Transformations come in three varieties:

• Scaling -- Change the size of an object
• Rotation -- Change the angular orientation of an object
• Translation -- Change the position of an object

Scaling results in an offset as a side effect. This must be accommodated by first translating to the center of scaling (usually the origin), scale, and then return the object to its rightful place.

Rotation also has this side effect. Translation is not subject to this effect since it is a non-linear operation.

A Grand Transformation, or Grand T, is the combination of all necessary transforms into one resultant matrix which is actually applied to every pixel of the object in question. This reduces the amount of calculations required tremendously. To this end, each manipulation should be viewed as an atomic transform to prevent unforeseen side effects from occurring.

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