Transformations and Bases in OpenGL and the Viewing Pipeline

AbstractGeometric transformations are fundamental aspects of all computer graphics rendering and are found throughout the computer graphics pipeline. In earlier work we presented mathematical treatment of this topic. The different concepts were combined into a general mathematical procedure based on the concept of vector spaces in linear algebra. While we established the mathematical aspects of transformations, we found the application of this in the OpenGL environment was not simple, especially when the modelview matrix was constructed using the viewing matrix obtained by the “gluLookAt” function. When the gluLookAt function is used, incremental changes in viewing were possible by first re-computing the viewing matrix in world coordinates and not by composing with incremental changes in the viewing coordinates. In this paper we look at alternative methods of application of the mathematical work in OpenGL. The two alternative procedures of rendering (transformations in world and transformation in viewing) are explored in the OpenGL environment.