NURBS, or Non Uniform Rational
B-Splines, are splines. They have "control points" located off
the curve that controls their shape. NURBS also have edit points
right in the curve, giving much more control. However, "edit
points" are a curve tool, so once the surface is created you have
only control points available. Surfaces in NURBS are defined with
UV coordinates. A UV coordinate is an exact point in the surface.
UVs are used to apply textures and insert isoparms on the surface.
Isoparms are a visual feedback of UV coordinate and control points.
They are also a great feature allowing you to easily add control
points over the surface. The space between isoparms is the "patch".
NURBS have the ability to create and edit curves. With them, you
can draw profiles, surface them and precisely blend, trim, merge
and match surfaces together in a very intuitive way. These surfaces
have infinite resolution as well. Adding details in a NURBS surface
is as tricky as it is with spline patches. You often end up with
too many control points off the isoparm. so it is difficult to
locate the right point. But, you can always create an object in
NURBS and then move to polygon modeling to add details on the mesh.
Mixing methods significantly speeds up production. 
POLYGONS are used to create an object. Polygons
are flat, so to create a smooth shape such as a ball or a human
head, you would need a lot of polygons if we didnt have
Subdivision Technology. Subdivision calculates a curve
between the polygon vertices, smoothing the shape. If a vertex is
close to another, it will have a "creased curve." Polygonal
modeling associated to subdivision technology is good for creating
low-resolution models which can later be converted into high
resolution meshes. Low-resolution models allow you to add details
to the surface quickly and but wont drive you nuts with a large
number of control points. You can also concentrate detail in only a
tiny part of the mesh to keep the poly-count low. Polygons are
great for characters with many details but it lacks precision and
infinite resolution curves. If you want to show a perfect sphere in
your scene, and its made with polygons, dont get too close or
everybody will see the polygons. SPLINE PATCHES are editable
curves controlled by "control points" and handles. By moving the
control points (located off the curve) you can deform the shape of
the spline. The handles (or beziers) change the influence the point
will have over the curve. It is a very intuitive method allowing
you to draw the profiles of objects, then PATCH the splines to
create a complex 3D object. A spline patch needs four intersecting
splines and it is like a four-sided polygon except it is curved.
For example, if you want to model an arm, you draw the profile
sections and then you define cross section curves to create four
spline intersections over the arm to patch it properly. 
Although you can create straight lines with splines,
its main feature is the ability to create flexible and editable
curves. Also, these curves have infinite resolutionno matter how
close you get to the object, the curve remains smooth. Adding
details in a spline patch mesh is more complicated than with
polygons because any detail you add will be smooth too. When
talking about wrinkles and bumps, smoothness is not what you want.
It is not impossible, but you end up with thousands of control
points, sometimes impossible to manage. UV mapping is one of the
best ways to texture NURBS surfaces or polygon meshes. A UV map is
based on UV coordinates which can be implicit or explicit: IMPLICIT
UV COORDINATES - NURBS surfaces have implicit UV coordinates. A
NURBS surface is a grid, where a set of curves running in an U
direction intersects with another set, running in a V direction.
Each point in that grid has its own and fixed UV coordinate. The
texture you apply in this grid will follow these coordinates,
implicitly. EXPLICIT UV COORDINATES - Polygon meshes are a free
structure, created by 3, 4 or more-sided polygons. They dont need
to be a grid to exist. Because of this, a polygon mesh uses an
explicit, or assigned UV map. That means you determinate the UV
coordinate of a point and apply your texture over it. Each approach
has its use and its own set of tools to deal with and each software
has its own tools and approaches to work with textures and UV maps.
About loganarts:
Loganarts' artistic career started at the early age of twelve by
copying drawings from Todd McFarlane's Spiderman. Growing from
these early drawings, loganarts moved on to attempt hyper-realism
work as inspired by Ingres and Velazques. However, it was during
his search for true self expression that loganarts returned to his
naive style and was re-inspired by artists like Matisse, Schielle,
Bacon and Freud. Loganarts' involvement in CG art was entirely
brought on by pure need. Survival from producing traditional art in
Brazil is virtually impossible. So, he bought a computer and
started to sculpt, using tools such as Rhino. With the great help
he received from people like Spike and Teyon (from Renderosity's
Rhino Forum), loganarts was able to adapt his traditional art
skills to CG quickly. After being active on the Brazilian CG scene
for 2 years, loganarts has reached the highest point in his career
so far - He was recently hired by the largest CG studio and finish
house in Brazil! Loganarts will soon have his first motion picture
FX credit! Loganarts' main goal for the near future is to work in
personal artistic projects such as a short movie or a series of
images representing his personal language to the world.
The Magazine Interact Forum's Back Room is the place to go for editorials, magazine excerpts, discussions, and plenty of surprises. Also, if you haven't done so yet, you can subscribe to the magazine or buy single issues. To find your way there, go to the Magazine Interact Forum, and click on the link to the Back Room at the top. Every couple of weeks, we'll be highlighting an article, review, or editorial from past issues of the magazine. Our second feature is an article from Issue #1, "Basic 3D Modeling Concepts." You can view this article in all of its original pdf glory by going to the Magazine Interact Forum Back Room and going to Special Features.
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