ABSTRACT
This chapter focuses on Geometric transformations like rotation, translation, scaling, and projection that can be accomplished with matrix multiplication, and the transformation matrices. It shows how a set of points transforms if the points are represented as offset vectors from the origin. The chapter discusses how these transforms operate differently on locations (points), displacement vectors, and surface normal vectors. It also discusses the in terms of the basic types of transformations. 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. Every matrix can be decomposed via singular value decomposition into a rotation times a scale times another rotation. Only symmetric matrices can be decomposed via eigenvalue diagonalization into a rotation times a scale times the inverse-rotation, and such matrices are a simple scale in an arbitrary direction.
