[Figure 14] Euler angles are represented as a 2D projection in the Graph Editor.

Euler Angles
The orientation of an object is calculated in a number of ways by 3D software. The most popular method, and the one we will focus on in this book, is Euler (pronounced “oiler”) angles. Euler angles are popular because they can be easily represented as 2D projections, or function curves, as in Figure 15. Function curves are important tools for visualizing the timing and acceleration of an animated object. People who use 3D software are accustomed to using Euler angles because of their ability to be viewed and edited in graph or function curve editors.

[Figure 15] Changing the rotation order in the Attribute Editor alters the rotation “hierarchy” of your object.

The Euler angles are the name given to the set of individual rotation angles that specify the rotation in each of the X, Y and Z rotation axes. There are three individual axes that control the orientation of the object you are rotating, which, of course, is the reason why you see three rotation function curves in your Graph Editor. A function curve is a representation of these individual rotation angles at a given time or frame. The software uses these values to resolve the orientation for an object by constructing a series of rotation matrices. (For more information on matrices, see “The Transformation Matrix” section later in this chapter.) I use the word “constructing” because the software is not using a simple additive or multiplication process to determine the orientation. It takes a complex combination of individual rotation matrices to determine an orientation. You may not understand the math, and, really, you don’t need to, but it is important to understand the results of these calculations. Try to think of this construction process as you would a hierarchy of individual nodes that are limited to rotate on one axis. This is what we call the rotation hierarchy.

Rotation Order In Maya, rotations are calculated on each of your objects based on the rotation order specified by the rotation order attribute (see Figure 15). This attribute is manipulated by a setting in the Attribute Editor. The rotation order — by default, X, Y, Z — specifies which axis rotates first, second, and last. Similar to a hierarchy built with the first axis on the bottom and last axis on top, the first axis inherits the rotation of the second and third. The second axis inherits the rotation of the third. The third acts as the parent of all the rotations.

In the default X, Y, Z rotation order, Z can be thought of as the parent of Y, and Y as the parent of X. In this order, the first axis listed, X, is evaluated without influencing the other axes. The purpose of changing the rotation order is to create an object that will allow us to easily understand the result of the rotations as visualized by the animation function curves, and avoid the presence of Gimbal lock. Gimbal lock is a nasty by-product of the Euler angles we use in Maya and other 3D packages. We will discuss this in the “Gimbal Lock” section later in this chapter.