## ABSTRACT

The machinery of linear algebra can be used to express many of the operations required to arrange objects in a 3D scene, view them with cameras, and get them onto the screen. This chapter discusses geometric transformations such as rotation, translation, scaling, and projection can be accomplished with matrix multiplication, and the transformation matrices used to do this. It shows how a set of points transform if the points are represented as offset vectors from the origin and discusses how the transforms operate differently on locations, displacement vectors, and surface normal vectors. Building up a transformation from rotation and scaling transformations actually works for any linear transformation, and this fact leads to a powerful way of thinking about these transformations. An immediate consequence of the existence of singular value decomposition is that all the 2D transformation matrices we have seen can be made from rotation matrices and scale matrices.