--- /dev/null
+.TH XScreenSaver 1 "" "X Version 11"
+.SH NAME
+romanboy - Draws a 3d immersion of the real projective plane that
+smoothly deforms between the Roman surface and the Boy surface.
+.SH SYNOPSIS
+.B romanboy
+[\-display \fIhost:display.screen\fP]
+[\-install]
+[\-visual \fIvisual\fP]
+[\-window]
+[\-root]
+[\-delay \fIusecs\fP]
+[\-fps]
+[\-mode \fIdisplay-mode\fP]
+[\-wireframe]
+[\-surface]
+[\-transparent]
+[\-appearance \fIappearance\fP]
+[\-solid]
+[\-distance-bands]
+[\-direction-bands]
+[\-colors \fIcolor-scheme\fP]
+[\-twosided-colors]
+[\-distance-colors]
+[\-direction-colors]
+[\-view-mode \fIview-mode\fP]
+[\-walk]
+[\-turn]
+[\-no-deform]
+[\-deformation-speed \fIfloat\fP]
+[\-initial-deformation \fIfloat\fP]
+[\-roman]
+[\-boy]
+[\-surface-order \fInumber\fP]
+[\-orientation-marks]
+[\-projection \fImode\fP]
+[\-perspective]
+[\-orthographic]
+[\-speed-x \fIfloat\fP]
+[\-speed-y \fIfloat\fP]
+[\-speed-z \fIfloat\fP]
+[\-walk-direction \fIfloat\fP]
+[\-walk-speed \fIfloat\fP]
+.SH DESCRIPTION
+The \fIromanboy\fP 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 deformation (homotopy) between these two famous immersions of
+the real projective plane was constructed by François Apéry.
+.PP
+The real projective plane 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 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).
+.PP
+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
+singled 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 circle. Points on the line at infinity are also used
+to model directions in projective geometry. The origin can be
+visualized in different manners. When using distance colors, the
+origin is the point that is displayed 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 orientation 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 magenta. 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.
+.PP
+Note that when the projective plane is displayed with bands, the
+orientation 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 remaining bands. This choice, however, also implies that the band
+at infinity 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.
+.PP
+The immersed projective plane can be projected to the screen either
+perspectively or orthographically. When using the walking modes,
+perspective projection to the screen will be used.
+.PP
+There are three display modes for the projective plane: mesh
+(wireframe), solid, or transparent. Furthermore, the appearance of
+the projective 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 increasing distances from the origin, or direction bands, i.e.,
+bands that lie at increasing angles with respect to the origin.
+.PP
+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.
+.PP
+Finally, the colors with with the projective plane is drawn can be set
+to two-sided, distance, or direction. In two-sided mode, the
+projective 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 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 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 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 projective plane is displayed as direction bands, each band
+will be displayed with a different color.
+.PP
+The rotation speed for each of the three coordinate axes around which
+the projective plane rotates can be chosen.
+.PP
+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
+projective 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.
+.PP
+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 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.
+.PP
+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
+topological 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).
+.PP
+This program is inspired by François Apéry's book "Models of the Real
+Projective Plane", Vieweg, 1987.
+.SH OPTIONS
+.I romanboy
+accepts the following options:
+.TP 8
+.B \-window
+Draw on a newly-created window. This is the default.
+.TP 8
+.B \-root
+Draw on the root window.
+.TP 8
+.B \-install
+Install a private colormap for the window.
+.TP 8
+.B \-visual \fIvisual\fP
+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.
+.TP 8
+.B \-delay \fImicroseconds\fP
+How much of a delay should be introduced between steps of the
+animation. Default 10000, or 1/100th second.
+.TP 8
+.B \-fps
+Display the current frame rate, CPU load, and polygon count.
+.PP
+The following four options are mutually exclusive. They determine how
+the projective plane is displayed.
+.TP 8
+.B \-mode random
+Display the projective plane in a random display mode (default).
+.TP 8
+.B \-mode wireframe \fP(Shortcut: \fB\-wireframe\fP)
+Display the projective plane as a wireframe mesh.
+.TP 8
+.B \-mode surface \fP(Shortcut: \fB\-surface\fP)
+Display the projective plane as a solid surface.
+.TP 8
+.B \-mode transparent \fP(Shortcut: \fB\-transparent\fP)
+Display the projective plane as a transparent surface.
+.PP
+The following four options are mutually exclusive. They determine the
+appearance of the projective plane.
+.TP 8
+.B \-appearance random
+Display the projective plane with a random appearance (default).
+.TP 8
+.B \-appearance solid \fP(Shortcut: \fB\-solid\fP)
+Display the projective plane as a solid object.
+.TP 8
+.B \-appearance distance-bands \fP(Shortcut: \fB\-distance-bands\fP)
+Display the projective plane as see-through bands that lie at
+increasing distances from the origin.
+.PP
+.TP 8
+.B \-appearance direction-bands \fP(Shortcut: \fB\-direction-bands\fP)
+Display the projective plane as see-through bands that lie at
+increasing angles with respect to the origin.
+.PP
+The following four options are mutually exclusive. They determine how
+to color the projective plane.
+.TP 8
+.B \-colors random
+Display the projective plane with a random color scheme (default).
+.TP 8
+.B \-colors twosided \fP(Shortcut: \fB\-twosided-colors\fP)
+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 projective plane meet,
+i.e., where the orientation of the projective plane reverses.
+.TP 8
+.B \-colors distance \fP(Shortcut: \fB\-distance-colors\fP)
+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 infinity is displayed in
+magenta. If the projective plane is displayed as distance bands, each
+band will be displayed with a different color.
+.TP 8
+.B \-colors direction \fP(Shortcut: \fB\-direction-colors\fP)
+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 projective plane is displayed as direction bands,
+each band will be displayed with a different color.
+.PP
+The following three options are mutually exclusive. They determine
+how to view the projective plane.
+.TP 8
+.B \-view-mode random
+View the projective plane in a random view mode (default).
+.TP 8
+.B \-view-mode turn \fP(Shortcut: \fB\-turn\fP)
+View the projective plane while it turns in 3d.
+.TP 8
+.B \-view-mode walk \fP(Shortcut: \fB\-walk\fP)
+View the projective plane as if walking on its surface.
+.PP
+The following options determine whether the surface is being deformed.
+.TP 8
+.B \-deform
+Deform the surface smoothly between the Roman and Boy surfaces
+(default).
+.TP 8
+.B \-no-deform
+Don't deform the surface.
+.PP
+The following option determines the deformation speed.
+.TP 8
+.B \-deformation-speed \fIfloat\fP
+The deformation speed is measured in percent of some sensible maximum
+speed (default: 10.0).
+.PP
+The following options determine the initial deformation of the
+surface. As described above, this is mostly useful if
+\fB\-no-deform\fP is specified.
+.TP 8
+.B \-initial-deformation \fIfloat\fP
+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.
+.TP 8
+.B \-roman
+This is a shortcut for \fB\-initial-deformation 0\fP.
+.TP 8
+.B \-boy
+This is a shortcut for \fB\-initial-deformation 1000\fP.
+.PP
+The following option determines the order of the surface to be
+displayed.
+.TP 8
+.B \-surface-order \fInumber\fP
+The surface order can be set to values between 2 and 9 (default: 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.
+.PP
+The following options determine whether orientation marks are shown on
+the projective plane.
+.TP 8
+.B \-orientation-marks
+Display orientation marks on the projective plane.
+.TP 8
+.B \-no-orientation-marks
+Don't display orientation marks on the projective plane (default).
+.PP
+The following three options are mutually exclusive. They determine
+how the projective plane is projected from 3d to 2d (i.e., to the
+screen).
+.TP 8
+.B \-projection random
+Project the projective plane from 3d to 2d using a random projection
+mode (default).
+.TP 8
+.B \-projection perspective \fP(Shortcut: \fB\-perspective\fP)
+Project the projective plane from 3d to 2d using a perspective
+projection.
+.TP 8
+.B \-projection orthographic \fP(Shortcut: \fB\-orthographic\fP)
+Project the projective plane from 3d to 2d using an orthographic
+projection.
+.PP
+The following three options determine the rotation speed of the
+projective plane 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.
+.TP 8
+.B \-speed-x \fIfloat\fP
+Rotation speed around the x axis (default: 1.1).
+.TP 8
+.B \-speed-y \fIfloat\fP
+Rotation speed around the y axis (default: 1.3).
+.TP 8
+.B \-speed-z \fIfloat\fP
+Rotation speed around the z axis (default: 1.5).
+.PP
+The following two options determine the walking speed and direction.
+.TP 8
+.B \-walk-direction \fIfloat\fP
+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 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.
+.TP 8
+.B \-walk-speed \fIfloat\fP
+The walking speed is measured in percent of some sensible maximum
+speed (default: 20.0).
+.SH 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
+examine 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.
+.SH ENVIRONMENT
+.PP
+.TP 8
+.B DISPLAY
+to get the default host and display number.
+.TP 8
+.B XENVIRONMENT
+to get the name of a resource file that overrides the global resources
+stored in the RESOURCE_MANAGER property.
+.SH SEE ALSO
+.BR X (1),
+.BR xscreensaver (1)
+.SH COPYRIGHT
+Copyright \(co 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
+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.
+.SH AUTHOR
+Carsten Steger <carsten@mirsanmir.org>, 03-oct-2014.
projects / xscreensaver / blobdiff