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romanboy(6)		      XScreenSaver manual		   romanboy(6)

NAME
       romanboy	 -  Draws  a  3d  immersion  of	the real projective plane that
       smoothly	deforms	between	the Roman surface and the Boy surface.

SYNOPSIS
       romanboy	[-display  host:display.screen]	 [-install]  [-visual  visual]
       [-window]  [-root]  [-delay  usecs] [-fps] [-mode display-mode] [-wire-
       frame]  [-surface]  [-transparent]  [-appearance	 appearance]  [-solid]
       [-distance-bands] [-direction-bands] [-colors color-scheme] [-twosided-
       colors] [-distance-colors] [-direction-colors]  [-view-mode  view-mode]
       [-walk]	[-turn]	 [-no-deform] [-deformation-speed float] [-initial-de-
       formation float]	[-roman] [-boy]	[-surface-order	number]	[-orientation-
       marks]  [-projection  mode]  [-perspective]  [-orthographic]  [-speed-x
       float]  [-speed-y  float]  [-speed-z  float]  [-walk-direction	float]
       [-walk-speed float]

DESCRIPTION
       The  romanboy program shows a 3d	immersion of the real projective plane
       that smoothly deforms between the Roman surface and  the	 Boy  surface.
       You  can	walk on	the projective plane or	turn in	3d.  The smooth	defor-
       mation (homotopy) between these two famous immersions of	the real  pro-
       jective plane was constructed by	Francois Apery.

       The  real  projective  plane is a non-orientable	surface.  To make this
       apparent, the two-sided color mode can be used.	Alternatively,	orien-
       tation  markers	(curling  arrows) can be drawn as a texture map	on the
       surface of the projective  plane.   While  walking  on  the  projective
       plane,  you  will  notice  that	the  orientation of the	curling	arrows
       changes (which it must because the projective plane is non-orientable).

       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.	The origin can be visualized in	different man-
       ners.  When using distance colors, the origin is	the point that is dis-
       played  as fully	saturated red, which is	easier to see as the center of
       the reddish area	on the projective plane.   Alternatively,  when	 using
       distance	bands, the origin is the center	of the only band that projects
       to a disk.  When	using direction	bands, the origin is the  point	 where
       all  direction  bands  collapse	to a point.  Finally, when orientation
       markers are being displayed, the	origin the the point where all	orien-
       tation  markers	are  compressed	 to a point.  The line at infinity can
       also be visualized in different ways.  When using distance colors,  the
       line  at	 infinity is the line that is displayed	as fully saturated ma-
       genta.  When two-sided colors are used, the line	at  infinity  lies  at
       the points where	the red	and green "sides" of the projective plane meet
       (of course, the real projective plane only has one side,	so this	 is  a
       design  choice  of the visualization).  Alternatively, when orientation
       markers are being displayed, the	line at	infinity is  the  place	 where
       the orientation markers change their orientation.

       Note that when the projective plane is displayed	with bands, the	orien-
       tation markers are placed in the	middle of  the	bands.	 For  distance
       bands,  the  bands are chosen in	such a way that	the band at the	origin
       is only half as wide as the remaining bands, which results  in  a  disk
       being displayed at the origin that has the same diameter	as the remain-
       ing bands.  This	choice,	however, also implies that the band at	infin-
       ity  is half as wide as the other bands.	 Since the projective plane is
       attached	to itself (in a	complicated fashion) at	the line at  infinity,
       effectively  the	 band  at  infinity  is	again as wide as the remaining
       bands.  However,	since the orientation markers  are  displayed  in  the
       middle  of  the bands, this means that only one half of the orientation
       markers will be displayed twice at the line  at	infinity  if  distance
       bands are used.	If direction bands are used or if the projective plane
       is displayed as a solid surface,	the orientation	markers	are  displayed
       fully at	the respective sides of	the line at infinity.

       The  immersed  projective  plane	 can be	projected to the screen	either
       perspectively or	orthographically.  When	using the walking modes,  per-
       spective	projection to the screen will be used.

       There  are  three  display  modes for the projective plane: mesh	(wire-
       frame), solid, or transparent.  Furthermore, the	appearance of the pro-
       jective	plane  can  be	as  a  solid object or as a set	of see-through
       bands.  The bands can be	distance bands,	i.e., bands that  lie  at  in-
       creasing	 distances  from  the  origin, or direction bands, i.e., bands
       that lie	at increasing angles with respect to the origin.

       When the	projective plane is displayed with direction bands,  you  will
       be  able	 to see	that each direction band (modulo the "pinching"	at the
       origin) is a Moebius strip, which also shows that the projective	 plane
       is non-orientable.

       Finally,	 the colors with with the projective plane is drawn can	be set
       to two-sided, distance, or direction.  In two-sided mode,  the  projec-
       tive  plane  is	drawn  with  red on one	"side" and green on the	"other
       side".  As described above, the projective plane	only has one side,  so
       the  color  jumps  from	red to green along the line at infinity.  This
       mode enables you	to see that the	projective  plane  is  non-orientable.
       In  distance  mode,  the	projective plane is displayed with fully satu-
       rated colors that depend	on the distance	of the points on  the  projec-
       tive  plane to the origin.  The origin is displayed in red, the line at
       infinity	is displayed in	magenta.  If the projective plane is displayed
       as  distance bands, each	band will be displayed with a different	color.
       In direction mode, the projective plane is displayed with  fully	 satu-
       rated  colors  that depend on the angle of the points on	the projective
       plane with respect to the origin.  Angles in opposite directions	to the
       origin (e.g., 15	and 205	degrees) are displayed in the same color since
       they are	projectively equivalent.  If the projective plane is displayed
       as direction bands, each	band will be displayed with a different	color.

       The  rotation  speed for	each of	the three coordinate axes around which
       the projective plane rotates can	be chosen.

       Furthermore, in the walking mode	the walking direction in the  2d  base
       square  of  the	projective  plane 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	of the projec-
       tive plane.  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  from  the
       origin  to  the	line  at  infinity  and	back (analogous	to a direction
       band).  Any other value results in a curved path	from the origin	to the
       line at infinity	and back.

       By default, the immersion of the	real projective	plane smoothly deforms
       between the Roman and Boy surfaces.  It is possible to choose the speed
       of the deformation.  Furthermore, it is possible	to switch the deforma-
       tion 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.

       As a final option, it is	possible to display  generalized  versions  of
       the  immersion  discussed above by specifying the order of the surface.
       The default surface order of 3 results in the  immersion	 of  the  real
       projective  described above.  The surface order can be chosen between 2
       and 9.  Odd surface orders result in generalized	immersions of the real
       projective  plane,  while even numbers result in	a immersion of a topo-
       logical sphere (which is	orientable).  The most interesting  even  case
       is  a  surface order of 2, which	results	in an immersion	of the halfway
       model of	Morin's	sphere eversion	(if the	deformation is switched	off).

       This program is inspired	by Francois Apery's book "Models of  the  Real
       Projective Plane", Vieweg, 1987.

OPTIONS
       romanboy	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 projective plane is displayed.

       -mode random
	       Display	the  projective	 plane	in  a random display mode (de-
	       fault).

       -mode wireframe (Shortcut: -wireframe)
	       Display the projective plane as a wireframe mesh.

       -mode surface (Shortcut:	-surface)
	       Display the projective plane as a solid surface.

       -mode transparent (Shortcut: -transparent)
	       Display the projective plane as a transparent surface.

       The following four options are mutually exclusive.  They	determine  the
       appearance of the projective plane.

       -appearance random
	       Display	the  projective	 plane	with  a	random appearance (de-
	       fault).

       -appearance solid (Shortcut: -solid)
	       Display the projective plane as a solid object.

       -appearance distance-bands (Shortcut: -distance-bands)
	       Display the projective plane as see-through bands that  lie  at
	       increasing distances from the origin.

       -appearance direction-bands (Shortcut: -direction-bands)
	       Display	the  projective	plane as see-through bands that	lie at
	       increasing angles with respect to the origin.

       The following four options are mutually exclusive.  They	determine  how
       to color	the projective plane.

       -colors random
	       Display	the  projective	 plane with a random color scheme (de-
	       fault).

       -colors twosided	(Shortcut: -twosided-colors)
	       Display the projective plane with two colors: red on one	"side"
	       and  green on the "other	side."	Note that the line at infinity
	       lies at the points where	the red	and green "sides" of the  pro-
	       jective	plane meet, i.e., where	the orientation	of the projec-
	       tive plane reverses.

       -colors distance	(Shortcut: -distance-colors)
	       Display the projective plane with fully saturated  colors  that
	       depend on the distance of the points on the projective plane to
	       the origin.  The	origin is displayed in red, the	line at	infin-
	       ity  is	displayed in magenta.  If the projective plane is dis-
	       played as distance bands, each band will	be  displayed  with  a
	       different color.

       -colors direction (Shortcut: -direction-colors)
	       Display	the  projective	plane with fully saturated colors that
	       depend on the angle of the points on the	projective plane  with
	       respect	to  the	 origin.  Angles in opposite directions	to the
	       origin (e.g., 15	and 205	degrees) are  displayed	 in  the  same
	       color  since  they are projectively equivalent.	If the projec-
	       tive plane is displayed as direction bands, each	band  will  be
	       displayed with a	different color.

       The following three options are mutually	exclusive.  They determine how
       to view the projective plane.

       -view-mode random
	       View the	projective plane in a random view mode (default).

       -view-mode turn (Shortcut: -turn)
	       View the	projective plane while it turns	in 3d.

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

       The following options determine whether the surface is being deformed.

       -deform Deform the surface smoothly between the Roman and Boy  surfaces
	       (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
	       1000.  A	value of 0 corresponds to the Roman surface,  while  a
	       value  of  1000	corresponds  to	 the Boy surface.  The default
	       value is	1000.

       -roman  This is a shortcut for -initial-deformation 0.

       -boy    This is a shortcut for -initial-deformation 1000.

       The following option determines the order of the	 surface  to  be  dis-
       played.

       -surface-order number
	       The  surface  order  can	 be set	to values between 2 and	9 (de-
	       fault: 3).  As described	above, odd surface  orders  result  in
	       generalized immersions of the real projective plane, while even
	       numbers result in a immersion of	a topological sphere.

       The following options determine whether orientation marks are shown  on
       the projective plane.

       -orientation-marks
	       Display orientation marks on the	projective plane.

       -no-orientation-marks
	       Don't  display  orientation  marks on the projective plane (de-
	       fault).

       The following three options are mutually	exclusive.  They determine how
       the projective plane is projected from 3d to 2d (i.e., to the screen).

       -projection random
	       Project	the projective plane from 3d to	2d using a random pro-
	       jection mode (default).

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

       -projection orthographic	(Shortcut: -orthographic)
	       Project	the  projective	 plane	from  3d to 2d using an	ortho-
	       graphic projection.

       The following three options determine the rotation speed	of the projec-
       tive  plane around the three possible axes.  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.

       -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 projective plane (default: 83.0).  A	 value	of  0  or  180
	       means that the walk is along a circle at	a randomly chosen dis-
	       tance from the origin (parallel to a distance band).   A	 value
	       of 90 or	270 means that the walk	is directly from the origin to
	       the line	at infinity and	back (analogous	to a direction	band).
	       Any other value results in a curved path	from the origin	to the
	       line at infinity	and back.

       -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 projective plane by dragging the mouse  while	 pressing  the
       left  mouse button.  This rotates the projective	plane in 3d.  To exam-
       ine the projective plane	at your	leisure, it is best to set all	speeds
       to 0.  Otherwise, the projective	plane 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 (C) 2013-2014 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 no-
       tice 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-oct-2014.

X Version 11		      5.36 (10-Oct-2016)		   romanboy(6)

NAME | SYNOPSIS | DESCRIPTION | OPTIONS | INTERACTION | ENVIRONMENT | SEE ALSO | COPYRIGHT | AUTHOR

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