hypertorus
XScreenSaver(1) XScreenSaver(1)
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] [-perspective-3d]
[-orthographic-3d] [-perspective-4d] [-orthographic-4d] [-speed-wx
float] [-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz
float] [-speed-yz 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 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.
OPTIONS
hypertorus accepts the following options:
-window Draw on a newly-created 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 see-through 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).
-perspective-3d
Project the torus from 3d to 2d using a perspective projection
(default).
-orthographic-3d
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.
-perspective-4d
Project the torus from 4d to 3d using a perspective projection
(default).
-orthographic-4d
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.
-speed-xw float
Rotation speed around the wx plane (default: 1.1).
-speed-xy float
Rotation speed around the wy plane (default: 1.3).
-speed-wz float
Rotation speed around the wz plane (default: 1.5).
-speed-xy float
Rotation speed around the xy plane (default: 1.7).
-speed-xz float
Rotation speed around the xz plane (default: 1.9).
-speed-yz 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 © 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 <carsten@mirsanmir.org>, 27-may-2003.
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