Lecture: Matrix Transformations

Dear students:

Geometry makes paintings, and transformations make movies. A transformation is achieved by simple adding and multiplying, but this arithmetic gets out of hand when we have a lot of transformations to apply. Enter matrices. These little grids of numbers offer a universal interface for transformations. A sequence of tranformations may be collapsed down to a single matrix by multiplying all of its steps together. Today we'll look at bringing some life into a renderer by moving models around with matrix transformations.

Matrices are a graphics superpower. Speaking of superpowers, this AI woman really knows how to rotate.

Mat Chat

Let's warm up with a friendly exploration of matrices. Find a partner and complete these steps:

1. Go to Transformula (transformula.twodee.org).
2. Each partner secretly chooses a transformation and configures it according to their desires. Make sure your transformation isn't the identity.
3. Take turns trying to figure out each other's matrix. On each turn, you can either query a single element (say something like “row 3, column 0”), or you can guess the transformation.

With the same partner, play another game:

1. Reload Transformula to reset it.
2. One partner secretly builds an interesting transformation using exactly two matrices: one translation and one of the three rotation matrices. Once composed, the partner unchecks Show matrices.
3. The other partner tries to match the transformation on their own computer. What rotation is being applied? In what order do the translation and rotation occur?
4. The roles flip.

Everything Creature

Next we'll apply the matrices you read about by making a creature that galumphs through the scene by rotating, just like in the game Everything:

We'll model the creature in Blender, color its vertices, load it in from a glTF file, and then have it rotate around in a circle.

TODO

Here's your list of things to do before we meet next:

See you next time.

P.S. It's time for a haiku!