Visualizing surfaces in Euclidean 3-space with VisuMath

Wendy Goemans () and Ignace Van de Woestyne ()
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Wendy Goemans: Hogeschool-Universiteit Brussel (HUB), Belgium
Ignace Van de Woestyne: Hogeschool-Universiteit Brussel (HUB), Belgium

No 2008/62, Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management

Abstract: As is well-known, surfaces in a 3-dimensional Euclidean Space can be represented locally by means of several types of equations. Although these are mathematically equivalent, this choice of representation can make a difference when it comes to visualizing the surface. More precisely, some representations may produce artifacts in the visualization that are merely a consequence of the visualization process itself. Sometimes, by rewriting equations or by switching to another representation, these can be avoided. In this paper, this phenomenon is explained and demonstrated by means of the new version of the visualization software VisuMath. Moreover, the new capabilities of the software and the geometry behind it, are explained. These include the possibility of dynamically changing the shape of surfaces by altering parameters in the representation. This feature can be useful in examining the precise role of parameters in the equation(s) representing the surface.

Keywords: VisuMath; visualization; Euclidean geometry (search for similar items in EconPapers)
Pages: 15 pages
Date: 2008-07-25
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