Graphics Reference
In-Depth Information
4
Trigonometry
When we split the word 'trigonometry' into its constituent parts, '
tri
''
gon
'
'
metry
', we see that it is to do with the measurement of three-sided poly-
gons, i.e. triangles. It is a very ancient subject, and one the reader requires
to understand for the analysis and solution of problems in computer
graphics.
Trigonometric functions arise in vectors, transforms, geometry, quater-
nions and interpolation, and in this chapter we will survey some of the basic
features with which the reader should be familiar.
The measurement of angles is at the heart of trigonometry, and two units of
angular measurement have survived into modern usage:
degrees
and
radians
.
The degree (or sexagesimal) unit of measure derives from defining one com-
plete rotation as 360
◦
. Each degree divides into 60 minutes, and each minute
divides into 60 seconds. The number 60 has survived from Mesopotamian days
and is rather incongruous when used alongside today's decimal system - which
is why the radian has secured a strong foothold in modern mathematics.
The radian of angular measure does not depend on any arbitrary constant.
It is the angle created by a circular arc whose length is equal to the circle's
radius. And because the perimeter of a circle is 2
π
r, 2
π
radians correspond to
one complete rotation. As 360
◦
correspond to 2
π
radians, 1 radian corresponds
to 180
/π
◦
, which is approximately 57.3
◦
.
The reader should try to memorize the following relationships between
radians and degrees:
π
2
3
π
2
=90
◦
,
π
= 180
◦
,
= 270
◦
,
2
π
= 360
◦
