CG Basics - An Introduction to Computer Graphics for Artists - page 16

Table 2.2 Transformation matrix

X-axis Y-axis Z-axis

Transform 1 0 1

Rotate 0 160 0

Scale 0 200 0

Fig. 2.9 Transforms allow users to adjust a CG object's position, orientation, and size

2.3.5 Transforms

There are several ways to modify geometry components by using the many tools
provided in your application. Regardless of the tool you use, the end result is a
modifi cation to the coordinate value of individual vertices. This is accomplished
with a transformation matrix. A transformation matrix is a group of values that tells
the software how a component or object has been modifi ed by altering its position,
orientation, or scale relative to the global origin.
When used in the context of CG, a matrix is a group of numerical values arranged
in columns and rows. Table 2.2 provides an example of what a transformation
matrix would look like for the three transforms illustrated in Fig. 2.9 .
A transformation matrix can be attached to a node on your object or the object
itself. The transformation matrix has nine attributes. They are:

• Transform X, Y, Z

• Rotate X, Y, Z

• Scale X, Y, Z

When an object is transformed, it functions as a node, or container, for the vertices
it is made of. The transformation matrix applies its changes to each of the vertices
within the object, and this is what causes the entire object to be transformed as
desired. However, just as direction is required to fi nd a location, for a transform to take
place, a pivot is required. A pivot allows the software to know from what coordinate
an object is moving, around which coordinate an object is rotated, and from which
coordinate an object is scaled. All geometry is given a pivot when it is created in any