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] [-wireframe] [-surface] [-transparent] [-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 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. 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 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 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 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-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 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>, 27-may-2003.