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

May 3 2011   2:31AM GMT

# Straight line 3D modeling with polygons, part 1

Profile: Roger King

I have had some trouble embedding images on this ITKE blog, so to see this blog entry properly formatted, with images, please view it on the blog I keep for my animation students: wordsbybuzz.com.

Curved line 3D modeling.

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 surfaces and objects.

Straight line 3D modeling.

Today, we look at modeling 3D objects with straight lines, not curved lines.  This is called polygon modeling, because the surfaces of objects are created out of flat, 2D polygons, usually of 3 and 4 sides.

Look at this:

This is a sphere, created with straight lines.  We see a problem with it, of course.  It’s not very smooth.

Consider this one:

This sphere has the same overall size, but much denser geometry.  This is one way that we can create smooth, seemingly curved objects by using straight line polygon modeling: increasing the number of vertices and lines until the object looks smooth to a human viewing the sphere on a computer display or a movie screen.

There is an advantage to doing it this way, instead of using curved lines, which produce smooth objects, no matter how few vertices and (curved) edges are involved.  It is computationally simpler to represent models by using straight lines, and that makes it faster to deform them (to make a human head, for instance).  This shortens rendering time when it comes to generating video of animated objects (objects in motion).

And rendering times can turn a seemingly simple animation project into an intractable effort.