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

Roger King Roger King 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:

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.

An advantage of straight lines.

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.

A more subtle advantage.

There is another advantage, too, and this one seems almost ironic.  While it may seem natural to model curved objects with curved lines, this doesn’t mix well with graphics cards. The rendering process consists of software that sits on top of computer hardware, of course, with low level rendering being performed by graphics cards.  And these cards want to render objects with straight lines anyway.

In other words, if you model with curved lines, the object has to be translated into straight line geometry at the time it is handed off by the software to the graphics card, anyway.  So it is all the slower to start with curved lined objects and then deform, animate, and render.

More next time…

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