

 
Manual Reference Pages  HYPERTORUS (6)
NAME
hypertorus  Draws a hypertorus that rotates in 4d
CONTENTS
Synopsis
Description
Options
Interaction
Environment
See Also
Copyright
Author
SYNOPSIS
hypertorus [display host:display.screen]
[install]
[visual visual]
[window]
[root]
[delay usecs]
[fps]
[wireframe]
[surface]
[transparent]
[solid]
[bands]
[spirals{1,2,4,8,16}]
[twosided]
[colorwheel]
[perspective3d]
[orthographic3d]
[perspective4d]
[orthographic4d]
[speedwx float]
[speedwy float]
[speedwz float]
[speedxy float]
[speedxz float]
[speedyz float]
DESCRIPTION
The hypertorus program 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 perspective or an orthographic projection. Of the two
alternatives, the perspective projection looks much more appealing.
In orthographic projections 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. Furthermore, the appearance of the torus can be as a
solid object or as a set of seethrough bands or seethrough spirals.
Finally, the colors with with the torus is drawn can be set to either
twosided 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 insideout 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 seethrough bands or
seethrough spirals 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 American Library, 1990.
OPTIONS
hypertorus accepts the following options:

window 
Draw on a newlycreated window. This is the default.

root 
Draw on the root window.

install 
Install a private colormap for the window.

visual visual  
Specify which visual to use. Legal values are the name of a visual
class, or the id number (decimal or hex) of a specific visual.

delay microseconds  
How 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.

wireframe 
Display the torus as a wireframe mesh.

surface 
Display the torus as a solid surface (default).

transparent  
Display the torus as a transparent surface.

The following seven options are mutually exclusive. They determine the
appearance of the torus.

solid 
Display the torus as a solid object.

bands 
Display the torus as seethrough bands (default).

spirals1, spirals2, spirals4, spirals8, spirals16  
Display the torus as seethrough spirals with the indicated number of
spirals.

The following two options are mutually exclusive. They determine how
to color the torus.

twosided 
Display the torus with two colors: red on the outside and green on
the inside.

colorwheel  
Display the torus with a fully saturated color wheel (default). If
the torus is displayed as seethrough bands each band will be
displayed with a different color. Likewise, if the torus is displayed
as seethrough spirals each spiral will receive a different color.

The following two options are mutually exclusive. They determine how
the torus is projected from 3d to 2d (i.e., to the screen).

perspective3d  
Project the torus from 3d to 2d using a perspective projection
(default).

orthographic3d  
Project the torus from 3d to 2d using an orthographic projection.

The following two options are mutually exclusive. They determine how
the torus is projected from 4d to 3d.

perspective4d  
Project the torus from 4d to 3d using a perspective projection
(default).

orthographic4d  
Project the torus from 4d to 3d using an orthographic projection.

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
values, e.g., less than 4 in magnitude.

speedwx float  
Rotation speed around the wx plane (default: 1.1).

speedwy float  
Rotation speed around the wy plane (default: 1.3).

speedwz float  
Rotation speed around the wz plane (default: 1.5).

speedxy float  
Rotation speed around the xy plane (default: 1.7).

speedxz float  
Rotation speed around the xz plane (default: 1.9).

speedyz float  
Rotation speed around the yz plane (default: 2.1).

fps 
Display the current frame rate, CPU load, and polygon count.


INTERACTION
If you run this program in standalone mode you can rotate the
hypertorus by dragging the mouse while pressing the left mouse button.
This rotates the hypertorus in 3D, i.e., around the wx, wy, and wz
planes. If you press the shift key while dragging the mouse with the
left button pressed the hypertorus is rotated in 4D, i.e., around the
xy, xz, and yz planes. To examine the hypertorus at your leisure, it
is best to set all speeds to 0. Otherwise, the hypertorus will rotate
while the left mouse button is not pressed.
ENVIRONMENT
DISPLAY 
to get the default host and display number.

XENVIRONMENT  
to get the name of a resource file that overrides the global resources
stored in the RESOURCE_MANAGER property.


SEE ALSO
X(1),
xscreensaver(1)
COPYRIGHT
Copyright © 20032005 by Carsten Steger. Permission to use, copy, modify,
distribute, and sell this software and its documentation for any purpose 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 representations are made about the
suitability of this software for any purpose. It is provided "as is" without
express or implied warranty.
AUTHOR
Carsten Steger <carsten@mirsanmir.org>, 28sep2005.
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