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hypertorus(6x)		      XScreenSaver manual		hypertorus(6x)

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 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 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 Graph‐
       ics, 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  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-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 hyper‐
       torus 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  but‐
       ton  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 © 2003-2005 by Carsten Steger.	 Permission to use, copy, mod‐
       ify, distribute, and sell this software and its documentation  for  any
       purpose	is  hereby  granted without fee, provided that the above copy‐
       right notice appear in all copies and that both that  copyright	notice
       and this permission notice appear in supporting documentation.  No rep‐
       resentations 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.

X Version 11		      5.07 (10-Aug-2008)		hypertorus(6x)
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