Mathematical Structures for Computer Graphics

Chapter 2Vector Algebra

Vectors are essential for computer graphics. As we saw in Chapter 1, they represent displacement as we describe an object by moving from point to point. If we wish to move from point to point , an arrow drawn starting at point and ending at point tells us which direction to go and how far to go. This arrow is the vector and has both direction and length.

Displacement alone is not sufficient reason to develop the notion of a vector. It turns out that we can define operations between vectors that connect with geometric operations. For example, adding two vectors means adding two displacements and we can geometrically understand what it should mean to add displacements. Although not as intuitive, we can also define the multiplication of two vectors in such a way that there are geometric interpretations of the result. The plan then is to develop an algebra of vectors that corresponds to geometric operations and may make the task of describing geometric objects for images just a little easier.

Vectors are especially useful because they are independent of any particular ...