[Bf-docboard] 3D Concepts and Fundamentals Chapter

[Jason Oppel]

It has been a long time since I promised to tackle the 3D Concepts and 
Fundamentals Chapter so I thought I'd show everyone what I have so far and 
hopefully get some feedback.

I managed to finish the first section and most of the second (one more 
section on rendering remains unwritten).  The second section obviously 
needs some more content but I thought I'd see what everyone has to say 
about what I've written so far. :-)   Comments and criticism are welcome!

Thanks,
-Jason <Pato>

Introduction
============
3D applications have never been more accessible or indeed more powerful 
than they are today.  Despite this fact most 3D modeling packages still 
cost thousands of dollars and are still well above means of most hobbyists 
and beginners to purchase.  Blender has eliminated this barrier of entry so 
that anyone can now use a powerful professional level 3D modeling package 
as Blender is available for free.  We the authors of this book and the 
Blender Foundation are thrilled to present you this Official Blender Manual 
which will undoubtably help you release the 3D artist lurking within you.  
By the end of reading this book you should have a firm understanding of 3D 
concepts and how to apply them using Blender.  Along the way you're also 
bound to create a some images and 3D scenes you can be proud of!

While Blender's interface is quite different from other 3D applications 
you'll find that as you use Blender more frequently (called "blending" by 
Blender users) that its interface will actually make you extremely 
productive and efficient.  While at times Blender may seem daunting to 
learn (as are all 3d modeling applications) remember that it was designed 
with a professional workflow in mind and there is a pot of gold at the end 
of the rainbow.  The reward from learning Blender is that you'll be able to 
fly around your 3D creations with astounding speed and produce impressive 
artwork at an astounding pace.

As you're reading through this book try not to forget that despite all the 
magical technology behind it Blender is really just a medium through which 
to create art.  Through the hands of a skilled artist whether they're 
painting a picture, sculpting clay or modeling a complex scene in Blender 
the same artistic skills and talents of composition, proportion, color and 
light are being used and it's only the medium changes.  We encourage any 
aspiring serious 3D artists to learn and practice traditional artforms such 
as sketching, modeling or painting.  The skills you learn in other art 
forms will make you a far better artist and give you a larger base of 
creative experience from which to use as a launching pad for your 3D 
creations.

We hope that you find 3D modeling a fun (and sometimes an addictive) 
pursuit as we do.  Blender will help you develop the skills necesarry to 
develop your 3D artistry as far as your aspirations will carry you.  Blend 
On!

Getting Oriented
=================
You may recall during your geometry and algebra classes at school seeing a 
graph similar to Figure 1 [show graph with x, y and z axis with a point 
mapped out at (1,1,0)].  The graphing system as seen in Figure 1 is called 
a Cartesian Coordinate System.  The Cartesian Coordinate System is the 
standard way that all 3D modeling applications use to define 3 dimensional 
objects (with a few minor variations).  Using this system we can describe 
any point in 3D space.  In this graph the horizontal axis (the x-axis) is 
used to describe the width of objects while the vertical axis (the y-axis) 
describes the height.  Of course we still a way to describe the depth of 
objects and that's the z-axis as seen in Figure 1.  Using the x, y and z- 
axis (commonly refered to as simply x, y and z respectively) we can use our 
new found knowledge to define any point or shape in 3D space.  As we see in 
Figure 1 the point mapped out is one unit to the right, one unit up and 
zero units deep.  To extend this concept to shapes we see that the cube in 
Fig. 2 [show cube with x, y and z mapped out on it] is one unit wide (x 
axis) one unit tall (y axis) and one unit deep (z axis).  Similarly you can 
describe any object whether that object is a car, a plant or even a human 
in 3D space no matter how complex using x, y and z coordinates.

Now that we have a way to plot locations and describe objects in all three 
dimensions let's take a look at how Blender handles 3D space.  Start 
Blender and press NUM1 to change our view so we're looking at our scene 
head on as seen in Fig. 3 [show standard blender startup scene in NUM1 view 
with the axis indicator highlighted in yellow].  If you look at the lower 
left hand corner of the 3D viewport you'll notice that there is x and z 
axis indicator (highlighted yellow in Fig. 3) to keep you oriented.  Now I 
hear you screaming from here that y and not z is supposed to denote height. 
 Well, this is one of the "slight variations" I spoke of earlier.  Blender 
(and many other 3D applications) uses what's called "left handed 3D 
coordinates."  In left handed coordinates two of the axis (the y and z in 
this case) are flipped with one another. In Blender (and other "left 
handed" 3D applications) the z-axis defines height while the y-axis defines 
depth.  Let's see if that's right.  Press the NUM7 pad to change our view 
so that we're look overhead on our 3D scene.  Sure enough the y-axis 
defines the depth of our default plane and the x-axis still defines width.

Modeling Approaches
====================
Just as a painter can use different kinds of paint to create a painting 
similarly as a 3D modeler you have lots of different methods you can use to 
create your 3D masterpiece.  Experience will guide you on when to use which 
method but we can start you on this road by describing the two most popular 
ways of creating objects.

Polygonal Modeling
===================
To understand polygonal modeling you first need to know that a polygon is 
any three or four points linked together to form a triangle, square or a 
rectangle (even irregular shaped ones) as shown in Figure 4 [picture of a 
few different looking polygons in edit mode].  Each of these individual 
points (seen as yellow dots in Figure 4) is called a "vertex."  The lines 
linking each vertex together is aptly named an "edge." The art of polygonal 
modeling at it's heart is stringing polygons together and manipulating them 
to create more complex objects as seen in Figure 5 [picture of some 
wireframe mesh (perhaps a human body)].  As you see in figure 4 the object 
is comprised of only triangles linked with one another.  It's worth noting 
that whenever you see a model rendered in this fashion it is often refered 
to as a "wireframe mesh" or simply a "mesh" as it looks like it's made of a 
wire mesh.  Polygonal modeling has a number of advantages as listed below:

1. Today's video cards efficiently handle polygons
2. blah
3. blah

blah blah blah.


Curve and NURBS Based Modeling
===============================
blah blah blah.

1. Well suited for creating organic forms such as humans.
2. User defineable resolution (the degree to which curves are rendered 
accurately)
3. blah

blah blah blah.