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

Apr 15 2011   8:19PM GMT

Perfect curves: Bezier, part 4

Roger King Roger King Profile: Roger King

I have had some problems posting images in this ITKE blog, so please click here to view this blog, with proper images, in the blog I keep for my 3D animation students at the University of Colorado:

In three previous postings of this blog (see 123), we’ve looked at how the compact, precise technique of Bezier and NURBS mathematics is used as the basis for specifying curves in graphical and animation applications.

Modeling with curves.

In this posting, we will look at one of the ways that curves are used as powerful modeling techniques by graphic artists and animators.  Consider the image below:

A NURBS curve.

This shows the four main design views that are used in the extremely popular Maya 3D animation application.  It is a curve drawn with a handful of mouse clicks and then transformed internally by Maya into a NURBS curve.

Revolving the curve.

Now look at this figure:

This is what happens when Maya is told to revolve this curve through 3-space.  Since the lower right view is flattened along the x axis, we see precisely the shape that results from the revolution.  Keep in mind that this revolution is done with a single command.

A bottle!

We see in the upper right what this shape looks like when viewed with perspective.

Now, look at this:

This was done with a couple of simple commands.  We put a material on the shape and colored it blue.

See how easily we made a perfectly smooth bottle out of a simple curve?

More next time.

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