Graphics Reference
In-Depth Information
Chapter 3
Vectors
3.1 Introduction
Vectors can be used to represent all sorts of data from weather maps to magnetic
fields, and in computer graphics they are used to represent oriented lines and lo-
cate points in space. In 1853 Sir William Rowan Hamilton (1805-1865) published
his topic
Lectures on Quaternions
[2] in which he described terms such as
vector
,
transvector
and
provector
. Hamilton had been looking for a 3D equivalent to com-
plex numbers and discovered quaternions. However his work was not widely ac-
cepted until 1884, when the American mathematician Josiah Willard Gibbs (1839-
1903) published his treatise
Elements of Vector Analysis
,[3] describing modern
vector analysis
.
3.2 Vector Notation
As a vector contains two or more numbers, its symbolic name is generally printed
using a
bold
font to distinguish it from a scalar variable. Examples being
n
,
i
and
q
.
When a vector is assigned its numeric values, the following notation is used
2
3
.
n
=
The numbers 2 and 3 are the
components
of
n
and their position within the brackets
is very important.
Two types of notation are in use today:
column vectors
and
row vectors
.Inthis
topic we use column vectors, although they can be transposed into a row vector
using this notation:
n
T
. The superscript
T
reminds us of the column to row
=[
23
]
transposition.
