Graphics Programs Reference
In-Depth Information
Chapter 1
Playing in Three
Dimensions
Before we get really deep into the nuts and
bolts of the major LightWave tools, we've
got to make sure everyone is on the same
page about understanding the core concepts
of 3D. Math and geometry figure heavily in
these core concepts, but they come into
play in such a way that they're fun. (This is
probably because when working in 3D,
math no longer represents abstract, almost
arcane, concepts. In 3D, math and geometry
are almost tangible. They give you immedi-
ate gratification with imagery that looks
awesome when you solve whatever prob-
lem you're working on.)
Note
If kids were taught math and geometry with
3D (making movies or exporting animations
into a public domain game engine), you
couldn't keep them away from it.
Using 3D, you not only see an immediate
use for all that nifty trigonometry, geome-
try, tensor calculus, and algebra, but you
also have a lot of fun
playing
with it (yes,
playing
)! So, as you explore this, keep in
mind that the whole objective is to have
fun, explore, and play. If you keep that focus
in mind, the nuts and bolts will be almost
effortless.
3D “Space”
To measure any three-dimensional object,
whether it be in “real” space or the “virtual
world” of a computer, you need to attribute
to that object three dimensions. In the real
world, these three dimensions are most
commonly thought of in terms of length,
width, and depth.
So, a “dimension” is really just a
vector
(a
line that extends infinitely in each direction
from its origin, never turning and never
stopping) laid along a specific
axis
(the
angles that define the vector's orientation).
Height is a dimension, just as width and
depth are. But the labels “height,” width,”
and “depth” are too subjective to be used
with any certainty within the precise areas
of mathematics, drafting, or computer-aided
design. Certain
conventions
(agreements
that, to make things easier for everyone, a
certain
symbol
will always represent a cer-
tain
concept
) were brought into play for the
defining of these three dimensions as they
exist within the conceptual space of a
computer.
In three-dimensional space, up and down
are defined as parts of the Y axis. The area
above the
ground plane
(defined where
Y=0) is measured with
positive values
(like
Y=5). Below the ground plane, the Y axis is
measured with
negative values
(like Y=-5).
Left and right are measured along the X
axis. Space to the left of X=0 is measured
