Game Development Reference
In-Depth Information
In fact, this isn
t even going to be an in-depth exploration of those
topics because they really aren
'
t necessary for most casual games.
In this chapter, we will cover the foundational concepts you
'
ll
need to understand to be able to handle a wide variety of chal-
lenges involved in game development. We will accomplish this in
two parts: Geometry and Trigonometry, and Physics, each with a
practical example illustrating the concepts. If when you
'
re done
with this chapter, your appetite is whetted for a more in-depth
look at these topics, I have provided links to further reading on
this topic
'
'
s Web site.
The Math Class
ActionScript includes a core library for performing a lot of the func-
tions we
re going to learn about in this chapter. It is the Math class,
and it will quickly become invaluable as we get into more compli-
cated problems later on in our code. It doesn
'
'
t include everything
'
'
we
functions we can write to make it even more useful.
ll eventually need, but later we
Part One: Geometry and Trigonometry
Geometry, specifically Euclidean geometry, is the branch of mathe-
matics that deals with, among other things, the relationship
between points, lines, and shapes in a space. From it, we derive
the formulas for finding the distance between two points, as well as
the entire x - y coordinate system (known as the Cartesian coordi-
nate system) on which Flash
s Stage is built. Figure 11.1 illustrates
a typical two-dimensional coordinate system.
Flash
'
s coordinate system is slightly different in that it is flipped
over the x-axis ,resultingin y values being reversed. The upper-left
corner of the Stage is at (0, 0) and expands down and to the right
from there, as shown in Fig. 11.2 . This is important to note because
it is diametrically opposed to the notion that numbers decrease as
they move
'
on a graph, and it can cause confusion later
when we move into some of the concepts of physics.
Trigonometry (or trig for short) is a related, but more specific,
branch that describes the relationships between the sides and
angles of triangles, specifically right triangles (triangles with one
angle of 90
down
°
). All triangles have some fundamental properties:
￿
A triangle
'
s interior angles always add up to 180
°
.
￿
Any triangle (regardless of orientation and type) can be split
into two right triangles.
￿
The relationships between any given side and angle of a triangle
are defined by ratios that are known as the trigonometric
functions .