Matrix Representation of Transformations in Two-dimensional Space

Abstract

In all pictures drawn so far the co-ordinate origin, axes and scale of the window have been identified with the ABSOLUTE axes defined for two-dimensional space. This is not the general case. Usually we want the window to move around in space, not necessarily being anchored to this arbitrary but fixed co-ordinate system. We must, therefore, consider what happens to the definition of an object, be it a point, line or curve, when the co-ordinate system is changed. As we have seen in previous chapters, the drawing of any object in computer graphics may ultimately be considered in terms of specifying and joining groups of points, and so all that is necessary is to discover what happens to the co-ordinate representation of a point with a change of co-ordinate system.