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hypertorus - Draws a hypertorus that rotates in 4d

hypertorus[-displayhost:display.screen] [-install] [-visualvisual] [-window] [-root] [-delayusecs] [-fps] [-mesh] [-surface] [-transpar- ent] [-solid] [-bands] [-twosided] [-colorwheel] [-perspective-3d] [-orthographic-3d] [-perspective-4d] [-orthographic-4d] [-speed-wxfloat] [-speed-wyfloat] [-speed-wzfloat] [-speed-xyfloat] [-speed-xzfloat] [-speed-yzfloat]

Thehypertorusprogram shows the Clifford torus as it rotates in 4d. The Clifford torus is a torus lies on the "surface" of the hypersphere in 4d. The program projects the 4d torus to 3d using either a perspec- tive or an orthographic projection. Of the two alternatives, the per- spective projection looks much more appealing. In orthographic projec- tions the torus degenerates into a doubly covered cylinder for some angles. The projected 3d torus can then be projected to the screen either perspectively or orthographically. There are three display modes for the torus: mesh (wireframe), solid, or transparent. Further- more, the appearance of the torus can be as a solid object or as a set of see-through bands. Finally, the colors with with the torus is drawn can be set to either two-sided or to a color wheel. In the first case, the torus is drawn with red on the outside and green on the inside. This mode enables you to see that the torus turns inside-out as it rotates in 4d. The second mode draws the torus with a fully saturated color wheel. This gives a very nice effect when combined with the see- through bands mode. The rotation speed for each of the six planes around which the torus rotates can be chosen. This program is very much inspired by Thomas Banchoff’s book "Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions", Scientific Ameri- can Library, 1990.

hypertorusaccepts the following options:-windowDraw on a newly-created window. This is the default.-rootDraw on the root window.-installInstall a private colormap for the window.-visualvisualSpecify which visual to use. Legal values are the name of a visual class, or the id number (decimal or hex) of a specific visual.-delaymicrosecondsHow much of a delay should be introduced between steps of the animation. Default 25000, or 1/40th second. The following three options are mutually exclusive. They determine how the torus is displayed.-meshDisplay the torus as a wireframe mesh.-surfaceDisplay the torus as a solid surface (default).-transparentDisplay the torus as a transparent surface. The following two options are mutually exclusive. They determine the appearance of the torus.-solidDisplay the torus as a solid object.-bandsDisplay the torus as see-through bands (default). The following two options are mutually exclusive. They determine how to color the torus.-twosidedDisplay the torus with two colors: red on the outside and green on the inside.-colorwheelDisplay the torus with a fully saturated color wheel (default). The following two options are mutually exclusive. They determine how the torus is projected from 3d to 2d (i.e., to the screen).-perspective-3dProject the torus from 3d to 2d using a perspective projection (default).-orthographic-3dProject the torus from 3d to 2d using an orthographic projec- tion. The following two options are mutually exclusive. They determine how the torus is projected from 4d to 3d.-perspective-4dProject the torus from 4d to 3d using a perspective projection (default).-orthographic-4dProject the torus from 4d to 3d using an orthographic projec- tion. The following six options determine the rotation speed of the torus around the six possible hyperplanes. The rotation speed is measured in degrees per frame. The speeds should be set to relatively small val- ues, e.g., less than 4 in magnitude.-speed-xwfloatRotation speed around the wx plane (default: 1.1).-speed-xyfloatRotation speed around the wy plane (default: 1.3).-speed-wzfloatRotation speed around the wz plane (default: 1.5).-speed-xyfloatRotation speed around the xy plane (default: 1.7).-speed-xzfloatRotation speed around the xz plane (default: 1.9).-speed-yzfloatRotation speed around the yz plane (default: 2.1).

DISPLAYto get the default host and display number.XENVIRONMENTto get the name of a resource file that overrides the global resources stored in the RESOURCE_MANAGER property.

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Copyright © 2003 by Carsten Steger. Permission to use, copy, modify, distribute, and sell this software and its documentation for any pur- pose is hereby granted without fee, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation. No repre- sentations are made about the suitability of this software for any pur- pose. It is provided "as is" without express or implied warranty.

Carsten Steger <carsten@mirsanmir.org>, 27-may-2003. X Version 11XScreenSaver(1)

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