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}] [-onesided]
12       [-twosided] [-colorwheel] [-change-colors]  [-perspective-3d]  [-ortho‐
13       graphic-3d]   [-perspective-4d]  [-orthographic-4d]  [-speed-wx  float]
14       [-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz float]
15       [-speed-yz float]
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DESCRIPTION

18       The  hypertorus  program  shows the Clifford torus as it rotates in 4d.
19       The Clifford torus is a torus lies on the "surface" of the  hypersphere
20       in 4d.  The program projects the 4d torus to 3d using either a perspec‐
21       tive or an orthographic projection.  Of the two alternatives, the  per‐
22       spective projection looks much more appealing.  In orthographic projec‐
23       tions the torus degenerates into a doubly covered cylinder for some an‐
24       gles.   The  projected 3d torus can then be projected to the screen ei‐
25       ther perspectively or orthographically.
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27       There are three display modes for the torus: mesh  (wireframe),  solid,
28       or  transparent.   Furthermore, the appearance of the torus can be as a
29       solid object or as a set of see-through bands or  see-through  spirals.
30       Finally,  the  colors  with  with the torus is drawn can be set to one-
31       sided, two-sided, or to a color wheel.  The colors  can  be  static  or
32       changing dynamically.  In one-sided color mode, the torus is drawn with
33       the same color on the inside and the outside.  In two-sided color mode,
34       the  torus  is drawn with red on the outside and green on the inside if
35       static colors are used.  If changing colors are used, dynamically vary‐
36       ing complementary colors are used for the two sides.  This mode enables
37       you to see that the 3d projection of the torus turns inside-out  as  it
38       rotates in 4d.  The color wheel mode draws the torus with a fully satu‐
39       rated color wheel.  If changing colors are  used,  the  colors  of  the
40       color wheel are varying dynamically.  The color wheel mode gives a very
41       nice effect when combined with the  see-through  bands  or  see-through
42       spirals mode.
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44       Finally, the rotation speed for each of the six planes around which the
45       torus rotates can be chosen.
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47       This program is inspired by Thomas Banchoff's book  "Beyond  the  Third
48       Dimension:  Geometry, Computer Graphics, and Higher Dimensions", Scien‐
49       tific American Library, 1990.
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OPTIONS

52       hypertorus accepts the following options:
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54       -window Draw on a newly-created window.  This is the default.
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56       -root   Draw on the root window.
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58       -install
59               Install a private colormap for the window.
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61       -visual visual
62               Specify which visual to use.  Legal values are the  name  of  a
63               visual  class,  or the id number (decimal or hex) of a specific
64               visual.
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66       -delay microseconds
67               How much of a delay should be introduced between steps  of  the
68               animation.  Default 25000, or 1/40th second.
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70       The following three options are mutually exclusive.  They determine how
71       the torus is displayed.
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73       -wireframe
74               Display the torus as a wireframe mesh.
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76       -surface
77               Display the torus as a solid surface (default).
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79       -transparent
80               Display the torus as a transparent surface.
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82       The following seven options are mutually exclusive.  They determine the
83       appearance of the torus.
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85       -solid  Display the torus as a solid object.
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87       -bands  Display the torus as see-through bands (default).
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89       -spirals-1, -spirals-2, -spirals-4, -spirals-8, -spirals-16
90               Display  the  torus  as  see-through spirals with the indicated
91               number of spirals.
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93       The following three options are mutually exclusive.  They determine how
94       to color the torus.
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96       -onesided
97               Display the torus with a single color.
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99       -twosided
100               Display the torus with two colors: one color on the outside and
101               the complementary on the inside.  For static colors, the colors
102               are red and green.
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104       -colorwheel
105               Display the torus with a fully saturated color wheel (default).
106               If the torus is displayed as see-through bands, each band  will
107               be displayed with a different color.  Likewise, if the torus is
108               displayed as see-through spirals, each spiral  will  receive  a
109               different color.
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111       The following options determine whether the colors with which the torus
112       is displayed are static or are changing dynamically.
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114       -change-colors
115               Change the colors with which the  torus  is  displayed  dynami‐
116               cally.
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118       -no-change-colors
119               Use static colors to display the torus (default).
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121       The  following  two options are mutually exclusive.  They determine how
122       the torus is projected from 3d to 2d (i.e., to the screen).
123
124       -perspective-3d
125               Project the torus from 3d to 2d using a perspective  projection
126               (default).
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128       -orthographic-3d
129               Project  the  torus from 3d to 2d using an orthographic projec‐
130               tion.
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132       The following two options are mutually exclusive.  They  determine  how
133       the torus is projected from 4d to 3d.
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135       -perspective-4d
136               Project  the torus from 4d to 3d using a perspective projection
137               (default).
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139       -orthographic-4d
140               Project the torus from 4d to 3d using an  orthographic  projec‐
141               tion.
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143       The  following  six  options  determine the rotation speed of the torus
144       around the six possible hyperplanes.  The rotation speed is measured in
145       degrees  per  frame.  The speeds should be set to relatively small val‐
146       ues, e.g., less than 4 in magnitude.
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148       -speed-wx float
149               Rotation speed around the wx plane (default: 1.1).
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151       -speed-wy float
152               Rotation speed around the wy plane (default: 1.3).
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154       -speed-wz float
155               Rotation speed around the wz plane (default: 1.5).
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157       -speed-xy float
158               Rotation speed around the xy plane (default: 1.7).
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160       -speed-xz float
161               Rotation speed around the xz plane (default: 1.9).
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163       -speed-yz float
164               Rotation speed around the yz plane (default: 2.1).
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166       -fps    Display the current frame rate, CPU load, and polygon count.
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INTERACTION

169       If you run this program in standalone mode you can  rotate  the  hyper‐
170       torus by dragging the mouse while pressing the left mouse button.  This
171       rotates the hypertorus in 3d, i.e., around the wx, wy, and  wz  planes.
172       If  you press the shift key while dragging the mouse with the left but‐
173       ton pressed the hypertorus is rotated in 4d, i.e., around the  xy,  xz,
174       and  yz  planes.  To examine the hypertorus at your leisure, it is best
175       to set all speeds to 0.  Otherwise, the hypertorus  will  rotate  while
176       the left mouse button is not pressed.
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ENVIRONMENT

179       DISPLAY to get the default host and display number.
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181       XENVIRONMENT
182               to  get  the  name of a resource file that overrides the global
183               resources stored in the RESOURCE_MANAGER property.
184

SEE ALSO

186       X(1), xscreensaver(1)
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189       Copyright © 2003-2020 by Carsten Steger.  Permission to use, copy, mod‐
190       ify,  distribute,  and sell this software and its documentation for any
191       purpose is hereby granted without fee, provided that  the  above  copy‐
192       right  notice  appear in all copies and that both that copyright notice
193       and this permission notice appear in supporting documentation.  No rep‐
194       resentations  are  made  about the suitability of this software for any
195       purpose.  It is provided "as is" without express or implied warranty.
196

AUTHOR

198       Carsten Steger <carsten@mirsanmir.org>, 11-jan-2020.
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202X Version 11               6.04-1.fc36 (06-Jun-2022)            hypertorus(6x)
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