What Are Transform(ation)s?
Transformations, in their strictest and broadest mathematical sense, are mathematical operations that map a set of items X onto another set, Y. In geometric terms, this means that we can apply a mathematical operation on a set of objects in space to map them onto a new space geometry.In layman's terms, we can take an object and apply what we call transformation groups. These are ordered lists of operations (called transforms) that we can use to move, scale, reflect, rotate and skew objects. Sounds simple enough, right?
But before we jump right into the whole business of object manipulation, we need to look into how these transformation groups work, exactly. As mentioned, transformation groups are an ordered set of transformation operations, the implication being that the order of transformations matters and gives different results depending on the ordering of those operations. This is because transformations take into account every object's geometric properties, including its current position.
http://msdn.microsoft.com/en-us/scriptjunkie/gg709742.aspx
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