klein(6x)							XScreenSaver manual							 klein(6x)

NAME

       kleinbottle - Draws a 4d Klein bottle.

SYNOPSIS

       kleinbottle  [-display host:display.screen] [-install] [-visual visual] [-window] [-root] [-delay usecs] [-fps] [-klein-bottle bottle-name]
       [-figure-8] [-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 kleinbottle program shows two different Klein bottles in 4d: the figure-8 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 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-ori-
       entable).  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.
       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 col-
       ors 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 Klein bottle does not intersect itself 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  more,
       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  Ban-
       choff's book "Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions", Scientific American Library, 1990.

OPTIONS

       kleinbottle 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 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 mea-
       sured 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

       X(1), xscreensaver(1)

COPYRIGHT

       Copyright (C) 2005-2009 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 <carsten@mirsanmir.org>, 03-aug-2009.

X Version 11							5.15 (28-Sep-2011)							 klein(6x)