IEEE CG&A

Andrew Glassner's Notebook is a regular column in
IEEE Computer Graphics & Applications. The articles
from January 1996 through March 1999 have been collected,
edited and expanded in the book Andrew Glassner's Notebook,
published by Morgan-Kaufmann. The articles from May 1999
to November 2001 have been edited and expanded in the
book Andrew Glassner's Other Notebook, published by AK Peters.
My columns from January 2002 to November 2004 have been
updated, revised, and expanded, and will be published in
Morphs, Mallards, and Montages: Computer-Aided Imagination
(published by AK Peters, to appear Summer 2004).

These pages collect notes, errata, and comments from the original
columns, and those that have not yet been printed in book form.

1996 - 1997 - 1998 - 1999 - 2000 - 2001 - 2002 - 2003 - 2004
Distance Metrics January

Going the Distance talked about tracing curves for 2D implicit surfaces. Jules Bloomenthal has graciously provided the following list of additional references on the topic:

Chandler, R.E. A Tracking Algorithm for Implicitly Defined Curves. IEEE Computer Graphics and Applications, Volume 8, Number 2, March 1988, pages 83-89.

Cohen, E. A Method for Plotting Curves Defined by Implicit Equations. ACM SIGGRAPH Computer Graphics, Volume 10, Number 2, Summer 1976, pages 263-265.

Hobby, J.D. Numerically Stable Implicitization of Cubic Curves. ACM Transactions on Graphics, Volume 10, Number 3, July 1991, pages 255-296.

Nakartsuyama, M., Kanno, K., Nagahashi, H. & Nishizuka, N. Curve Generation of Implicit Functions by Incremental Computers. Computers and Graphics, Volume 7, Number 2, 1983, pages 161-168.

Sutcliffe, D.C. An Algorithm for Drawing the Curve f(x,y)=0. The Computer Journal, Volume 19, Number 3, August 1976, pages 246-249.

Taubin, G. Distance Approximation for Rasterizing Implicit Curves. ACM Transactions on Graphics, Volume 13, Number 1, January 1994, pages 3-42.

There are also lots of commercial packages out there that will plot implicit curves with a variety of features and guaranteed accuracies. The most popular are probably the symbolic algebra packages, though there are some scientific-visualization programs out there that do a great job of making high-quality plots.

 

Phong Curves March

Situation Normal talked about the surfaces that we're looking at, assuming that Gouraud and Phong shading actually were rendering curved surfaces accurately. The shapes of the surfaces are not always what we would have expected.

 

Segmented Display May

Signs of Significance discussed different ways of representing characters with digital displays.

Michael Newman has noted that the Vienna "V" could be improved using a few of the little 45-degree bevelled segments. He also pointed out that the caption for Figure 4 should read "14-segment display", not 16. I'd like to point out that the light internal lines in Figure 4 were a printing error, and should have been just as dark as the others.

If the upper and lower pieces in Figure 4 are broken into two pieces, you indeed get a 16-segment display. Referring to such an arrangement, David Walton wrote: "I have an old TI-66 Programmable Calculator. It has a 10-digit display. The 5th, 6th, and 7th digits from the left are 16-segment, to facilitate the display of opcodes while programming. The rest of the digits are 8-segment-the middle bar is broken, presumably to give the numbers that use it a consistent appearance. The segments are not as thick as figure 2, perhaps 2/3 the thickness, and are beveled."

I made a mistake preparing the numeral "4" in Figure 6; the four little triangles around the central octagon should have been turned on.

 

Kaleidocycle July

Net Results talked about building interesting polyhedra based on their unfolded representation, or net. I discussed the five Platonic solids, the unfolding flower, and how to make a kaleidocycle, as well as the connectivity relations for making continuous pictures across the face of a kaleidocycle as it turns.

 

Schwarz Surface September

The Perils of Problematic Parameterization presented a little-known mathematical curiosity called the Schwarz paradox. It's a technique for chopping a cylinder up into triangles that all lie on the surface, with the unusual property that as the triangles get smaller and more numerous, the sum of their surface area (which should tend to the surface area of the cylinder) actually goes to infinity!

At first it looks like a bit of sleight-of-hand with limits, but it's a real phenomenon. It's a cautionary tale about being too casual when choosing a polygonal approximation for a curved surface.

 

Moire pattern November

Inside Moire Patterns discusses the geometry of various types of Moire patterns. Knowing this, one can control them and reduce them when desired. You can also have fun creating new kinds of Moire effects.

1996 - 1997 - 1998 - 1999 - 2000 - 2001 - 2002 - 2003 - 2004