Basic transformations for OpenGL

On to Chapter 3 Viewing of the Red Book. Matrices and Transformations determine how an object is shown on screen. To manipulate the different matrices, we first have to set the kind of matrix (texture, projection or modelview=default) with glMatrixMode(). And all transformations after that will apply to that particular matrix. Before every group of transformations, we have to initialize the matrix with glLoadIdentity() so that we work with a whole new matrix, not the previous matrix created.

Modelview

To rasterize 3-dimensional objects to the 2-d screen, the following kinds of matrixes are applied in this order:

(1) Viewing transformations

(2) Modeling transformations

Why this order? Transformations are applied to an object as functions, so if we let viewing matrix V be viewFn, modeling matrix M be modFn, and object be O, then the code will look like this:

viewFn();

modFn();

O;

In matrix form, it will look like this:

T(x) = VMx

This makes sense because we want to rotate an object, then look at it. The above matrices will make up the ModelView matrix.

Projection

The 3-D models are projected onto a screen. The projection can be:

(1) Perspective - Since further objects will seem smaller than nearer objects, we want to reflect this. One easy way to think about this is like a frustum, which has a larger base than the other side. The larger base is closer to us. We can transform the initial perspective matrix with glFrustum(). 

(2) Orthographic - The object is flattened directly onto the screen, regardless of the angle or distance that a viewer might see it in real life.

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After drawing something, we can use gluLookAt() to see the scene from another angle. This is useful for when something looks correct from the front, but when seen at an elevated angle, is actually out of shape.

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Matrix Stack

When creating multiple models that are related to each other, it would be useful to transform from one point at model_1 to make a model_2, then go back to the origin, and transform somewhere else to make another model_2. Thus, the two model_2s are created relative to model_1. This process of doing transform_1, undo, transform_2, undo, transform_3, undo can be contained LIFO-style, which is what a stack does.

Modelview stacks can contain 32 matrices, while Perspective stacks can hold 2 matrices.

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Planet System tutorial

Demonstrated modelview and perspective transformations, matrix stacks and keyboard control.