Fundamentals of 3D Space - Flash 3D: Animation, Interactivity, and Games - page 199

It is important to note the relationship between yc and yo , the vertical origin of the
3D coordinate system. Our original values, yo = 0 and yc = -250 , were selected so
that the objects would display approximately in the center of the Stage. As the rotation
plane moves up or down, we will see that the objects begin to move off the Stage if yo
remains constant. If we want to keep the objects generally centered on the Stage, we
must make adjustments to yo as yc is moved. Referring to Figure 6.26, we see that the
difference between yo and yc is equal to 250 in each case. Keeping the same relative
distance between yo and yc will result in the objects staying in the center of the Stage.
Horizontal Center of the Circle
Suppose you want your objects to orbit on a tilted path. One solution, of course, would
be to tilt the orbital path. However, there's another, easier solution. Changing the hori-
zontal center, xc , of the orbital circle either to the left or right moves it farther away
from the center of vision. This in turn will change the perspective of the orbit as shown
in Figure 6.27 with xc values of xc = 300 and xc = -300 .
Figure 6.27 Changing the horizontal center of the circular path
The farther the paths are from the horizontal center of vision xo , the greater the angle
of tilt when they are converted to screen coordinates. As we saw with changes in the
vertical center, changes in the horizontal center xc need to be accompanied by adjust-
ments to xo in order to display the rotating objects in the center of the Stage.
Rotation in the y-z Plane
A circular path rotation in the y-z plane is equivalent to a rotation about the x-axis or
a line parallel to the x-axis. Everything that we discussed regarding rotation about the
y-axis also holds for rotation about the x-axis. We can use the same functions