Tetraview
المؤلف:
Banchoff, T.
المصدر:
"Surfaces Beyond the Third Dimension." http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/wall-1a.html.
الجزء والصفحة:
...
3-10-2021
1770
Tetraview
A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function 
can be considered as a hypersurface in 
with four real coordinates ![(R[z],I[z],R[w(z)],I[w(z)])](https://mathworld.wolfram.com/images/equations/Tetraview/Inline3.gif)
. Carrying out a rotation in four dimensions and projecting the first three coordinates into (ordinary) 
then allows the changes from ![(R[z],I[z],R[w(z)])](https://mathworld.wolfram.com/images/equations/Tetraview/Inline5.gif)
to ![(R[z],I[z],I[w(z)])](https://mathworld.wolfram.com/images/equations/Tetraview/Inline6.gif)
to ![(R[w(z)],I[w(z)],R[z])](https://mathworld.wolfram.com/images/equations/Tetraview/Inline7.gif)
to ![(R[w(z)],I[w(z)],I[z])](https://mathworld.wolfram.com/images/equations/Tetraview/Inline8.gif)
to be visualized continuously.
REFERENCES:
Banchoff, T. "Surfaces Beyond the Third Dimension." http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/wall-1a.html.
Banchoff, T. "The Mathematics of the Tetraview." http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/tetra-Z2/tetra-math.html.
Banchoff, T. "A Virtual Reconstruction of a Virtual Exhibit." In Multimedia Tools for Communicating Mathematics. Papers from the International Workshop Held at the University of Lisbon, Lisbon, November 2000 (Ed. J. Borwein, M. H. Morales, K. Polthier, and J. F. Rodrigues). Berlin: Springer-Verlag, Berlin, pp. 29-38, 2002.
Banchoff, T. F. "Computer Graphics in Mathematical Research, from ICM 1978 to ICM 2002: A Personal Reflection." In Proceedings of the 1st International Conference held in Beijing, August 17-19, 2002 (Ed. A. M. Cohen, X.-S. Gao, and N. Takayama). Singapore: World Scientific, pp. 180-189, 2002.
Banchoff, T. and Cervone, D. P. "Understanding Complex Function Graphs." Commun. Visual Math. 1, July 1998. http://www.math.union.edu/~dpvc/CVM-07-98/1998/01/ucfg/.
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