Once you start looking under the hood, you'll get some sense of the lay of the

land with matrices and how they relate to transforms. Here's a map of the sort

of things you'll find. The upper left area of the matrix is where rotations and

scales show up. If a transform changes only this area of the matrix, it's called

a linear transformation. I'm not going to spend time on the formal definition of

this term. The additional course materials include resources for more on the

underlying math. The definition is fairly basic stuff about how addition and

multiplication are preserved. But doesn't have much effect on how we actually do

computer graphics. The upper right is where the translations accumulate. These

translation values will get effected by multiplication with other matrices of

course. Translations only effect points since vectors have zero for their fourth

coordinate. 3JS provides a function called decompose to extract the translation,

rotation and scale factors from a matrix. The translation and scale factors come

back as vectors, as you might expect. The rotation comes back as a quaternion.

Something we'll talk about when we get to animation. The short version is that a

quaternion is a compact way to store the axis and angle of rotation for a

rotation matrix. One useful property quarternions have is that you can easily

interpolate between them, which is useful for interpolating between two

different orientation. Notice that the bottom row is always 0, 0, 0 1. The

transforms we covered here are called affine transforms. Parallel lines stay

parallel when an affine transform is applied. In modeling you'll essentially

always use affine transforms. So we never change this last row. Since GPUs are

tuned to use four by four matrices Most of us just use four by fours everywhere

for simplicites sake. When we discuss perspective cameras, we'll set the values

in this last row. We'll then be using a projective transform. With affine

transforms, when a points coordinates are multipied by the matrix. The fourth

coordinate starts out as one and ends up as one. This last row in a projection

matrix modifies that fourth coordinate to be something other than one. What that

means is something we'll leave til a later lesson.