ABSTRACT

Two-dimensional transformations are used to change the location, orientation, and shapes of splines in 2D plane. These transformations are translation, rotation, scaling, reflection, and shear applied individually or in combination of two or more, whence they are known as composite transformation. Given known coordinates of a point, each of these transformations is represented by a matrix which when multiplied to the original coordinates produce a new set of transformed coordinates. An entire spline is transformed by transforming all the points of the spline. To calculate the coordinates and directions a 2D right-handed coordinate system is necessary. This chapter formally introduces a 2D coordinate system and then lays the foundations of a homogeneous coordinate system using which all the transformations can be represented in a uniform manner. The transformation matrices are first derived and then their applications are illustrated using examples, MATLAB codes and graphical plots. The chapter ends with a discussion on viewing transformations used for mapping a window to a viewport, and coordinate system transformation used for mapping between multiple coordinate systems.