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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