Selection in 3D Graphics Environments
Christine Albert and Lindsey Press

The third week we explored different ways of transforming objects into the world space. In order to reverse the effects of translation, rotation, and scaling, we experimented with the inverses of these functions. The goal of performing the inverse function is to transform the vertex from world space back to local space. The inverses of these operations are also solved using matrix manipulation, but the order of the operations is reversed; translation, rotation, and finally scaling. If the original transformation is known, applying these inverse operations to a transformed vertex will produce the original vertex as the result. Listed below are the results of the inverse transformations.

As a continuation of the example in week 2, we reversed the operations below. You will notice that the final vertex is (1,1,0,1), which is the original vertex and thus the desired result!