs.85).aspx