CG Modeling 2: NURBS - An Introduction to Computer Graphics for Artists - page 253

Fig. 14.13 Any object of any number of sides can be divided into four-sided patches by bisecting
each edge and drawing an edge to the center

14.3.1 How to See Four-Sidedness in Targets

Because NURBS objects are always four-sided, if you intend to build with them,
you need to be able to break objects down into four-sided pieces (Fig. 14.13 ). To do
this, you must learn how to see four-sidedness in objects. For some things, like a
sheet of paper or a cube, it is easy. For other things, like a triangle or the Y-shaped
intersection of branches in a tree, it can be more diffi cult.
There are such a wide variety of shapes in the world that it can be hard to imagine
all of them as four-sided patches. It can be done, but it requires an eye for topology.
Look at something in your room and think of the folding carton exercise. How
would that object pull apart and fl atten out if it was a folding carton? Ask yourself
if the object is made of one piece or more. If more than one, then each separate piece
must be built of a minimum of one patch. Do the pieces have insets, holes, or projec-
tions? All of these things will require more patches. Practice drawing directly on
objects, to fi nd the best places to divide them into four sided patches, and to give
you a better idea what the curves should look like.

14.3.2 Number of Patches

Breaking an object into pieces is the fi rst step to understanding four-sidedness.
Unless you do this, you will have to imagine a square sheet of fl exible material
draped over your object and then sucked onto it, as if in a vacuum mold. NURBS
objects may be built this way, but can be extremely complicated to build because of
the large numbers of isoparms required to hold the shape of every detail in a com-
plex target. If you break it into smaller pieces, it will be easier to spot pieces that can
be made of four sides and those that need to be broken down further.