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[Twin Peaks]


Twin Peaks

For the second printing of Banchoff's book, Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions, in 1994, we had the opportunity to replace some of the computer-generated artwork with versions produced by more modern software. This sequence of slices of the graph of a function replaced ones that had no shading; there the three-dimensional effect is much enhanced. The slices show how the level set changes from two curves in the slices in the upper images to a single curve in the lower right. The change occurs at a "critical point" when the level set forms a figure-8, shown here at the lower left.

These images were produced using software that I had written as a graduate student at Brown University. This was an early predecessor of the StageTools package [Link] that I began developing while at the Geometry Center and continue to improve here at Union.

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Created: 08 Sep 2001
Last modified: Jan 6, 2002 10:44:05 PM
Comments to: dpvc@union.edu
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