etruscanvenus(6x) XScreenSaver manual etruscanvenus(6x)
NAME
etruscanvenus - Draws a 3d immersion of a Klein bottle that smoothly
deforms between the Etruscan Venus surface, the Roman surface, the Boy
surface surface, and the Ida surface.
SYNOPSIS
etruscanvenus [-display host:display.screen] [-install] [-visual vis-
ual] [-window] [-root] [-delay usecs] [-fps] [-mode display-mode]
[-wireframe] [-surface] [-transparent] [-appearance appearance]
[-solid] [-distance-bands] [-direction-bands] [-colors color-scheme]
[-onesided-colors] [-twosided-colors] [-distance-colors] [-direction-
colors] [-no-change-colors] [-view-mode view-mode] [-walk] [-turn]
[-no-deform] [-deformation-speed float] [-initial-deformation float]
[-etruscan-venus] [-roman] [-boy] [-ida] [-orientation-marks] [-projec-
tion mode] [-perspective] [-orthographic] [-speed-x float] [-speed-y
float] [-speed-z float] [-walk-direction float] [-walk-speed float]
DESCRIPTION
The etruscanvenus program shows a 3d immersion of a Klein bottle that
smoothly deforms between the Etruscan Venus surface, the Roman surface,
the Boy surface, and the Ida surface. You can walk on the Klein bottle
or turn it in 3d. Topologically, all surfaces are Klein bottles, even
the Roman and Boy surfaces, which are doubly covered and therefore ap-
pear to be an immersed real projective plane. The smooth deformation
between these surfaces was constructed by George K. Francis.
The Klein bottle is a non-orientable surface. To make this apparent,
the two-sided color mode can be used. Alternatively, orientation mark-
ers (curling arrows) can be drawn as a texture map on the surface of
the Klein bottle. While walking on the Klein bottle, you will notice
that the orientation of the curling arrows changes (which it must be-
cause the Klein bottle is non-orientable). Since all the surfaces ex-
cept the Ida surface have points where the surface normal is not well
defined for some points, walking is only performed on the Ida surface.
As mentioned above, the Roman and Boy surfaces are doubly covered and
therefore appear to be an immersed real projective plane. Since some
of the parameter names are based on this interpretation of the surface,
the geometry of the real projective plane will be briefly disussed.
The real projective plane is a model for the projective geometry in 2d
space. One point can be singled out as the origin. A line can be sin-
gled out as the line at infinity, i.e., a line that lies at an infinite
distance to the origin. The line at infinity is topologically a cir-
cle. Points on the line at infinity are also used to model directions
in projective geometry. Direction and distance bands refer to this in-
terpretation of the surface. If direction bands are used, the bands
extend from the origin of the projective plane in different directions
to the line at infinity and back to the origin. If distance bands are
used, the bands lie at constant distances to the origin. The same in-
terpretation is used for distance and direction colors. Although there
is no conceptually equivalent geometric interpretation for the two
Klein bottle surfaces (the Etruscan Venus and Ida surfaces), the smooth
deformation between the surfaces results in a natural extension of
these concepts to the Klein bottle surfaces.
The immersed surfaces can be projected to the screen either perspec-
tively or orthographically. When using the walking mode, perspective
projection to the screen will be used.
There are three display modes for the Klein bottle: mesh (wireframe),
solid, or transparent. Furthermore, the appearance of the surface can
be as a solid object or as a set of see-through bands. The bands can
be distance bands or direction bands, as explained above.
The colors with with the surface is drawn can be set to one-sided, two-
sided, distance, or direction. In one-sided mode, the surface is drawn
with the same color on both sides of the underlying triangles. In two-
sided mode, the surface is drawn with one color on one side of the un-
derlying triangles and the complementary color on the other side.
Since the surface actually only has one side, the color jumps from red
to green along a line on the surface. This mode enables you to see
that the surface is non-orientable. In distance mode, the surface is
displayed with fully saturated colors that depend on the distance of
the points on the projective plane to the origin, as described above.
If the surface is displayed as distance bands, each band will be dis-
played with a different color. In direction mode, the surface is dis-
played with fully saturated colors that depend on the angle of the
points on the projective plane with respect to the origin (see above
for an explanation). If the surface is displayed as direction bands,
each band will be displayed with a different color. The colors used to
color the surface can either be static or can be changed dynamically.
The rotation speed for each of the three coordinate axes around which
the Klein bottle rotates can be chosen.
Furthermore, in the walking mode the walking direction in the 2d base
square of the surface and the walking speed can be chosen. The walking
direction is measured as an angle in degrees in the 2d square that
forms the coordinate system of the surface. A value of 0 or 180 means
that the walk is along a circle at a randomly chosen distance from the
origin (parallel to a distance band). A value of 90 or 270 means that
the walk is directly along a direction band. Any other value results
in a curved path along the surface. As noted above, walking is per-
formed only on the Ida surface.
By default, the immersion of the Klein bottle smoothly deforms between
the Etruscan Venus surface, the Roman surface, the Boy surface, and the
Ida surface. It is possible to choose the speed of the deformation.
Furthermore, it is possible to switch the deformation off. It is also
possible to determine the initial deformation of the immersion. This
is mostly useful if the deformation is switched off, in which case it
will determine the appearance of the surface. A value of 0 corresponds
to the Etruscan Venus surface, a value of 1000 to the Roman surface, a
value of 2000 to the Boy surface, and a value of 3000 to the Ida sur-
face.
This program is inspired by George K. Francis's book "A Topological
Picturebook", Springer, 1987, by George K. Francis's paper "The Etr-
uscan Venus" in P. Concus, R. Finn, and D. A. Hoffman: "Geometric
Analysis and Computer Graphics", Springer, 1991, and by a video enti-
tled "The Etruscan Venus" by Donna J. Cox, George K. Francis, and Ray-
mond L. Idaszak, presented at SIGGRAPH 1989.
OPTIONS
etruscanvenus accepts the following options:
-window Draw on a newly-created window. This is the default.
-root Draw on the root window.
-install
Install a private colormap for the window.
-visual visual
Specify which visual to use. Legal values are the name of a
visual class, or the id number (decimal or hex) of a specific
visual.
-delay microseconds
How much of a delay should be introduced between steps of the
animation. Default 10000, or 1/100th second.
-fps Display the current frame rate, CPU load, and polygon count.
The following four options are mutually exclusive. They determine how
the Klein bottle is displayed.
-mode random
Display the Klein bottle in a random display mode (default).
-mode wireframe (Shortcut: -wireframe)
Display the Klein bottle as a wireframe mesh.
-mode surface (Shortcut: -surface)
Display the Klein bottle as a solid surface.
-mode transparent (Shortcut: -transparent)
Display the Klein bottle as a transparent surface.
The following four options are mutually exclusive. They determine the
appearance of the Klein bottle.
-appearance random
Display the Klein bottle with a random appearance (default).
-appearance solid (Shortcut: -solid)
Display the Klein bottle as a solid object.
-appearance distance-bands (Shortcut: -distance-bands)
Display the Klein bottle as see-through bands that lie at in-
creasing distances from the origin (see above for an explana-
tion).
-appearance direction-bands (Shortcut: -direction-bands)
Display the Klein bottle as see-through bands that lie at in-
creasing angles with respect to the origin (see above for an
explanation).
The following five options are mutually exclusive. They determine how
to color the Klein bottle.
-colors random
Display the Klein bottle with a random color scheme (default).
-colors onesided (Shortcut: -onesided-colors)
Display the Klein bottle with a single color.
-colors twosided (Shortcut: -twosided-colors)
Display the Klein bottle with two colors: one color on one
"side" and the complementary color on the "other side."
-colors distance (Shortcut: -distance-colors)
Display the Klein bottle with fully saturated colors that de-
pend on the distance of the points on the projective plane to
the origin (see above for an explanation). If the Klein bottle
is displayed as distance bands, each band will be displayed
with a different color.
-colors direction (Shortcut: -direction-colors)
Display the Klein bottle with fully saturated colors that de-
pend on the angle of the points on the projective plane with
respect to the origin (see above for an explanation). If the
Klein bottle is displayed as direction bands, each band will be
displayed with a different color.
The following options determine whether the colors with which the Klein
bottle are displayed are static or are changing dynamically.
-change-colors
Change the colors with which the Klein bottle is displayed dy-
namically (default).
-no-change-colors
Use static colors to display the Klein bottle.
The following three options are mutually exclusive. They determine how
to view the Klein bottle.
-view-mode random
View the Klein bottle in a random view mode (default). The
walking mode will be randomly selected in approximately 10% of
the cases.
-view-mode turn (Shortcut: -turn)
View the Klein bottle while it turns in 3d.
-view-mode walk (Shortcut: -walk)
View the Klein bottle as if walking on its surface.
The following options determine whether the surface is being deformed.
-deform Deform the surface smoothly between the Etruscan Venus surface,
the Roman surface, the Boy surface surface, and the Ida surface
(default).
-no-deform
Don't deform the surface.
The following option determines the deformation speed.
-deformation-speed float
The deformation speed is measured in percent of some sensible
maximum speed (default: 10.0).
The following options determine the initial deformation of the surface.
As described above, this is mostly useful if -no-deform is specified.
-initial-deformation float
The initial deformation is specified as a number between 0 and
4000. A value of 0 corresponds to the Etruscan Venus surface,
a value of 1000 to the Roman surface, a value of 2000 to the
Boy surface, and a value of 3000 to the Ida surface. The de-
fault value is 0.
-etruscan-venus
This is a shortcut for -initial-deformation 0.
-roman This is a shortcut for -initial-deformation 1000.
-boy This is a shortcut for -initial-deformation 2000.
-ida This is a shortcut for -initial-deformation 3000.
The following options determine whether orientation marks are shown on
the Klein bottle.
-orientation-marks
Display orientation marks on the Klein bottle.
-no-orientation-marks
Don't display orientation marks on the Klein bottle (default).
The following three options are mutually exclusive. They determine how
the Klain bottle is projected from 3d to 2d (i.e., to the screen).
-projection random
Project the Klein bottle from 3d to 2d using a random projec-
tion mode (default).
-projection perspective (Shortcut: -perspective)
Project the Klein bottle from 3d to 2d using a perspective pro-
jection.
-projection orthographic (Shortcut: -orthographic)
Project the Klein bottle from 3d to 2d using an orthographic
projection.
The following three options determine the rotation speed of the Klein
bottle around the three possible axes. The rotation speed is measured
in degrees per frame. The speeds should be set to relatively small
values, e.g., less than 4 in magnitude. In walk mode, all speeds are
ignored.
-speed-x float
Rotation speed around the x axis (default: 1.1).
-speed-y float
Rotation speed around the y axis (default: 1.3).
-speed-z float
Rotation speed around the z axis (default: 1.5).
The following two options determine the walking speed and direction.
-walk-direction float
The walking direction is measured as an angle in degrees in the
2d square that forms the coordinate system of the surface of
the Klein bottle (default: 83.0). A value of 0 or 180 means
that the walk is along a circle at a randomly chosen distance
from the origin (parallel to a distance band). A value of 90
or 270 means that the walk is directly along a direction band.
Any other value results in a curved path along the surface. As
noted above, walking is performed only on the Ida surface.
-walk-speed float
The walking speed is measured in percent of some sensible maxi-
mum speed (default: 20.0).
INTERACTION
If you run this program in standalone mode in its turn mode, you can
rotate the Klein bottle by dragging the mouse while pressing the left
mouse button. This rotates the Klein bottle in 3d. To examine the
Klein bottle at your leisure, it is best to set all speeds to 0. Oth-
erwise, the Klein bottle will rotate while the left mouse button is not
pressed. This kind of interaction is not available in the walk mode.
ENVIRONMENT
DISPLAY to get the default host and display number.
XENVIRONMENT
to get the name of a resource file that overrides the global
resources stored in the RESOURCE_MANAGER property.
SEE ALSO
X(1), xscreensaver(1)
COPYRIGHT
Copyright © 2019-2020 by Carsten Steger. Permission to use, copy, mod-
ify, distribute, and sell this software and its documentation for any
purpose is hereby granted without fee, provided that the above copy-
right notice appear in all copies and that both that copyright notice
and this permission notice appear in supporting documentation. No rep-
resentations are made about the suitability of this software for any
purpose. It is provided "as is" without express or implied warranty.
AUTHOR
Carsten Steger <carsten@mirsanmir.org>, 05-jan-2020.
X Version 11 5.45 (08-Dec-2020) etruscanvenus(6x)
Generated by dwww version 1.14 on Fri Jan 24 06:15:52 CET 2025.