hello and welcome to my basic mesh tutorial series.
well, this is mostly a tutorial for Blender 2.62
and i will use this program throughout the course
of this tutorial. However, i believe that a lot of what
i cover here is not limitted to Blender, but is valid
for other 3D content creation tools as well.

So, lets begin with the most basic part of 3D modelling, the vertex.
A vertex simply describes a point in a 3 dimensional space,
and it has 3 coordinates for the 3 orientation axes: x,y, and z.
Vertices are best described as the atoms of modelling.

Here is another vertex. It has a different location and thus it
has different coordinates. Both vertices can be connected.
The connection is named: edge.

so, we can say, an edge is a straight connection between two vertices.
And there is no exception from this rule. And this is a definition.
Edges always are made out of 2 vertices and a straight connection.

This is a third vertex with yet another location.
We can connect this new vertex with either of the
other existing vertices, or even to both of them.
Now we have 3 edges.
Each edge consists of 2 vertices and one straight connection.
And because it has 3 corners and 3 angles, this surface is also named triangle.
By a matter of fact 3 vertices, hence one triangle, also define
a plane in 3D space.
And the part of the plane that is located inside the triangle
defines a triangular surface, and is also named Triangle in our context.

This is yet another vertex.
Let me connect it to the already existing triangle with 2 additional edges.
Now we have 2 adjacent triangles,
which share one edge.
When we remove the shared edge,
we end up with a Quadruple,
Triangles and Quads are often called: faces, or mathematically correct: polygons.

By now, we have all necessary ingredients for making 3D models,
the vertex as the basic atom, the edge,
as a connection between 2 vertices,
the triangle as the most basic surface element,
which can always be constructed from 2 triangles.
And remember, Quads and triangles are also named: faces, or polygons.
Of course there are polygons with more than 4 angles, but
we will not cover them in this tutorial.

So, let us take another look at the triangle.
I already mentioned that the triangle defines a surface.
But in contradiction to the expectations this surface
has only one single side. This is very important to know,
because you always must be aware
that surfaces become transparent on the backside.
And so this triangle simply disappears when you look at its back.

And finally let us take a closer look at the Quad.
As i mentioned before,
which make them by far more complicated as you might expect.
first and most important,
a quad does not define a plane surface.
All 4 corners can be located at arbitrary locations,
and thus the surface is in general not planar.
But Quads can always be decomposed into 2 Triangles.
And if we break up a Quad into its 2 triangles,
we instantly see, how it is actually constructed.

But unfortunately this construction is not unique,
and we end up with 2 very different surfaces
depending on how the de-composition was done.
This may result in different behaviour
regarding lighting, and your surface might
sometimes look incorrect because the
quad was decomposed in the wrong direction.

By now i have introduced all basic ingredients
for the creation of mesh based three dee content.