Provided by: xscreensaver-gl_6.02+dfsg1-2ubuntu1_amd64 
NAME
hypertorus - Draws a hypertorus that rotates in 4d
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}] [-onesided] [-twosided] [-colorwheel] [-change-colors]
[-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 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 see-
through bands or see-through spirals. Finally, the colors with with the torus is drawn
can be set to one-sided, two-sided, or to a color wheel. The colors can be static or
changing dynamically. In one-sided color mode, the torus is drawn with the same color on
the inside and the outside. In two-sided color mode, the torus is drawn with red on the
outside and green on the inside if static colors are used. If changing colors are used,
dynamically varying complementary colors are used for the two sides. This mode enables
you to see that the 3d projection of the torus turns inside-out as it rotates in 4d. The
color wheel mode draws the torus with a fully saturated color wheel. If changing colors
are used, the colors of the color wheel are varying dynamically. The color wheel mode
gives a very nice effect when combined with the see-through bands or see-through spirals
mode.
Finally, the rotation speed for each of the six planes around which the torus rotates can
be chosen.
This program is 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 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.
-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 see-through bands (default).
-spirals-1, -spirals-2, -spirals-4, -spirals-8, -spirals-16
Display the torus as see-through spirals with the indicated number of spirals.
The following three options are mutually exclusive. They determine how to color the
torus.
-onesided
Display the torus with a single color.
-twosided
Display the torus with two colors: one color on the outside and the complementary
on the inside. For static colors, the colors are red and green.
-colorwheel
Display the torus with a fully saturated color wheel (default). If the torus is
displayed as see-through bands, each band will be displayed with a different
color. Likewise, if the torus is displayed as see-through spirals, each spiral
will receive a different color.
The following options determine whether the colors with which the torus is displayed are
static or are changing dynamically.
-change-colors
Change the colors with which the torus is displayed dynamically.
-no-change-colors
Use static colors to display the torus (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 projection.
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 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.
-speed-wx float
Rotation speed around the wx plane (default: 1.1).
-speed-wy 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).
-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 © 2003-2020 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>, 11-jan-2020.