At the end of Section 3.4 we indicated that Euler angles can in some cases lead to undesirable artifacts. The most common is called “gimbal lock.” Describe gimbal lock, give an example, and explain why gimbal lock can cause problems.

Section 3.4

In graphics, matrices are typically used for performing transformations on objects. For example, a matrix can be used to move a point from one location to another. In this chapter we will learn several useful transformation matrices:

•Translation

•Rotation

•Scale

•Projection

•Look-At

An important property of our transformation matrices is that they are all of size 4x4. This is made possible by our decision to use the homogeneous notation. Otherwise, some of the transforms would be of diverse and incompatible dimensions. As we have seen, ensuring they are the same size is not just for convenience; it also makes it possible to combine them arbitrarily and pre-compute groups of transforms for improved performance.