13 - Linear Transformations in Computer Graphics

Abstract

Linear transformations are matrix operations that describe movements of points in a space. The coordinates of a point make up a 2×1 matrix. A 2×2 matrix that describes the transformation is multiplied with the coordinate matrix, resulting in a 1×2 matrix that holds the coordinates of the transformed point. Linear transformations provide a powerful set of tools for such things as rotating an object, moving it around the screen (translating it), shearing it, flipping it, and so on. This chapter discusses basic matrix operations, shear in X and Y. It also discusses how linear transformations might be implemented and used in a drawing tool. If the tool is object oriented, then each object can have its own origin, or anchor point. The object is made of one or more primitive shapes. Not every pixel needs to be stored, only an enumeration indicating which primitive should be used to create the shape, where the shape is in relation to the object's origin, and various shape-specific information.