1sphereeversion(6x) XScreenSaver manual sphereeversion(6x)
2
6 sphereeversion - Displays a sphere eversion.
7
9 sphereeversion [-display host:display.screen] [-install] [-visual vis‐
10 ual] [-window] [-root] [-delay usecs] [-fps] [-mode display-mode]
11 [-surface] [-transparent] [-appearance appearance] [-solid] [-parallel-
12 bands] [-meridian-bands] [-graticule mode] [-surface-order order]
13 [-colors color-scheme] [-twosided-colors] [-parallel-colors] [-merid‐
14 ian-colors] [-deformation-speed float] [-projection mode] [-perspec‐
15 tive] [-orthographic] [-speed-x float] [-speed-y float] [-speed-z
16 float]
17
19 The sphereeversion program shows a sphere eversion, i.e., a smooth
20 deformation (homotopy) that turns a sphere inside out. During the
21 eversion, the deformed sphere is allowed to intersect itself transver‐
22 sally. However, no creases or pinch points are allowed to occur.
23 The deformed sphere can be projected to the screen either perspectively
25 or orthographically.
26 There are three display modes for the sphere: solid, transparent, or
28 random. If random mode is selected, the mode is changed each time an
29 eversion has been completed.
30 The appearance of the sphere can be as a solid object, as a set of see-
32 through bands, or random. The bands can be parallel bands or meridian
33 bands, i.e., bands that run along the parallels (lines of latitude) or
34 bands that run along the meridians (lines of longitude) of the sphere.
35 If random mode is selected, the appearance is changed each time an
36 eversion has been completed.
37 It is also possible to display a graticule (i.e., a coordinate grid
39 consisting of parallel and meridian lines) on top of the surface. The
40 graticule mode can be set to on, off, or random. If random mode is
41 selected, the graticule mode is changed each time an eversion has been
42 completed.
43 It is possible to define a surface order of the sphere eversion as ran‐
45 dom or as a value between 2 and 5. This determines the the complexity
46 of the deformation. For higher surface orders, some z-fighting might
47 occur around the central stage of the eversion, which might lead to
48 some irregular flickering of the displayed surface if it is displayed
49 as a solid object. For odd surface orders, z-fighting will occur very
50 close to the central stage of the eversion since the deformed sphere is
51 a doubly covered Boy surface (for surface order 3) or a doubly covered
52 generalized Boy surface (for surface order 5) in this case. If you
53 find this distracting, you should set the surface order to 2. If a
54 random surface order is selected, the surface order is changed each
55 time an eversion has been completed.
56 The colors with with the sphere is drawn can be set to two-sided, par‐
58 allel, meridian, or random. In two-sided mode, the sphere is drawn
59 with red on one side and green on the other side. In parallel mode,
60 the sphere is displayed with colors that run from red to cyan on one
61 side of the surface and from green to violet on the other side. The
62 colors are aligned with the parallels of the sphere in this mode. In
63 meridian mode, the the sphere is displayed with colors that run from
64 red to white to cyan to black and back to red on one side of the sur‐
65 face and from green to white to violet to black and back to green on
66 the other side. The colors are aligned with the meridians of the
67 sphere in this mode. If random mode is selected, the color scheme is
68 changed each time an eversion has been completed.
69 By default, the sphere is rotated to a new viewing position each time
71 an eversion has been completed. In addition, it is possible to rotate
72 the sphere while it is deforming. The rotation speed for each of the
73 three coordinate axes around which the sphere rotates can be chosen
74 arbitrarily. For best effects, however, it is suggested to rotate only
75 around the z axis while the sphere is deforming.
76 This program is inspired by the following paper: Adam Bednorz, Witold
78 Bednorz: "Analytic sphere eversion using ruled surfaces", Differential
79 Geometry and its Applications 64:59-79, 2019.
80
82 sphereeversion accepts the following options:
83 -window Draw on a newly-created window. This is the default.
85 -root Draw on the root window.
87 -install
89 Install a private colormap for the window.
90 -visual visual
92 Specify which visual to use. Legal values are the name of a
93 visual class, or the id number (decimal or hex) of a specific
94 visual.
95 -delay microseconds
97 How much of a delay should be introduced between steps of the
98 animation. Default 10000, or 1/100th second.
99 -fps Display the current frame rate, CPU load, and polygon count.
101 The following three options are mutually exclusive. They determine how
103 the deformed sphere is displayed.
104 -mode random
106 Display the sphere in a random display mode (default).
107 -mode surface (Shortcut: -surface)
109 Display the sphere as a solid surface.
110 -mode transparent (Shortcut: -transparent)
112 Display the sphere as a transparent surface.
113 The following four options are mutually exclusive. They determine the
115 appearance of the deformed sphere.
116 -appearance random
118 Display the sphere with a random appearance (default).
119 -appearance solid (Shortcut: -solid)
121 Display the sphere as a solid object.
122 -appearance parallel-bands (Shortcut: -parallel-bands)
124 Display the sphere as see-through bands that lie along the par‐
125 allels of the sphere.
126 -appearance meridian-bands (Shortcut: -meridian-bands)
128 Display the sphere as see-through bands that lie along the
129 meridians of the sphere.
130 The following three options are mutually exclusive. They determine
132 whether a graticule is displayed on top of the sphere.
133 -graticule random
135 Randomly choose whether to display a graticule (default).
136 -graticule on
138 Display a graticule.
139 -graticule off
141 Do not display a graticule.
142 The following option determines the order of the surface to be dis‐
144 played.
145 -surface-order order
147 The surface order can be set to random or to a value between 2
148 and 5 (default: random). This determines the the complexity of
149 the deformation.
150 The following four options are mutually exclusive. They determine how
152 to color the deformed sphere.
153 -colors random
155 Display the sphere with a random color scheme (default).
156 -colors twosided (Shortcut: -twosided-colors)
158 Display the sphere with two colors: red on one side and green
159 on the other side.
160 -colors parallel (Shortcut: -parallel-colors)
162 Display the sphere with colors that run from red to cyan on one
163 side of the surface and from green to violet on the other side.
164 The colors are aligned with the parallels of the sphere. If
165 the sphere is displayed as parallel bands, each band will be
166 displayed with a different color.
167 -colors meridian (Shortcut: -meridian-colors)
169 Display the sphere with colors that run from red to white to
170 cyan to black and back to red on one side of the surface and
171 from green to white to violet to black and back to green on the
172 other side. The colors are aligned with the meridians of the
173 sphere. If the sphere is displayed as meridian bands, each
174 band will be displayed with a different color.
175 The following option determines the deformation speed.
177 -deformation-speed float
179 The deformation speed is measured in percent of some sensible
180 maximum speed (default: 10.0).
181 The following three options are mutually exclusive. They determine how
183 the deformed sphere is projected from 3d to 2d (i.e., to the screen).
184 -projection random
186 Project the sphere from 3d to 2d using a random projection mode
187 (default).
188 -projection perspective (Shortcut: -perspective)
190 Project the sphere from 3d to 2d using a perspective projec‐
191 tion.
192 -projection orthographic (Shortcut: -orthographic)
194 Project the sphere from 3d to 2d using an orthographic projec‐
195 tion.
196 The following three options determine the rotation speed of the
198 deformed sphere around the three possible axes. The rotation speed is
199 measured in degrees per frame. The speeds should be set to relatively
200 small values, e.g., less than 4 in magnitude.
201 -speed-x float
203 Rotation speed around the x axis (default: 0.0).
204 -speed-y float
206 Rotation speed around the y axis (default: 0.0).
207 -speed-z float
209 Rotation speed around the z axis (default: 0.0).
210
212 If you run this program in standalone mode, you can rotate the deformed
213 sphere by dragging the mouse while pressing the left mouse button.
214 This rotates the sphere in 3d. To examine the deformed sphere at your
215 leisure, it is best to set all speeds to 0. Otherwise, the deformed
216 sphere will rotate while the left mouse button is not pressed.
217
219 DISPLAY to get the default host and display number.
220 XENVIRONMENT
222 to get the name of a resource file that overrides the global
223 resources stored in the RESOURCE_MANAGER property.
224
226 X(1), xscreensaver(1)
227
229 Copyright © 2020 by Carsten Steger. Permission to use, copy, modify,
230 distribute, and sell this software and its documentation for any pur‐
231 pose is hereby granted without fee, provided that the above copyright
232 notice appear in all copies and that both that copyright notice and
233 this permission notice appear in supporting documentation. No repre‐
234 sentations are made about the suitability of this software for any pur‐
235 pose. It is provided "as is" without express or implied warranty.
236
238 Carsten Steger <carsten@mirsanmir.org>, 01-jun-2020.
239X Version 11 5.45-1.fc33 (10-Dec-2020) sphereeversion(6x)