Transformations of Two-dimensional Space; Matrix Representation

Abstract

It is now time to consider what happens to an object, be it a point, line or curve, when the coordinate system is changed. As we have seen in previous chapters, all computer graphics reduces to specifying and joining points, and so all that is necessary is to discover what happens to the coordinate representation of points with a change of coordinate system. Up to now the coordinate origin, axes and dimensions defined for the two-dimensional space have been identified with the origin, axes and scale of the screen (the so-called observer coordinate system). This is not the general case, and so it is necessary to change from the old defined system to the observer coordinate system of the screen. There need only be three basic forms of coordinate-system change, that is, translation of origin, change of scale and rotation of axes; all other changes can be formulated in terms of these three types. Remember that initially the space is not changed; it is simply the position, direction and scale of the coordinate system used to define the position of points in space that are altered.