Datasheet

Chapter 1: Understanding Flash3D
7
From the law of similar triangles, it follows that
h
fl
H
fl  z

By cross - multiplying, you get the scaling equation:
Scale
h
H
fl
fl  z

That ’ s all there is to its derivation, but examining the equation reveals an interesting phenomenon: a
singularity (blow up) in z. As z approaches – fl your equation ’ s denominator goes to zero and your scale
blows up to infinity. And as shown in the figure below after you pass – fl your figure goes through an
inversion (it flips over).
You ’ re probably wondering how fl (focal length) is assigned. Is it actually the distance of your eye to the
computer screen? No! It ’ s a virtual quantity that was used in the derivation of the scaling equation. But
that doesn ’ t mean it doesn ’ t have meaning. It is the focal length of your camera, and its assignment
changes the appearance of what you see on your computer screen.
The figure below illustrates a number of important occurrences in the life of the scaling equation:
When z = 0 your image scale is 1 (image is its actual size)
When z = fl your image scale is ½ (image is half its size)
As z approaches ⫺ fl your scale approaches infinity (image is infinitely large)
As z approaches infinity your scale approaches zero (image has vanished)
Of the four conditions listed above, two are used most by mathematicians to quickly define the behavior
of a function, the singularity (blow up point) and asymptotic behavior (as z approaching infinity). The
asymptotic behavior is important here since as your object moves towards infinity it vanishes. This is
referred to as the vanishing point and occurs at a specific x, y position of your screen. In Flash, that
position is at the origin that occurs at the upper left corner of your computer screen. Later in this chapter
you ’ ll find out how to change your vanishing point.
This may cause you a little confusion since you ’ ve already learned that the vanishing point occurs at the
eye as shown in Figure 1.2 previously. So are there two vanishing points? Definitely, but the first one that
occurred at the eye was used for derivation purposes and is where your singularity occurs (shown in
Figure 1.4). The second vanishing point occurs at infinity. It ’ s the one that you ’ ll now be most interested
in working with. It determines where your 3D object goes (on the x,y screen) as it gets further away
from you.
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