1sphereeversion(6x)            XScreenSaver manual           sphereeversion(6x)
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NAME

6       sphereeversion - Displays a sphere eversion.
7

SYNOPSIS

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

DESCRIPTION

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
24       The deformed sphere can be projected to the screen either perspectively
25       or orthographically.
26
27       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
31       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.
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38       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
44       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
57       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
70       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.
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77       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

OPTIONS

82       sphereeversion accepts the following options:
83
84       -window Draw on a newly-created window.  This is the default.
85
86       -root   Draw on the root window.
87
88       -install
89               Install a private colormap for the window.
90
91       -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
96       -delay microseconds
97               How much of a delay should be introduced between steps  of  the
98               animation.  Default 10000, or 1/100th second.
99
100       -fps    Display the current frame rate, CPU load, and polygon count.
101
102       The following three options are mutually exclusive.  They determine how
103       the deformed sphere is displayed.
104
105       -mode random
106               Display the sphere in a random display mode (default).
107
108       -mode surface (Shortcut: -surface)
109               Display the sphere as a solid surface.
110
111       -mode transparent (Shortcut: -transparent)
112               Display the sphere as a transparent surface.
113
114       The following four options are mutually exclusive.  They determine  the
115       appearance of the deformed sphere.
116
117       -appearance random
118               Display the sphere with a random appearance (default).
119
120       -appearance solid (Shortcut: -solid)
121               Display the sphere as a solid object.
122
123       -appearance parallel-bands (Shortcut: -parallel-bands)
124               Display the sphere as see-through bands that lie along the par‐
125               allels of the sphere.
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127       -appearance meridian-bands (Shortcut: -meridian-bands)
128               Display the sphere as see-through  bands  that  lie  along  the
129               meridians of the sphere.
130
131       The  following  three  options  are mutually exclusive.  They determine
132       whether a graticule is displayed on top of the sphere.
133
134       -graticule random
135               Randomly choose whether to display a graticule (default).
136
137       -graticule on
138               Display a graticule.
139
140       -graticule off
141               Do not display a graticule.
142
143       The following option determines the order of the  surface  to  be  dis‐
144       played.
145
146       -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
151       The  following four options are mutually exclusive.  They determine how
152       to color the deformed sphere.
153
154       -colors random
155               Display the sphere with a random color scheme (default).
156
157       -colors twosided (Shortcut: -twosided-colors)
158               Display the sphere with two colors: red on one side  and  green
159               on the other side.
160
161       -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
168       -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
176       The following option determines the deformation speed.
177
178       -deformation-speed float
179               The deformation speed is measured in percent of  some  sensible
180               maximum speed (default: 10.0).
181
182       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
185       -projection random
186               Project the sphere from 3d to 2d using a random projection mode
187               (default).
188
189       -projection perspective (Shortcut: -perspective)
190               Project  the  sphere  from 3d to 2d using a perspective projec‐
191               tion.
192
193       -projection orthographic (Shortcut: -orthographic)
194               Project the sphere from 3d to 2d using an orthographic  projec‐
195               tion.
196
197       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
202       -speed-x float
203               Rotation speed around the x axis (default: 0.0).
204
205       -speed-y float
206               Rotation speed around the y axis (default: 0.0).
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208       -speed-z float
209               Rotation speed around the z axis (default: 0.0).
210

INTERACTION

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.
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ENVIRONMENT

219       DISPLAY to get the default host and display number.
220
221       XENVIRONMENT
222               to get the name of a resource file that  overrides  the  global
223               resources stored in the RESOURCE_MANAGER property.
224

SEE ALSO

226       X(1), xscreensaver(1)
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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

AUTHOR

238       Carsten Steger <carsten@mirsanmir.org>, 01-jun-2020.
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242X Version 11               5.45-1.fc33 (10-Dec-2020)        sphereeversion(6x)
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