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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}] [-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 or see-through spirals.  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 or see-through  spirals
       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 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 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).
               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 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  (C)  2003-2005  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>, 28-sep-2005.