Fundamentals of 3D Space - Flash 3D: Animation, Interactivity, and Games - page 161

6

Fundamentals of 3D Space

So far we have dealt with creating the illusion of 3D space while staying within a 2D
environment. It's time that we take a step into the third dimension. Working in 3D
space brings a sense of depth and movement that can be difficult to achieve in a strictly
two-dimensional world. Like anything, there are various degrees of complexity when
working in 3D. In this chapter we will be dealing with movie clips that are defined in
3D space. We can think of these as two-dimensional planes that are living in a three-
dimensional world. This will give us simpler expressions while providing a wealth of
imagery to work with. We will work with more complex 3D shapes later.

This chapter is broken down into the basic concepts of 3D space that you will need
to become familiar with. Following is what we will be covering:

• Perspective projection

• Degrees of freedom

• Translation

• Rotation

Perspective Projection

Since all 3D drawings are projections onto a picture plane, what we need to know is
how to create the rays from the object to the picture plane for a perspective projection.
While this might seem to be a bit complicated, it is actually a quite simple and straight-
forward procedure.

Figure 6.1 illustrates the basic concepts of perspective drawing where a viewer is
observing an object's two-dimensional image on the surface of a picture plane. Straight
line projections extend from the viewer's eye position to points on the object to be
drawn in perspective. The intersections of the projections with the transparent picture
plane yield points on the perspective drawing of the object. Connecting these points