Consolidating Windowing Transformations Discussion with Applications to Screen Savers Program in Computer Graphics

摘要

Consider the screen saver output shown in Figure 1. The screen saver is an output of a program written in the OpenGL API. Missing from the output is the rotation animation of each scene within its own viewport. The scenes generated are based on parametric equations and the concept of turtle graphics. The program resulting in the screen saver output incorporates many of the special 2D windowing transformations found in the OpenGL fixed-function model pipeline. We propose a methodology of covering the needed important windowing transformations and mathematical derivation during the early part of a first course in computer graphics. The windowing transformations used are the affine transformation, a generalization of linear transformations. In the later part of the course, these same concepts can be applied using matrix algebra as a method of concatenating transformations. Covering these topics, and formulating the mathematical basis, early in a first course in computer graphics eliminates many of the ambiguities found in the transformations in the OpenGL pipeline. We include additional constraints not found in OpenGL to enhance the topics coverage. WebGL is a graphics API developed from a version of OpenGL used in mobile devices and is based on OpenGL ES (embedded systems). Hence, the methodology of coverage applies to WebGL as well. While current computer graphics APIs offer a very powerful set of graphics tools, the underlying understanding of the mathematics used in constructing the APIs remain important. We feel consolidating the coverage of topics on windowing early in the course is also important. In particular the different windowing transformations found throughout the graphics pipeline.