## Points, Edges, Polys & Objects

99% of what you see in a computer generated scene is made up of polygons. Some parts of a rendered image might be special procedural effects, such as light rays or hair, but most actual "objects" are just numerous polygons arranged to look like a more complex object.

The number of polygons in an object is decided on based on the purpose of the object. A video game from the 90's for instace would have used objects of very low poly-counts for instance because the game consoles were not powerful enough to handle too many at a time.

On the other hand you have newer games or pre-rendered effects, in movies for instance, which can easily have objects and scenes where the polygon count can reach into the millions.

Let's look at the parts of a polygon and how they are joined together.

A vertex is a single point defined by an X, Y, and Z position.
1. The vertex (plural; vertices or vertexes) is the essential part of any polygon. "Polys" are rarely measured by their dimensions or center points. If math is done on a polygon it is done using the position of the vertecies that make it up.

Vertices have no size or mass, they are measured only by their position in 3d space.

2. Edges are line segments that connect two vertecies.
3. The lines between vertices make up the edges. Most software allows you to select them so that you can move two points at once, change the "sharpness" of an edge between two polygons, or to decide where to seperate joined polygons. They are also useful for texturing objects as you'll see.
4. A polygon is the surface area defined by a set of edges.
5. Polygons are typically a set of connected edges or vertecies that can be selected as once piece. If a polygon has enough "hidden edges" it can have more than 3 or 4 edges (though this should only be allowed on flat surfaces). Polygons of different edge counts can exist in the same model.

"Faces" are sometimes used interchangeably with "polygons", but should probably be cosntrained to refer to a single triangle *within* a polygon.
6. As a whole, a set of polygons that make up a single object will either just be called an Object (C4D) or sometimes an Element (3DS Max). Though it is debatable whether or not this component should be considered the same as the first three, since it is comprised of them. 3DS Max for instance has a "Border" sub object, which is just a line of multiple edges.

The names for these components differ between programs. Some will call them "sub-objects" (3DS Max), some will just call them each an editing "mode" (C4D).

Here are some common things to remember about these components.

• Multiple polygons can share a single vertex on their outer edge.
• Multiple polygons can also share the same border edges, but never allow more than two polys to share a single edge at once. Visual errors will result.
• Multiple polygons cannot overlap and share one faces.
• "N-gon" refers to a polygon made up of "N" faces, where N means more than the traditional 3 or 4.
• Even though most programs will display polgyons with four sides, if not more, these are simply triangles with one edge hidden. Combining triangluar polygons to display quadrangles is a workflow consideration. It also helps with smoothing as we will later see.
• Even though we refer to 4 sided polygons as "Quads", they are not necessarily "quadrangles" in the geometric sense (a flat plane). Remember we are talking about 3-Dimensional spaces. Polygons with more than 3 points can possibly "bend" along their hidden edges.

## Object & world spaces

It's important to realize that all of the vertices and polygons you see in a seen aren't just a big soup of points. Each and every point on a model has a stored coordinate. Since we are working in a 3d space those coordinates come in the form of an "X", a "Y", and a "Z".

But what is that relative to? For a point to exist at "10, 14.5, 6.23" it has to measure those positions from another point. This point of reference can have different names depending on the software and geometry being affected. Sometimes it is the "axis" point, sometimes the "registration" point, other times it is simply the "point of origin". "Axis" typically denotes some kind of rotation so we will use "origin" for the time being.

If you've ever worked with graphing paper in alegebra where you asked to plot a graph or find the slope of a line then realize it's very similar. All points start with "X" and "Y", all we're doing is adding a third dimension in the form of "Z".

Now if we were dealing with just one model then all we would ever need is one coordinate system. But most 3d scenes will be comprised on multiple objects. Even scenes that visualize one object might also have a seperate light or camera objects that have their own origin point. Because of this we need a coordinate system "above" each object system. This is our world system.

The example to the right visualizes this. It's important to also realize that modern 3d computing is almost never as simple as this. Always remember one simple concept; Coordinate systems are hierarchical. This means that not only does each object have a coordinate system based on the axis of the object but that those axis exist within the coordinate system of the world.

Let's look at a second image where we have two objects in a 3d space. Notice that one object is centered on the grid that represents world space while the other is not. So again, coordinates of an axis are relative to the "world" origin. In a 3d space the "world" simply refers to the entire 3d space itself. So a "world origin" is the ultimate reference point. For any coordinates to exist at all there needs to be some starting point. The world origin is this point.

To summerize...

1. Vertices are relative to their object origin.
2. Object origins' are relative to the world origin.

Later on you'll learn about how objects can have children which adopt a parents coordinate system as well. This allows you to have multiple "levels" of coordinate systems - each relative to one another. That is covered in the groups and organization section.