Selection in 3D Graphics Environments
Christine Albert and Lindsey Press

In week two, we focused on understanding the theory behind 3D graphics enviornments. Because every object in a 3D scene is drawn in its own coordinate system called local space, to be selected these objects need to be transformed into world space, which is a coordinate system common to all objects. This is done by performing translation, rotation, and scaling; mathematical operations that are solved by matrix manipulation. After studying the theory behind scaling, rotating, and translating objects, we practiced performing the actual matrix multiplication for each of the three properties. Listed below are the results of the transformations.

Shown below is an example of the base vertex v=(1, 1, 0, 1) being scaled by (10,10,10), rotated 45 degrees about the z axis, and translated by (100, 100, 0).