1hypertorus(6x) XScreenSaver manual hypertorus(6x)
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6 hypertorus - Draws a hypertorus that rotates in 4d
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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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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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40 hypertorus accepts the following options:
41 -window Draw on a newly-created window. This is the default.
43 -root Draw on the root window.
45 -install
47 Install a private colormap for the window.
48 -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.
53 -delay microseconds
55 How much of a delay should be introduced between steps of the
56 animation. Default 25000, or 1/40th second.
57 The following three options are mutually exclusive. They determine how
59 the torus is displayed.
60 -wireframe
62 Display the torus as a wireframe mesh.
63 -surface
65 Display the torus as a solid surface (default).
66 -transparent
68 Display the torus as a transparent surface.
69 The following seven options are mutually exclusive. They determine the
71 appearance of the torus.
72 -solid Display the torus as a solid object.
74 -bands Display the torus as see-through bands (default).
76 -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.
80 The following two options are mutually exclusive. They determine how
82 to color the torus.
83 -twosided
85 Display the torus with two colors: red on the outside and green
86 on the inside.
87 -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.
94 The following two options are mutually exclusive. They determine how
96 the torus is projected from 3d to 2d (i.e., to the screen).
97 -perspective-3d
99 Project the torus from 3d to 2d using a perspective projection
100 (default).
101 -orthographic-3d
103 Project the torus from 3d to 2d using an orthographic projec‐
104 tion.
105 The following two options are mutually exclusive. They determine how
107 the torus is projected from 4d to 3d.
108 -perspective-4d
110 Project the torus from 4d to 3d using a perspective projection
111 (default).
112 -orthographic-4d
114 Project the torus from 4d to 3d using an orthographic projec‐
115 tion.
116 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.
121 -speed-wx float
123 Rotation speed around the wx plane (default: 1.1).
124 -speed-wy float
126 Rotation speed around the wy plane (default: 1.3).
127 -speed-wz float
129 Rotation speed around the wz plane (default: 1.5).
130 -speed-xy float
132 Rotation speed around the xy plane (default: 1.7).
133 -speed-xz float
135 Rotation speed around the xz plane (default: 1.9).
136 -speed-yz float
138 Rotation speed around the yz plane (default: 2.1).
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141 If you run this program in standalone mode you can rotate the hyper‐
142 torus by dragging the mouse while pressing the left mouse button. This
143 rotates the hypertorus in 3D, i.e., around the wx, wy, and wz planes.
144 If you press the shift key while dragging the mouse with the left but‐
145 ton pressed the hypertorus is rotated in 4D, i.e., around the xy, xz,
146 and yz planes. To examine the hypertorus at your leisure, it is best
147 to set all speeds to 0. Otherwise, the hypertorus will rotate while
148 the left mouse button is not pressed.
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151 DISPLAY to get the default host and display number.
152 XENVIRONMENT
154 to get the name of a resource file that overrides the global
155 resources stored in the RESOURCE_MANAGER property.
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158 X(1), xscreensaver(1)
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161 Copyright © 2003-2005 by Carsten Steger. Permission to use, copy, mod‐
162 ify, distribute, and sell this software and its documentation for any
163 purpose is hereby granted without fee, provided that the above copy‐
164 right notice appear in all copies and that both that copyright notice
165 and this permission notice appear in supporting documentation. No rep‐
166 resentations are made about the suitability of this software for any
167 purpose. It is provided "as is" without express or implied warranty.
168
170 Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
171X Version 11 5.05-3 (06-Apr-2008) hypertorus(6x)