Chapter 2 - 3D Transformations

Abstract

This chapter provides an overview of vertex, normal, and texture coordinate transformations and the related OpenGL functionality. OpenGL has a simple and powerful transformation model. Vertices can be created with position, normal direction, and sets of texture coordinates. These values are manipulated by a series of affine transformations (a linear combination of translation, rotation, scaling, and shearing) that are set by application. The fundamental transformation representation in OpenGL is a 4 X 4 matrix. Application-controlled transforms, along with the perspective division functionality available in both positional and texture coordinate pipelines, offer substantial control to the application program. The OpenGL transformation pipeline can be thought of as a series of Cartesian coordinate spaces connected by transformations that can be directly set by the application. Texture coordinates have their own transformation pipeline, simpler than the one used for geometry transformations. Modeling transforms are used to place objects within the scene.