Introduction - Computer Graphics: Principles and Practice - page 10

But often in graphics we seek not a physical simulation but a way to present
information visually (like a book or newspaper layout). In these cases, the typical
viewing situation is a well-lit room, with light of approximately constant intensity
arriving from all directions, and with the reflectance of the items on the page
varying by a factor of perhaps 10 3 . Simply setting the intensities of screen pixels
to reasonable values that vary over a similar range works well, and there's no
reason to do a physical simulation of the reflecting page. However, there may
be a reason to be sure that what's displayed is faithful to the original (i.e., that
the colors you see on your display are the same ones I see on mine); displays of
fashion items or paint colors need to be accurate for users to understand how they
really look.
Indeed, such a situation is a good opportunity for abstraction, which is a key
element in visual communication in general: Because the physical characteristics
of the document will not have a large impact on the viewer's experience as s/he
encounters it, one can instead discuss the document in more abstract terms of
shape and color and form. It's imperative, of course, that these abstractions cap-
ture what's important and leave out what's unimportant about whatever is being
discussed; this is a key characteristic of the process of modeling, which we will
return to frequently throughout this topic.
1.4 Goals, Resources, and Appropriate
Abstractions
The lightbulb example gives us another principle: In any simulation, first under-
stand the underlying physical or mathematical processes (to the degree they're
known), and then determine which approximations will best provide the results
we need (our goals ), given the constraints of time, processor power, and similar
factors (our resources ).
This approach applies both to 2D display graphics—the kinds of graphical
objects found in the interface to your web browser, for instance, like the buttons
that help you navigate and the display of the successive lines of text—and to 3D
renderings used for special effects. In the former case, the dominant phenomena
may not be those of physics but of perception and design, but they must still be
understood. In addition to choosing a rich-enough abstraction, part of modeling
wisely is choosing the right representation in which to work: To represent a real-
valued function on a plane, you might use a rectangular array of values; divide the
plane into triangular regions of various shapes and sizes, with values stored at the
triangle vertices (this is common when making models of things like fluid flow);
or use a data structure that stores the rectangular value array in such a way that
whenever adjacent values agree they are merged into a larger “cell” so that detail
is only present in the areas where the function is changing rapidly.
We summarize the preceding discussion in a principle:
T HE WISE MODELING PRINCIPLE : When modeling a phenomenon, under-
stand the phenomenon you're modeling and your goal in modeling it, then
choose a rich-enough abstraction, and then choose adequate representations
to capture your abstraction within the bounds of your resources. Once this is
done, test to verify that your abstraction was appropriate.