XScreenSaver(6x) XScreenSaver(6x)
NAME
hypertorus  Draws a hypertorus that rotates in 4d
SYNOPSIS
hypertorus [display host:display.screen] [install] [visual visual]
[window] [root] [delay usecs] [fps] [mesh] [surface] [transpar
ent] [solid] [bands] [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 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 seethrough bands. 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 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.
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.
mesh 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 two 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).
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).
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 projec
tion.
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 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.
speedxw float
Rotation speed around the wx plane (default: 1.1).
speedxy 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).
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 (C) 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.
AUTHOR
Carsten Steger <carstenATmirsanmir.org>, 27may2003.
X Version 11 4.21 (01Mar2005) XScreenSaver(6x)
