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}] [-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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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.
26 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.
43 Finally, the rotation speed for each of the six planes around which the
45 torus rotates can be chosen.
46 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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52 hypertorus accepts the following options:
53 -window Draw on a newly-created window. This is the default.
55 -root Draw on the root window.
57 -install
59 Install a private colormap for the window.
60 -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.
65 -delay microseconds
67 How much of a delay should be introduced between steps of the
68 animation. Default 25000, or 1/40th second.
69 The following three options are mutually exclusive. They determine how
71 the torus is displayed.
72 -wireframe
74 Display the torus as a wireframe mesh.
75 -surface
77 Display the torus as a solid surface (default).
78 -transparent
80 Display the torus as a transparent surface.
81 The following seven options are mutually exclusive. They determine the
83 appearance of the torus.
84 -solid Display the torus as a solid object.
86 -bands Display the torus as see-through bands (default).
88 -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.
92 The following three options are mutually exclusive. They determine how
94 to color the torus.
95 -onesided
97 Display the torus with a single color.
98 -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.
103 -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.
110 The following options determine whether the colors with which the torus
112 is displayed are static or are changing dynamically.
113 -change-colors
115 Change the colors with which the torus is displayed dynami‐
116 cally.
117 -no-change-colors
119 Use static colors to display the torus (default).
120 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 -perspective-3d
125 Project the torus from 3d to 2d using a perspective projection
126 (default).
127 -orthographic-3d
129 Project the torus from 3d to 2d using an orthographic projec‐
130 tion.
131 The following two options are mutually exclusive. They determine how
133 the torus is projected from 4d to 3d.
134 -perspective-4d
136 Project the torus from 4d to 3d using a perspective projection
137 (default).
138 -orthographic-4d
140 Project the torus from 4d to 3d using an orthographic projec‐
141 tion.
142 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.
147 -speed-wx float
149 Rotation speed around the wx plane (default: 1.1).
150 -speed-wy float
152 Rotation speed around the wy plane (default: 1.3).
153 -speed-wz float
155 Rotation speed around the wz plane (default: 1.5).
156 -speed-xy float
158 Rotation speed around the xy plane (default: 1.7).
159 -speed-xz float
161 Rotation speed around the xz plane (default: 1.9).
162 -speed-yz float
164 Rotation speed around the yz plane (default: 2.1).
165 -fps Display the current frame rate, CPU load, and polygon count.
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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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179 DISPLAY to get the default host and display number.
180 XENVIRONMENT
182 to get the name of a resource file that overrides the global
183 resources stored in the RESOURCE_MANAGER property.
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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
198 Carsten Steger <carsten@mirsanmir.org>, 11-jan-2020.
199X Version 11 6.02-4.fc35 (09-Nov-2021) hypertorus(6x)