iPhone 3D Programming

Chapter 2. Math and Metaphors

There’s a pizza place near where I live that sells only slices. In the back you can see a guy tossing a triangle in the air.

—Stephen Wright, comedian

Computer graphics requires more mathematics than many other fields in computer science. But if you’re a pragmatic OpenGL programmer, all you really need is a basic grasp of linear algebra and an understanding of a few metaphors.

In this chapter, I explain these metaphors and review the relevant linear algebra concepts. Along the way I’ll tick off various OpenGL functions that relate to these concepts. Several of such functions were used in the HelloArrow sample, so code that may have seemed mysterious should now become clear.

Near the end of the chapter, we’ll leverage these math concepts to push the HelloArrow sample into the third dimension, transforming it into HelloCone.

The Assembly Line Metaphor

You can think of any graphics API, including OpenGL ES, as an assembly line that takes an assortment of raw materials such as textures and vertices for input and eventually produces a neatly packaged grid of colors.

The inputs to the assembly line are the natural starting points for learning OpenGL, and in this chapter we’ll focus on vertices. Figure 2-1 depicts the gradual metamorphosis of vertices into pixels. First, a series of transformations is performed on the vertices; next the vertices are assembled into primitives; and finally, primitives are rasterized into pixels.

Figure 2-1. The OpenGL ES assembly line ...