Multiple Coordinate Spaces - 3D Math Primer for Graphics and Game Development - page 88

of these two perspectives is so common that we will will take a little bit of
extra space to work through some examples.
Now for that ridiculous example. Let's say that we are working for a
advertising agency that has just landed a big account with a food manufac-
turer. We are assigned to the project to make a slick computer-generated
ad promoting one of their most popular items, Herring Packets, which are
microwaveable herring food products for robots.

Of course, the client has a tendency to want
changes made at the last minute, so we might
need models of the product and robot in all pos-
sible positions and orientations. Our first at-
tempt to accomplish this is to request, from the
art department, the robot model and the product
model in every possible configuration of positions
and orientations. Unfortunately, they estimate
that since this is an infinite amount, it will take
all of eternity to produce this many assets, even
after factoring in Moore's law and the fact that
the product model is just a box. The director sug-
gests increasing the art staff in order to achieve
her vision, but unfortunately, after crunching the
numbers, the producer discovers that this doesn't
decrease the time required to finish the project. 4
In fact, the company can afford resources to pro-
duce only one robot model and one box of mi-
crowaveable herring food product.
Although you may regret spending the past 60 seconds of your life
reading the preceding paragraph, this example does illustrate the funda-
mental necessity of coordinate space transformations. It's also a relatively
accurate depiction of the creative process. Time estimates are always
padded, project managers will throw more people at a project in despera-
tion, projects must be done by a certain date to meet a quarter, and, most
pertinent to this topic, artists will deliver only one model, leaving it up to
us to move it around in the world.
The 3D model we get from the artist is a mathematical representation
of a robot. This description likely includes control points, called vertices,
and some sort of surface description, which tells how to connect the vertices
together to form the surface of the object. Depending on what tools were
used by the artist to create the model, the surface description might be a
polygon mesh or a subdivision surface. We're not too concerned about the

Figure 3.4
One serving contains 100%
of a robot's recommended
daily allowance of essential
oils.

4 Although this is an extreme example, it illustrates a well-known principle that, in
most creative projects, total project time is not simply the amount of work divided by
the number of workers. As the saying goes, “Nine women can't make a baby in a month.”