Graphics Reference
In-Depth Information
'I am no good at mathematics' is a common response from most people
when asked about their mathematical abilities. Some suggest that their brain
is unable to cope with numbers, some claim that it's boring, and others put it
down to inadequate teaching. Personally, I am not very good at mathematics,
but I delight in reading topics about mathematicians and the history of math-
ematics, and applying mathematics to solve problems in computer graphics.
I am easily ba
ed by pages of abstract mathematical symbols, but readily
understand the application of mathematics in a practical context.
It was only when I started programming computers to produce drawings
and pictures that I really appreciated the usefulness of mathematics. Multi-
plication became synonymous with scaling; division created perspective; sines
and cosines rotated objects; tangents produced shearing, and geometry and
trigonometry provided the analytical tools to solve all sorts of other problems.
Such a toolkit is readily understood and remembered.
1.1 Is Mathematics Difficult?
'Is mathematics di
cult?' I suppose that there is no real answer to this ques-
tion, because it all depends upon what we mean by 'mathematics' and 'di
-
cult'. But if the question is rephrased slightly: 'Is the mathematics of computer
graphics di
cult?' then the answer is a definite no. What's more, I believe
that the subject of computer graphics can instill in someone a love for math-
ematics. Perhaps 'love' is too strong a word, but I am convinced that it is
possible to 'make friends' with mathematics.
For me, mathematics should be treated like a foreign language: You only
need to learn an appropriate vocabulary to survive while visiting another
country. If you attempt to memorize an extended vocabulary, and do not
put it into practice, it is highly likely that you will forget it. Mathematics is
the same. I know that if I attempted to memorize some obscure branch of
mathematics, such as vector calculus, I would forget it within days if I did
not put it to some practical use.
Fortunately, the mathematics needed for computer graphics is reasonably
simple and covers only a few branches such as algebra, trigonometry, vectors,
geometry, transforms, interpolation, curves and patches. Although these topics
do have an advanced side to them, in most applications we only need to explore
their intermediate levels.
1.2 Who should Read this Topic?
I have written this topic as a reference for anyone intending to study topics
such as computer graphics, computer animation, computer games or virtual
reality, especially for people who want to understand the technical aspects.
