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

6       etruscanvenus  -  Draws  a 3d immersion of a Klein bottle that smoothly
7       deforms between the Etruscan Venus surface, the Roman surface, the  Boy
8       surface surface, and the Ida surface.
9

SYNOPSIS

11       etruscanvenus  [-display  host:display.screen] [-install] [-visual vis‐
12       ual] [-window]  [-root]  [-delay  usecs]  [-fps]  [-mode  display-mode]
13       [-wireframe]   [-surface]   [-transparent]   [-appearance   appearance]
14       [-solid] [-distance-bands]  [-direction-bands]  [-colors  color-scheme]
15       [-onesided-colors]  [-twosided-colors]  [-distance-colors] [-direction-
16       colors]  [-no-change-colors]  [-view-mode  view-mode]  [-walk]  [-turn]
17       [-no-deform]  [-deformation-speed  float]  [-initial-deformation float]
18       [-etruscan-venus] [-roman] [-boy] [-ida] [-orientation-marks] [-projec‐
19       tion  mode]  [-perspective]  [-orthographic] [-speed-x float] [-speed-y
20       float] [-speed-z float] [-walk-direction float] [-walk-speed float]
21

DESCRIPTION

23       The etruscanvenus program shows a 3d immersion of a Klein  bottle  that
24       smoothly deforms between the Etruscan Venus surface, the Roman surface,
25       the Boy surface, and the Ida surface.  You can walk on the Klein bottle
26       or  turn it in 3d.  Topologically, all surfaces are Klein bottles, even
27       the Roman and Boy surfaces, which  are  doubly  covered  and  therefore
28       appear to be an immersed real projective plane.  The smooth deformation
29       between these surfaces was constructed by George K. Francis.
30
31       The Klein bottle is a non-orientable surface.  To make  this  apparent,
32       the two-sided color mode can be used.  Alternatively, orientation mark‐
33       ers (curling arrows) can be drawn as a texture map on  the  surface  of
34       the  Klein  bottle.  While walking on the Klein bottle, you will notice
35       that the orientation of the  curling  arrows  changes  (which  it  must
36       because  the  Klein  bottle is non-orientable).  Since all the surfaces
37       except the Ida surface have points where the surface normal is not well
38       defined for some points, walking is only performed on the Ida surface.
39
40       As  mentioned  above, the Roman and Boy surfaces are doubly covered and
41       therefore appear to be an immersed real projective plane.   Since  some
42       of the parameter names are based on this interpretation of the surface,
43       the geometry of the real projective plane  will  be  briefly  disussed.
44       The  real projective plane is a model for the projective geometry in 2d
45       space.  One point can be singled out as the origin.  A line can be sin‐
46       gled out as the line at infinity, i.e., a line that lies at an infinite
47       distance to the origin.  The line at infinity is topologically  a  cir‐
48       cle.   Points on the line at infinity are also used to model directions
49       in projective geometry.  Direction and distance  bands  refer  to  this
50       interpretation  of the surface.  If direction bands are used, the bands
51       extend from the origin of the projective plane in different  directions
52       to  the line at infinity and back to the origin.  If distance bands are
53       used, the bands lie at constant distances  to  the  origin.   The  same
54       interpretation  is  used  for  distance and direction colors.  Although
55       there is no conceptually equivalent geometric  interpretation  for  the
56       two  Klein  bottle  surfaces (the Etruscan Venus and Ida surfaces), the
57       smooth deformation between the surfaces results in a natural  extension
58       of these concepts to the Klein bottle surfaces.
59
60       The  immersed  surfaces  can be projected to the screen either perspec‐
61       tively or orthographically.  When using the walking  mode,  perspective
62       projection to the screen will be used.
63
64       There  are  three display modes for the Klein bottle: mesh (wireframe),
65       solid, or transparent.  Furthermore, the appearance of the surface  can
66       be  as  a solid object or as a set of see-through bands.  The bands can
67       be distance bands or direction bands, as explained above.
68
69       The colors with with the surface is drawn can be set to one-sided, two-
70       sided, distance, or direction.  In one-sided mode, the surface is drawn
71       with the same color on both sides of the underlying triangles.  In two-
72       sided  mode,  the  surface  is  drawn with one color on one side of the
73       underlying triangles and the complementary color  on  the  other  side.
74       Since  the surface actually only has one side, the color jumps from red
75       to green along a line on the surface.  This mode  enables  you  to  see
76       that  the  surface is non-orientable.  In distance mode, the surface is
77       displayed with fully saturated colors that depend on  the  distance  of
78       the  points  on the projective plane to the origin, as described above.
79       If the surface is displayed as distance bands, each band will  be  dis‐
80       played  with a different color.  In direction mode, the surface is dis‐
81       played with fully saturated colors that depend  on  the  angle  of  the
82       points  on  the  projective plane with respect to the origin (see above
83       for an explanation).  If the surface is displayed as  direction  bands,
84       each band will be displayed with a different color.  The colors used to
85       color the surface can either be static or can be changed dynamically.
86
87       The rotation speed for each of the three coordinate axes  around  which
88       the Klein bottle rotates can be chosen.
89
90       Furthermore,  in  the walking mode the walking direction in the 2d base
91       square of the surface and the walking speed can be chosen.  The walking
92       direction  is  measured  as  an  angle in degrees in the 2d square that
93       forms the coordinate system of the surface.  A value of 0 or 180  means
94       that  the walk is along a circle at a randomly chosen distance from the
95       origin (parallel to a distance band).  A value of 90 or 270 means  that
96       the  walk  is directly along a direction band.  Any other value results
97       in a curved path along the surface.  As noted above,  walking  is  per‐
98       formed only on the Ida surface.
99
100       By  default, the immersion of the Klein bottle smoothly deforms between
101       the Etruscan Venus surface, the Roman surface, the Boy surface, and the
102       Ida  surface.   It  is possible to choose the speed of the deformation.
103       Furthermore, it is possible to switch the deformation off.  It is  also
104       possible  to  determine the initial deformation of the immersion.  This
105       is mostly useful if the deformation is switched off, in which  case  it
106       will determine the appearance of the surface.  A value of 0 corresponds
107       to the Etruscan Venus surface, a value of 1000 to the Roman surface,  a
108       value  of  2000 to the Boy surface, and a value of 3000 to the Ida sur‐
109       face.
110
111       This program is inspired by George K.  Francis's  book  "A  Topological
112       Picturebook",  Springer,  1987,  by George K. Francis's paper "The Etr‐
113       uscan Venus" in P. Concus, R. Finn, and D. A. Hoffman: "Geometric Anal‐
114       ysis  and  Computer  Graphics", Springer, 1991, and by a video entitled
115       "The Etruscan Venus" by Donna J. Cox, George K. Francis, and Raymond L.
116       Idaszak, presented at SIGGRAPH 1989.
117

OPTIONS

119       etruscanvenus accepts the following options:
120
121       -window Draw on a newly-created window.  This is the default.
122
123       -root   Draw on the root window.
124
125       -install
126               Install a private colormap for the window.
127
128       -visual visual
129               Specify  which  visual  to use.  Legal values are the name of a
130               visual class, or the id number (decimal or hex) of  a  specific
131               visual.
132
133       -delay microseconds
134               How  much  of a delay should be introduced between steps of the
135               animation.  Default 10000, or 1/100th second.
136
137       -fps    Display the current frame rate, CPU load, and polygon count.
138
139       The following four options are mutually exclusive.  They determine  how
140       the Klein bottle is displayed.
141
142       -mode random
143               Display the Klein bottle in a random display mode (default).
144
145       -mode wireframe (Shortcut: -wireframe)
146               Display the Klein bottle as a wireframe mesh.
147
148       -mode surface (Shortcut: -surface)
149               Display the Klein bottle as a solid surface.
150
151       -mode transparent (Shortcut: -transparent)
152               Display the Klein bottle as a transparent surface.
153
154       The  following four options are mutually exclusive.  They determine the
155       appearance of the Klein bottle.
156
157       -appearance random
158               Display the Klein bottle with a random appearance (default).
159
160       -appearance solid (Shortcut: -solid)
161               Display the Klein bottle as a solid object.
162
163       -appearance distance-bands (Shortcut: -distance-bands)
164               Display the Klein bottle  as  see-through  bands  that  lie  at
165               increasing distances from the origin (see above for an explana‐
166               tion).
167
168       -appearance direction-bands (Shortcut: -direction-bands)
169               Display the Klein bottle  as  see-through  bands  that  lie  at
170               increasing  angles with respect to the origin (see above for an
171               explanation).
172
173       The following five options are mutually exclusive.  They determine  how
174       to color the Klein bottle.
175
176       -colors random
177               Display the Klein bottle with a random color scheme (default).
178
179       -colors onesided (Shortcut: -onesided-colors)
180               Display the Klein bottle with a single color.
181
182       -colors twosided (Shortcut: -twosided-colors)
183               Display  the  Klein  bottle  with  two colors: one color on one
184               "side" and the complementary color on the "other side."
185
186       -colors distance (Shortcut: -distance-colors)
187               Display the Klein  bottle  with  fully  saturated  colors  that
188               depend on the distance of the points on the projective plane to
189               the origin (see above for an explanation).  If the Klein bottle
190               is  displayed  as  distance  bands, each band will be displayed
191               with a different color.
192
193       -colors direction (Shortcut: -direction-colors)
194               Display the Klein  bottle  with  fully  saturated  colors  that
195               depend  on the angle of the points on the projective plane with
196               respect to the origin (see above for an explanation).   If  the
197               Klein bottle is displayed as direction bands, each band will be
198               displayed with a different color.
199
200       The following options determine whether the colors with which the Klein
201       bottle are displayed are static or are changing dynamically.
202
203       -change-colors
204               Change  the  colors  with  which  the Klein bottle is displayed
205               dynamically (default).
206
207       -no-change-colors
208               Use static colors to display the Klein bottle.
209
210       The following three options are mutually exclusive.  They determine how
211       to view the Klein bottle.
212
213       -view-mode random
214               View  the  Klein  bottle  in a random view mode (default).  The
215               walking mode will be randomly selected in approximately 10%  of
216               the cases.
217
218       -view-mode turn (Shortcut: -turn)
219               View the Klein bottle while it turns in 3d.
220
221       -view-mode walk (Shortcut: -walk)
222               View the Klein bottle as if walking on its surface.
223
224       The following options determine whether the surface is being deformed.
225
226       -deform Deform the surface smoothly between the Etruscan Venus surface,
227               the Roman surface, the Boy surface surface, and the Ida surface
228               (default).
229
230       -no-deform
231               Don't deform the surface.
232
233       The following option determines the deformation speed.
234
235       -deformation-speed float
236               The  deformation  speed is measured in percent of some sensible
237               maximum speed (default: 10.0).
238
239       The following options determine the initial deformation of the surface.
240       As described above, this is mostly useful if -no-deform is specified.
241
242       -initial-deformation float
243               The  initial deformation is specified as a number between 0 and
244               4000.  A value of 0 corresponds to the Etruscan Venus  surface,
245               a  value  of  1000 to the Roman surface, a value of 2000 to the
246               Boy surface, and a value of  3000  to  the  Ida  surface.   The
247               default value is 0.
248
249       -etruscan-venus
250               This is a shortcut for -initial-deformation 0.
251
252       -roman  This is a shortcut for -initial-deformation 1000.
253
254       -boy    This is a shortcut for -initial-deformation 2000.
255
256       -ida    This is a shortcut for -initial-deformation 3000.
257
258       The  following options determine whether orientation marks are shown on
259       the Klein bottle.
260
261       -orientation-marks
262               Display orientation marks on the Klein bottle.
263
264       -no-orientation-marks
265               Don't display orientation marks on the Klein bottle (default).
266
267       The following three options are mutually exclusive.  They determine how
268       the Klain bottle is projected from 3d to 2d (i.e., to the screen).
269
270       -projection random
271               Project  the  Klein bottle from 3d to 2d using a random projec‐
272               tion mode (default).
273
274       -projection perspective (Shortcut: -perspective)
275               Project the Klein bottle from 3d to 2d using a perspective pro‐
276               jection.
277
278       -projection orthographic (Shortcut: -orthographic)
279               Project  the  Klein  bottle from 3d to 2d using an orthographic
280               projection.
281
282       The following three options determine the rotation speed of  the  Klein
283       bottle  around the three possible axes.  The rotation speed is measured
284       in degrees per frame.  The speeds should be  set  to  relatively  small
285       values,  e.g.,  less than 4 in magnitude.  In walk mode, all speeds are
286       ignored.
287
288       -speed-x float
289               Rotation speed around the x axis (default: 1.1).
290
291       -speed-y float
292               Rotation speed around the y axis (default: 1.3).
293
294       -speed-z float
295               Rotation speed around the z axis (default: 1.5).
296
297       The following two options determine the walking speed and direction.
298
299       -walk-direction float
300               The walking direction is measured as an angle in degrees in the
301               2d  square  that  forms the coordinate system of the surface of
302               the Klein bottle (default: 83.0).  A value of 0  or  180  means
303               that  the  walk is along a circle at a randomly chosen distance
304               from the origin (parallel to a distance band).  A value  of  90
305               or  270 means that the walk is directly along a direction band.
306               Any other value results in a curved path along the surface.  As
307               noted above, walking is performed only on the Ida surface.
308
309       -walk-speed float
310               The walking speed is measured in percent of some sensible maxi‐
311               mum speed (default: 20.0).
312

INTERACTION

314       If you run this program in standalone mode in its turn  mode,  you  can
315       rotate  the  Klein bottle by dragging the mouse while pressing the left
316       mouse button.  This rotates the Klein bottle in  3d.   To  examine  the
317       Klein  bottle at your leisure, it is best to set all speeds to 0.  Oth‐
318       erwise, the Klein bottle will rotate while the left mouse button is not
319       pressed.  This kind of interaction is not available in the walk mode.
320

ENVIRONMENT

322       DISPLAY to get the default host and display number.
323
324       XENVIRONMENT
325               to  get  the  name of a resource file that overrides the global
326               resources stored in the RESOURCE_MANAGER property.
327

SEE ALSO

329       X(1), xscreensaver(1)
330
332       Copyright © 2019-2020 by Carsten Steger.  Permission to use, copy, mod‐
333       ify,  distribute,  and sell this software and its documentation for any
334       purpose is hereby granted without fee, provided that  the  above  copy‐
335       right  notice  appear in all copies and that both that copyright notice
336       and this permission notice appear in supporting documentation.  No rep‐
337       resentations  are  made  about the suitability of this software for any
338       purpose.  It is provided "as is" without express or implied warranty.
339

AUTHOR

341       Carsten Steger <carsten@mirsanmir.org>, 05-jan-2020.
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345X Version 11               5.44-2.fc32 (16-Apr-2020)         etruscanvenus(6x)
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