1sphereeversion(6x)            XScreenSaver manual           sphereeversion(6x)
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3
4

NAME

6       sphereeversion - Displays a sphere eversion.
7

SYNOPSIS

9       sphereeversion  [--display  host:display.screen]  [--install] [--visual
10       visual]  [--window]  [--root]  [--window-id  number]  [--delay   usecs]
11       [--fps]   [--eversion-method   method]   [--analytic]  [--corrugations]
12       [--mode display-mode] [--surface] [--transparent] [--appearance appear‐
13       ance]   [--solid]  [--parallel-bands]  [--meridian-bands]  [--graticule
14       mode] [--colors color-scheme]  [--twosided-colors]  [--parallel-colors]
15       [--meridian-colors]    [--earth-colors]   [--deformation-speed   float]
16       [--projection mode] [--perspective]  [--orthographic]  [--surface-order
17       order]   [--lunes-1]   [--lunes-2]   [--lunes-4]  [--lunes-8]  [--hemi‐
18       spheres-1]  [--hemispheres-2]  [--speed-x  float]   [--speed-y   float]
19       [--speed-z float]
20

DESCRIPTION

22       The  sphereeversion program shows a sphere eversion, i.e., a smooth de‐
23       formation (homotopy) that turns a sphere inside out.  During the  ever‐
24       sion, the deformed sphere is allowed to intersect itself transversally.
25       However, no creases or pinch points are allowed to occur.
26
27       The sphere can be deformed with two eversion methods: analytic or  cor‐
28       rugations. The analytic sphere eversion method is described in the fol‐
29       lowing paper: Adam Bednorz, Witold Bednorz: "Analytic  sphere  eversion
30       using  ruled  surfaces",  Differential  Geometry  and  its Applications
31       64:59-79, 2019. The corrugations sphere eversion method is described in
32       the  video  "Outside  In" by the Geometry Center (Bill Thurston, Silvio
33       Levy, Delle Maxwell, Tamara Munzner, Nathaniel Thurston, David Ben-Zvi,
34       Matt  Headrick,  et  al.),  1994,  and the accompanying booklet: Silvio
35       Levy: "Making Waves - A Guide to the Ideas Behind Outside In", A K  Pe‐
36       ters,  Wellesley,  MA, 1995. See also the section "Brief Description of
37       the Corrugations Sphere Eversion Method" below.
38
39       The deformed sphere can be projected to the screen either perspectively
40       or orthographically.
41
42       There  are  three  display modes for the sphere: solid, transparent, or
43       random.  If random mode is selected, the mode is changed each  time  an
44       eversion has been completed.
45
46       The appearance of the sphere can be as a solid object, as a set of see-
47       through bands, or random.  The bands can be parallel bands or  meridian
48       bands,  i.e., bands that run along the parallels (lines of latitude) or
49       bands that run along the meridians (lines of longitude) of the  sphere.
50       If  random mode is selected, the appearance is changed each time an ev‐
51       ersion has been completed.
52
53       For the analytic sphere eversion, it is  also  possible  to  display  a
54       graticule  (i.e., a coordinate grid consisting of parallel and meridian
55       lines) on top of the surface.  The graticule mode can  be  set  to  on,
56       off,  or  random.   If  random  mode is selected, the graticule mode is
57       changed each time an eversion has been completed.
58
59       The colors with with the sphere is drawn can be set to two-sided,  par‐
60       allel,  meridian,  earth,  or random.  In two-sided mode, the sphere is
61       drawn with red on one side and green on the other side (analytic  ever‐
62       sion)  or  with gold on one side and purple on the other side (corruga‐
63       tions eversion).  In parallel mode, the sphere is displayed with colors
64       that  run  from  blue to white to orange on one side of the surface and
65       from magenta to black to green on  the  other  side.   The  colors  are
66       aligned  with  the  parallels  of the sphere in this mode.  In meridian
67       mode, the the sphere is displayed with colors that  run  from  blue  to
68       white  to  orange  to black and back to blue on one side of the surface
69       and from magenta to white to green to black and back to magenta on  the
70       other side.  The colors are aligned with the meridians of the sphere in
71       this mode.  In earth mode, the sphere is drawn with a texture of  earth
72       by  day  on  one side and with a texture of earth by night on the other
73       side.  Initially, the earth by day is on the outside and the  earth  by
74       night on the inside.  After the first eversion, the earth by night will
75       be on the outside.  All points of the earth on the inside  and  outside
76       are  at the same positions on the sphere.  Since an eversion transforms
77       the sphere into its inverse, the earth by night will  appear  with  all
78       continents  mirror  reversed.   If  random  mode is selected, the color
79       scheme is changed each time an eversion has been completed.
80
81       By default, the sphere is rotated to a new viewing position  each  time
82       an  eversion has been completed.  In addition, it is possible to rotate
83       the sphere while it is deforming.  The rotation speed for each  of  the
84       three coordinate axes around which the sphere rotates can be chosen ar‐
85       bitrarily.  For best effects, however, it is suggested to  rotate  only
86       around the z axis while the sphere is deforming.
87
88       For  the  analytic  sphere eversion, it is possible to define a surface
89       order of the sphere eversion as random or as a value between 2  and  5.
90       This determines the the complexity of the deformation.  For higher sur‐
91       face orders, some z-fighting might occur around the  central  stage  of
92       the eversion, which might lead to some irregular flickering of the dis‐
93       played surface if it is displayed as a solid object.  For  odd  surface
94       orders,  z-fighting  will  occur very close to the central stage of the
95       eversion since the deformed sphere is a doubly covered Boy surface (for
96       surface  order 3) or a doubly covered generalized Boy surface (for sur‐
97       face order 5) in this case.  If you find this distracting,  you  should
98       set the surface order to 2.  If a random surface order is selected, the
99       surface order is changed each time an eversion has been completed.
100

BRIEF DESCRIPTION OF THE CORRUGATIONS SPHERE EVERSION METHOD

102       The corrugations sphere eversion method is described in detail  in  the
103       video  and  booklet  mentioned above. Briefly, the method works as fol‐
104       lows: Imagine the sphere cut  into  eight  spherical  lunes  (spherical
105       biangles).   Now  imagine each lune to be a belt.  The ends of the belt
106       (which correspond to the north and  south  poles  of  the  sphere)  are
107       pushed  past each other.  This creates a loop in the belt.  If the belt
108       were straightened out, it would contain a 360  degree  rotation.   This
109       rotation  can  be  removed  by rotating each end of the belt by 180 de‐
110       grees.  Finally, the belt is pushed to the opposite side of the sphere,
111       which  causes the side of the belt that initially was inside the sphere
112       to appear on the outside.
113
114       The method described so far only works for a single lune (belt) and not
115       for the entire sphere.  To make it work for the entire sphere, corruga‐
116       tions (i.e., waves) must be added to the sphere.  This happens  in  the
117       first  phase  of the eversion.  Then, the method described above is ap‐
118       plied to the eight lunes.  Finally, the corrugations are removed to ob‐
119       tain the everted sphere.
120
121       To  see  the  eversion  for  a single lune, the option --lunes-1 can be
122       used.  Using this option, the eversion, as described above,  is  easier
123       to  understand.   It  is  also  possible  to  display  two  lunes using
124       --lunes-2 and four lunes using --lunes-4.  Using fewer than eight lunes
125       reduces  the  visual  complexity of the eversion and may help to under‐
126       stand the method.
127
128       Furthermore, it is possible to display only one  hemisphere  using  the
129       option  --hemispheres-1.   This  allows to see what is happening in the
130       center of the sphere during the eversion.   Note  that  the  north  and
131       south  half  of the sphere move in a symmetric fashion during the ever‐
132       sion.  Hence, the  eversion  is  actually  composed  of  16  semi-lunes
133       (spherical  triangles from the equator to the poles) that all deform in
134       the same manner.  By specifying --lunes-1 --hemispheres-1, the deforma‐
135       tion of one semi-lune can be observed.
136
137       Note that the options described above are only intended for educational
138       purposes.  They are not used if none of them are explicitly specified.
139
140

OPTIONS

142       sphereeversion accepts the following options:
143
144       --window
145               Draw on a newly-created window.  This is the default.
146
147       --root  Draw on the root window.
148
149       --window-id number
150               Draw on the specified window.
151
152       --install
153               Install a private colormap for the window.
154
155       --visual visual
156               Specify which visual to use.  Legal values are the  name  of  a
157               visual  class,  or the id number (decimal or hex) of a specific
158               visual.
159
160       --delay microseconds
161               How much of a delay should be introduced between steps  of  the
162               animation.  Default 10000, or 1/100th second.
163
164       --fps   Display the current frame rate, CPU load, and polygon count.
165
166       The  following  three  options  are mutually exclusive.  They determine
167       which sphere eversion method is used.
168
169       --eversion-method random
170               Use a random sphere eversion method (default).
171
172       --eversion-method analytic (Shortcut: --analytic)
173               Use the analytic sphere eversion method.
174
175       --eversion-method corrugations (Shortcut: --corrugations)
176               Use the corrugations sphere eversion method.
177
178       The following three options are mutually exclusive.  They determine how
179       the deformed sphere is displayed.
180
181       --mode random
182               Display the sphere in a random display mode (default).
183
184       --mode surface (Shortcut: --surface)
185               Display the sphere as a solid surface.
186
187       --mode transparent (Shortcut: --transparent)
188               Display the sphere as a transparent surface.
189
190       The  following four options are mutually exclusive.  They determine the
191       appearance of the deformed sphere.
192
193       --appearance random
194               Display the sphere with a random appearance (default).
195
196       --appearance solid (Shortcut: --solid)
197               Display the sphere as a solid object.
198
199       --appearance parallel-bands (Shortcut: --parallel-bands)
200               Display the sphere as see-through bands that lie along the par‐
201               allels of the sphere.
202
203       --appearance meridian-bands (Shortcut: --meridian-bands)
204               Display  the  sphere  as  see-through  bands that lie along the
205               meridians of the sphere.
206
207       The following three options are  mutually  exclusive.   They  determine
208       whether  a  graticule is displayed on top of the sphere.  These options
209       only have an effect if the analytic sphere eversion method is selected.
210
211       --graticule random
212               Randomly choose whether to display a graticule (default).
213
214       --graticule on
215               Display a graticule.
216
217       --graticule off
218               Do not display a graticule.
219
220       The following five options are mutually exclusive.  They determine  how
221       to color the deformed sphere.
222
223       --colors random
224               Display the sphere with a random color scheme (default).
225
226       --colors twosided (Shortcut: --twosided-colors)
227               Display  the  sphere with two colors: red on one side and green
228               on the other side (analytic eversion) or gold on one  side  and
229               purple on the other side (corrugations eversion).
230
231       --colors parallel (Shortcut: --parallel-colors)
232               Display the sphere with colors that run from from blue to white
233               to orange on one side of the surface and from magenta to  black
234               to  green  on  the other side.  The colors are aligned with the
235               parallels of the sphere.  If the sphere is displayed as  paral‐
236               lel bands, each band will be displayed with a different color.
237
238       --colors meridian (Shortcut: --meridian-colors)
239               Display the sphere with colors that run from from blue to white
240               to orange to black and back to blue on one side of the  surface
241               and from magenta to white to green to black and back to magenta
242               on the other side.  The colors are aligned with  the  meridians
243               of  the  sphere.  If the sphere is displayed as meridian bands,
244               each band will be displayed with a different color.
245
246       --colors earth (Shortcut: --earth-colors)
247               Display the sphere with a texture of earth by day on  one  side
248               and  with  a texture of earth by night on the other side.  Ini‐
249               tially, the earth by day is on the outside  and  the  earth  by
250               night  on  the  inside.  After the first eversion, the earth by
251               night will be on the outside.  All points of the earth  on  the
252               inside  and  outside  are  at the same positions on the sphere.
253               Since an eversion transforms the sphere into its  inverse,  the
254               earth by night will appear with all continents mirror reversed.
255
256       The following option determines the deformation speed.
257
258       --deformation-speed float
259               The  deformation  speed is measured in percent of some sensible
260               maximum speed (default: 10.0).
261
262       The following three options are mutually exclusive.  They determine how
263       the deformed sphere is projected from 3d to 2d (i.e., to the screen).
264
265       --projection random
266               Project the sphere from 3d to 2d using a random projection mode
267               (default).
268
269       --projection perspective (Shortcut: --perspective)
270               Project the sphere from 3d to 2d using  a  perspective  projec‐
271               tion.
272
273       --projection orthographic (Shortcut: --orthographic)
274               Project  the sphere from 3d to 2d using an orthographic projec‐
275               tion.
276
277       The following option determines the order of the  surface  to  be  dis‐
278       played.  This option only has an effect if the analytic sphere eversion
279       method is selected.
280
281       --surface-order order
282               The surface order can be set to random or to a value between  2
283               and 5 (default: random).  This determines the the complexity of
284               the deformation.
285
286       The following four options are mutually exclusive.  They determine  how
287       many lunes of the sphere are displayed.  These options only have an ef‐
288       fect if the corrugations sphere eversion method is selected.
289
290       --lunes-1
291               Display one of the eight lunes that form the sphere.
292
293       --lunes-2
294               Display two of the eight lunes that form the sphere.
295
296       --lunes-4
297               Display four of the eight lunes that form the sphere.
298
299       --lunes-8
300               Display all eight lunes that form the sphere (default).
301
302       The following two options are mutually exclusive.  They  determine  how
303       many  hemispheres of the sphere are displayed.  These options only have
304       an effect if the corrugations sphere eversion method is selected.
305
306       --hemispheres-1
307               Display only one hemisphere of the sphere.
308
309       --hemispheres-2
310               Display both hemispheres of the sphere (default).
311
312       The following three options determine the rotation  speed  of  the  de‐
313       formed  sphere  around  the three possible axes.  The rotation speed is
314       measured in degrees per frame.  The speeds should be set to  relatively
315       small values, e.g., less than 4 in magnitude.
316
317       --speed-x float
318               Rotation speed around the x axis (default: 0.0).
319
320       --speed-y float
321               Rotation speed around the y axis (default: 0.0).
322
323       --speed-z float
324               Rotation speed around the z axis (default: 0.0).
325

INTERACTION

327       If you run this program in standalone mode, you can rotate the deformed
328       sphere by dragging the mouse while  pressing  the  left  mouse  button.
329       This  rotates the sphere in 3d.  To examine the deformed sphere at your
330       leisure, it is best to set all speeds to 0.   Otherwise,  the  deformed
331       sphere will rotate while the left mouse button is not pressed.
332

ENVIRONMENT

334       DISPLAY to get the default host and display number.
335
336       XENVIRONMENT
337               to  get  the  name of a resource file that overrides the global
338               resources stored in the RESOURCE_MANAGER property.
339
340       XSCREENSAVER_WINDOW
341               The window ID to use with --root.
342

SEE ALSO

344       X(1), xscreensaver(1),
345       https://profs.etsmtl.ca/mmcguffin/eversion/,
346       http://www.geom.uiuc.edu/docs/outreach/oi/software.html
347
349       Copyright © 2020 by Carsten Steger.  Permission to use,  copy,  modify,
350       distribute,  and  sell this software and its documentation for any pur‐
351       pose is hereby granted without fee, provided that the  above  copyright
352       notice  appear  in  all  copies and that both that copyright notice and
353       this permission notice appear in supporting documentation.   No  repre‐
354       sentations are made about the suitability of this software for any pur‐
355       pose.  It is provided "as is" without express or implied warranty.
356
357       Parts of the code in this program are based on the program "sphereEver‐
358       sion  0.4" by Michael J. McGuffin, which, in turn, is based on the pro‐
359       gram "Evert" developed by Nathaniel Thurston at  the  Geometry  Center.
360       The modified code is used with permission.
361

AUTHOR

363       Carsten Steger <carsten@mirsanmir.org>, 01-jun-2020.
364
365
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367X Version 11               6.06-1.fc37 (12-Dec-2022)        sphereeversion(6x)
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