Game Development Reference
In-Depth Information
Figure 7.5
Translation preserves the symmetry of the graph across the y axis.
If you add a value to the absolute value of
x
, you can move the resulting graph up
or down the
y
axis. A positive value moves it up. A negative value moves it down.
To see how this is so, consider an equation that involves translating the graph up
by 4:
y ¼
4
þj
x
j
Even if
x
is a negative value, the absolute value sign makes it positive. For this
reason, adding 4 to the value of
x
always increases the corresponding
y
value by 4.
As Figure 7.5 illustrates, on both the positive and negative sides of the
y
axis, then,
the slope of the line remains consistent but is shifted upward. Both lines are
translated in a consistent, symmetrical way.
As Figure 7.5 reveals, adding a value to the absolute value of
x
, you translate
coordinates vertically upward. On the other hand, if the value you add is
negative, the translation moves the line downward.
