Ubuntu Manpage: klein – Draws a 4d Klein bottle.

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NAME

       klein - Draws a 4d Klein bottle.

SYNOPSIS

       klein [-display host:display.screen] [-install] [-visual visual] [-window] [-root] [-delay
       usecs] [-fps] [-klein-bottle bottle-name] [-figure-8] [-squeezed-torus]  [-lawson]  [-mode
       display-mode]  [-wireframe]  [-surface]  [-transparent]  [-appearance appearance] [-solid]
       [-bands] [-colors color-scheme] [-twosided]  [-rainbow]  [-depth]  [-view-mode  view-mode]
       [-walk]  [-turn] [-walk-turn] [-orientation-marks] [-projection-3d mode] [-perspective-3d]
       [-orthographic-3d] [-projection-4d mode] [-perspective-4d]  [-orthographic-4d]  [-speed-wx
       float]  [-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz float] [-speed-yz
       float] [-walk-direction float] [-walk-speed float]

DESCRIPTION

       The klein program shows three different Klein bottles in 4d: the  figure-8  Klein  bottle,
       the  squeezed  torus  Klein bottle, or the Lawson Klein bottle.  You can walk on the Klein
       bottle, see it turn in 4d, or walk on it while it turns in 4d.  The figure-8 Klein  bottle
       is  well known in its 3d form.  The 4d form used in this program is an extension of the 3d
       form to 4d that does not intersect itself in 4d (which can be seen  in  the  depth  colors
       mode).  The squeezed torus Klein bottle also does not intersect itself in 4d (which can be
       seen in the depth colors mode).   The  Lawson  Klein  bottle,  on  the  other  hand,  does
       intersect  itself in 4d.  Its primary use is that it has a nice appearance for walking and
       for turning in 3d.  The Klein bottle is a non-orientable surface.  To make this  apparent,
       the two-sided color mode can be used.  Alternatively, orientation markers (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 because the Klein bottle is non-orientable).   The  program  projects  the  4d  Klein
       bottle  to  3d using either a perspective or an orthographic projection.  Which of the two
       alternatives looks more appealing depends on the viewing mode and the Klein  bottle.   For
       example,  the Lawson Klein bottle looks nicest when projected perspectively.  The figure-8
       Klein bottle, on the other hand, looks nicer while walking when projected orthographically
       from  4d.   For  the  squeezed  torus  Klein  bottle,  both  projection modes give equally
       acceptable projections.  The projected Klein bottle can then be projected  to  the  screen
       either  perspectively  or  orthographically.   When  using  the walking modes, perspective
       projection to the screen should be used.  There are three  display  modes  for  the  Klein
       bottle: mesh (wireframe), solid, or transparent.  Furthermore, the appearance of the Klein
       bottle can be as a solid object or as a set of see-through  bands.   Finally,  the  colors
       with  with  the  Klein bottle is drawn can be set to two-sided, rainbow, or depth.  In the
       first case, the Klein bottle is drawn with red on one  "side"  and  green  on  the  "other
       side".   Of  course,  the  Klein  bottle only has one side, so the color jumps from red to
       green along a curve on the surface of the Klein bottle.  This mode enables you to see that
       the  Klein  bottle  is  non-orientable.  The second mode draws the Klein bottle with fully
       saturated rainbow colors.  This gives a very nice  effect  when  combined  with  the  see-
       through  bands mode or with the orientation markers drawn.  The third mode draws the Klein
       bottle with colors that are chosen according to the 4d "depth" of the points.   This  mode
       enables  you  to  see  that the figure-8 and squeezed torus Klein bottles do not intersect
       themselves in 4d, while the Lawson Klein bottle does intersect itself.  The rotation speed
       for  each  of the six planes around which the Klein bottle rotates can be chosen.  For the
       walk-and-turn mode, only the rotation speeds around the true 4d planes are used  (the  xy,
       xz,  and  yz  planes).   Furthermore, in the walking modes the walking direction in the 2d
       base square of the Klein bottle and the walking speed can  be  chosen.   This  program  is
       somewhat  inspired  by  Thomas  Banchoff's  book  "Beyond  the  Third Dimension: Geometry,
       Computer Graphics, and Higher Dimensions", Scientific American Library, 1990.

OPTIONS

       klein 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 three options are mutually exclusive.  They determine which Klein bottle  is
       displayed.

       -klein-bottle random
               Display a random Klein bottle (default).

       -klein-bottle figure-8 (Shortcut: -figure-8)
               Display the figure-8 Klein bottle.

       -klein-bottle squeezed-torus (Shortcut: -squeezed-torus)
               Display the squeezed torus Klein bottle.

       -klein-bottle lawson (Shortcut: -lawson)
               Display the Lawson Klein bottle.

       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 three 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 bands (Shortcut: -bands)
               Display the Klein bottle as see-through bands.

       The  following four 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 twosided (Shortcut: -twosided)
               Display the Klein bottle with two colors: red on  one  "side"  and  green  on  the
               "other side".

       -colors rainbow (Shortcut: -rainbow)
               Display the Klein bottle with fully saturated rainbow colors.  If the Klein bottle
               is displayed as see-through bands, each band will be displayed  with  a  different
               color.

       -colors depth (Shortcut: -depth)
               Display  the  Klein  bottle  with colors chosen depending on the 4d "depth" of the
               points.

       The following four 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).

       -view-mode walk (Shortcut: -walk)
               View the Klein bottle as if walking on its surface.

       -view-mode turn (Shortcut: -turn)
               View the Klein bottle while it turns in 4d.

       -view-mode walk-turn (Shortcut: -walk-turn)
               View  the  Klein  bottle  as  if  walking on its surface.  Additionally, the Klein
               bottle turns around the true 4d planes (the xy, xz, and yz planes).

       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  Klein  bottle
       is projected from 3d to 2d (i.e., to the screen).

       -projection-3d random
               Project the Klein bottle from 3d to 2d using a random projection mode (default).

       -projection-3d perspective (Shortcut: -perspective-3d)
               Project the Klein bottle from 3d to 2d using a perspective projection.

       -projection-3d orthographic (Shortcut: -orthographic-3d)
               Project the Klein bottle from 3d to 2d using an orthographic projection.

       The  following  three options are mutually exclusive.  They determine how the Klein bottle
       is projected from 4d to 3d.

       -projection-4d random
               Project the Klein bottle from 4d to 3d using a random projection mode (default).

       -projection-4d perspective (Shortcut: -perspective-4d)
               Project the Klein bottle from 4d to 3d using a perspective projection.

       -projection-4d orthographic (Shortcut: -orthographic-4d)
               Project the Klein bottle from 4d to 3d using an orthographic projection.

       The following six options determine the rotation speed of the Klein bottle around the  six
       possible  hyperplanes.   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.  In walk-and-turn mode, the 3d rotation speeds are ignored (i.e.,
       the wx, wy, and wz speeds).  In walk-and-turn mode, smaller speeds must be  used  than  in
       the  turn  mode  to  achieve  a  nice visualization.  Therefore, in walk-and-turn mode the
       speeds you have selected are divided by 5 internally.

       -speed-wx float
               Rotation speed around the wx plane (default: 1.1).

       -speed-wy float
               Rotation speed around the wy plane (default: 1.3).

       -speed-wz float
               Rotation speed around the wz plane (default: 1.5).

       -speed-xy float
               Rotation speed around the xy plane (default: 1.7).

       -speed-xz float
               Rotation speed around the xz plane (default: 1.9).

       -speed-yz float
               Rotation speed around the yz plane (default: 2.1).

       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: 7.0).

       -walk-speed float
               The  walking speed is measured in percent of some sensible maximum 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, i.e., around the wx, wy, and wz planes.  If you press the  shift  key  while
       dragging  the  mouse with the left button pressed the Klein bottle is rotated in 4D, i.e.,
       around the xy, xz, and yz planes.  To examine the Klein bottle at your leisure, it is best
       to  set  all  speeds  to  0.  Otherwise, the Klein bottle will rotate while the left mouse
       button is not pressed.  This kind of interaction is not available in the two walk modes.

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

COPYRIGHT

       Copyright © 2005-2014 by Carsten Steger.  Permission to use, copy, modify, distribute, and
       sell this software and its documentation for any purpose is hereby  granted  without  fee,
       provided that the above copyright notice appear in all copies and that both that copyright
       notice and this permission notice appear in supporting documentation.  No  representations
       are  made  about the suitability of this software for any purpose.  It is provided "as is"
       without express or implied warranty.

AUTHOR

       Carsten Steger <[email protected]>, 03-oct-2014.

Provided by: xscreensaver-gl-extra_5.34-2ubuntu1_amd64