1hypertorus(6x)                XScreenSaver manual               hypertorus(6x)
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NAME

6       hypertorus - Draws a hypertorus that rotates in 4d
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SYNOPSIS

9       hypertorus  [-display  host:display.screen] [-install] [-visual visual]
10       [-window]  [-root]  [-delay  usecs]  [-fps]   [-wireframe]   [-surface]
11       [-transparent]  [-solid]  [-bands]  [-spirals-{1,2,4,8,16}] [-twosided]
12       [-colorwheel]  [-perspective-3d]  [-orthographic-3d]  [-perspective-4d]
13       [-orthographic-4d]   [-speed-wx  float]  [-speed-wy  float]  [-speed-wz
14       float] [-speed-xy float] [-speed-xz float] [-speed-yz float]
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DESCRIPTION

17       The hypertorus program shows the Clifford torus as it  rotates  in  4d.
18       The  Clifford torus is a torus lies on the "surface" of the hypersphere
19       in 4d.  The program projects the 4d torus to 3d using either a perspec‐
20       tive  or an orthographic projection.  Of the two alternatives, the per‐
21       spective projection looks much more appealing.  In orthographic projec‐
22       tions  the  torus  degenerates  into a doubly covered cylinder for some
23       angles.  The projected 3d torus can then be  projected  to  the  screen
24       either  perspectively  or  orthographically.   There  are three display
25       modes for the torus: mesh (wireframe), solid, or transparent.  Further‐
26       more,  the appearance of the torus can be as a solid object or as a set
27       of see-through bands or see-through spirals.  Finally, the colors  with
28       with  the  torus  is drawn can be set to either two-sided or to a color
29       wheel.  In the first case, the torus is drawn with red on  the  outside
30       and  green  on the inside.  This mode enables you to see that the torus
31       turns inside-out as it rotates in 4d.  The second mode draws the  torus
32       with a fully saturated color wheel.  This gives a very nice effect when
33       combined with the see-through bands or see-through spirals  mode.   The
34       rotation  speed  for  each  of  the  six  planes around which the torus
35       rotates can be chosen.  This program is very much  inspired  by  Thomas
36       Banchoff's  book "Beyond the Third Dimension: Geometry, Computer Graph‐
37       ics, and Higher Dimensions", Scientific American Library, 1990.
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OPTIONS

40       hypertorus accepts the following options:
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42       -window Draw on a newly-created window.  This is the default.
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44       -root   Draw on the root window.
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46       -install
47               Install a private colormap for the window.
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49       -visual visual
50               Specify which visual to use.  Legal values are the  name  of  a
51               visual  class,  or the id number (decimal or hex) of a specific
52               visual.
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54       -delay microseconds
55               How much of a delay should be introduced between steps  of  the
56               animation.  Default 25000, or 1/40th second.
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58       The following three options are mutually exclusive.  They determine how
59       the torus is displayed.
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61       -wireframe
62               Display the torus as a wireframe mesh.
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64       -surface
65               Display the torus as a solid surface (default).
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67       -transparent
68               Display the torus as a transparent surface.
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70       The following seven options are mutually exclusive.  They determine the
71       appearance of the torus.
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73       -solid  Display the torus as a solid object.
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75       -bands  Display the torus as see-through bands (default).
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77       -spirals-1, -spirals-2, -spirals-4, -spirals-8, -spirals-16
78               Display  the  torus  as  see-through spirals with the indicated
79               number of spirals.
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81       The following two options are mutually exclusive.  They  determine  how
82       to color the torus.
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84       -twosided
85               Display the torus with two colors: red on the outside and green
86               on the inside.
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88       -colorwheel
89               Display the torus with a fully saturated color wheel (default).
90               If  the  torus is displayed as see-through bands each band will
91               be displayed with a different color.  Likewise, if the torus is
92               displayed  as  see-through  spirals  each spiral will receive a
93               different color.
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95       The following two options are mutually exclusive.  They  determine  how
96       the torus is projected from 3d to 2d (i.e., to the screen).
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98       -perspective-3d
99               Project  the torus from 3d to 2d using a perspective projection
100               (default).
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102       -orthographic-3d
103               Project the torus from 3d to 2d using an  orthographic  projec‐
104               tion.
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106       The  following  two options are mutually exclusive.  They determine how
107       the torus is projected from 4d to 3d.
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109       -perspective-4d
110               Project the torus from 4d to 3d using a perspective  projection
111               (default).
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113       -orthographic-4d
114               Project  the  torus from 4d to 3d using an orthographic projec‐
115               tion.
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117       The following six options determine the rotation  speed  of  the  torus
118       around the six possible hyperplanes.  The rotation speed is measured in
119       degrees per frame.  The speeds should be set to relatively  small  val‐
120       ues, e.g., less than 4 in magnitude.
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122       -speed-wx float
123               Rotation speed around the wx plane (default: 1.1).
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125       -speed-wy float
126               Rotation speed around the wy plane (default: 1.3).
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128       -speed-wz float
129               Rotation speed around the wz plane (default: 1.5).
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131       -speed-xy float
132               Rotation speed around the xy plane (default: 1.7).
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134       -speed-xz float
135               Rotation speed around the xz plane (default: 1.9).
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137       -speed-yz float
138               Rotation speed around the yz plane (default: 2.1).
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140       -fps    Display the current frame rate, CPU load, and polygon count.
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INTERACTION

143       If  you  run  this program in standalone mode you can rotate the hyper‐
144       torus by dragging the mouse while pressing the left mouse button.  This
145       rotates  the  hypertorus in 3D, i.e., around the wx, wy, and wz planes.
146       If you press the shift key while dragging the mouse with the left  but‐
147       ton  pressed  the hypertorus is rotated in 4D, i.e., around the xy, xz,
148       and yz planes.  To examine the hypertorus at your leisure, it  is  best
149       to  set  all  speeds to 0.  Otherwise, the hypertorus will rotate while
150       the left mouse button is not pressed.
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ENVIRONMENT

153       DISPLAY to get the default host and display number.
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155       XENVIRONMENT
156               to get the name of a resource file that  overrides  the  global
157               resources stored in the RESOURCE_MANAGER property.
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SEE ALSO

160       X(1), xscreensaver(1)
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163       Copyright © 2003-2005 by Carsten Steger.  Permission to use, copy, mod‐
164       ify, distribute, and sell this software and its documentation  for  any
165       purpose  is  hereby  granted without fee, provided that the above copy‐
166       right notice appear in all copies and that both that  copyright  notice
167       and this permission notice appear in supporting documentation.  No rep‐
168       resentations are made about the suitability of this  software  for  any
169       purpose.  It is provided "as is" without express or implied warranty.
170

AUTHOR

172       Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
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176X Version 11               5.43-2.fc31 (27-Aug-2019)            hypertorus(6x)
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