Buzz’s Blog: On Web 3.0 and the Semantic Web

May 8 2011   1:55AM GMT

Straight line 3D modeling with polygons, part 2

Roger King Roger King Profile: Roger King

Note: this blog entry also appears in the blog I maintain for my animation students.  I have had some trouble with inserting images properly in this ITKE blog.  So, please view this entry at: wordsbybuzz.com.

In five recent postings, (12345), we looked at the simple, powerful mathematical techniques that underly the specification of curved lines in 3D graphics and how they are used to create 3D models.

Modeling with straight lines.

In the last posting (6), we turned to straight lines, and how 3D models can be built entirely out of 2D straight lines, using polygons.

Representing models inside the graphics application.

Today, we look at the way a 3D model can be specified inside a 3D product design, CAD, or animation application.

A reminder: non-angular objects.

As a reminder, we can obviously represent angular objects, like straight back chairs this way, but we can also represent smooth objects, like balls, if we increase the number of polygons until the model looks smooth:

Straight line modeling: coordinates and lines.

How are 3D models represented internally?

And how are they manipulated into dogs and rocket ships?

Let’s consider the first question.  In the next posting, we’ll consider the second question.

The minimal information we need to unambiguously represent a 3D model made entirely out of straight lines is a set of 3D coordinates, along with a set of lines, each beginning and ending with coordinates from this set.

In formal notation.

To put that in mathematical notation, consider the following:

It is as simple as that: a set of points and a set of lines.

Indeed, that’s all we need to specify a model such as this:

But we don’t create objects by laying down points and edges between the points and crafting things out of sticks.  We start with larger things, prefab 3D objects, and deform them to create models.

Next time, we’ll come back to this and look at how, inside an application, we can represent the process of molding the shape of an object.

As a hint, we start with a set of 3D points, along with the edges that connect them, and then we start pushing and pulling points, edges, and polygon surfaces to form the desired shape.  That’s how we can take the ball above, a basic modeling primitive, and turn it into Micky Mouse’s head.

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