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-.TH XScreenSaver 1 "" "X Version 11"
-.SH NAME
-sphereeversion - Displays a sphere eversion.
-.SH SYNOPSIS
-.B sphereeversion
-[\-display \fIhost:display.screen\fP]
-[\-install]
-[\-visual \fIvisual\fP]
-[\-window]
-[\-root]
-[\-delay \fIusecs\fP]
-[\-fps]
-[\-mode \fIdisplay-mode\fP]
-[\-surface]
-[\-transparent]
-[\-appearance \fIappearance\fP]
-[\-solid]
-[\-parallel-bands]
-[\-meridian-bands]
-[\-graticule \fImode\fP]
-[\-surface-order \fIorder\fP]
-[\-colors \fIcolor-scheme\fP]
-[\-twosided-colors]
-[\-parallel-colors]
-[\-meridian-colors]
-[\-deformation-speed \fIfloat\fP]
-[\-projection \fImode\fP]
-[\-perspective]
-[\-orthographic]
-[\-speed-x \fIfloat\fP]
-[\-speed-y \fIfloat\fP]
-[\-speed-z \fIfloat\fP]
-.SH DESCRIPTION
-The \fIsphereeversion\fP program shows a sphere eversion, i.e., a
-smooth deformation (homotopy) that turns a sphere inside out.  During
-the eversion, the deformed sphere is allowed to intersect itself
-transversally.  However, no creases or pinch points are allowed to
-occur.
-.PP
-The deformed sphere can be projected to the screen either
-perspectively or orthographically.
-.PP
-There are three display modes for the sphere: solid, transparent, or
-random.  If random mode is selected, the mode is changed each time an
-eversion has been completed.
-.PP
-The appearance of the sphere can be as a solid object, as a set of
-see-through bands, or random.  The bands can be parallel bands or
-meridian bands, i.e., bands that run along the parallels (lines of
-latitude) or bands that run along the meridians (lines of longitude)
-of the sphere.  If random mode is selected, the appearance is changed
-each time an eversion has been completed.
-.PP
-It is also possible to display a graticule (i.e., a coordinate grid
-consisting of parallel and meridian lines) on top of the surface.  The
-graticule mode can be set to on, off, or random.  If random mode is
-selected, the graticule mode is changed each time an eversion has been
-completed.
-.PP
-It is possible to define a surface order of the sphere eversion as
-random or as a value between 2 and 5.  This determines the the
-complexity of the deformation.  For higher surface orders, some
-z-fighting might occur around the central stage of the eversion, which
-might lead to some irregular flickering of the displayed surface if it
-is displayed as a solid object.  For odd surface orders, z-fighting
-will occur very close to the central stage of the eversion since the
-deformed sphere is a doubly covered Boy surface (for surface order 3)
-or a doubly covered generalized Boy surface (for surface order 5) in
-this case.  If you find this distracting, you should set the surface
-order to 2.  If a random surface order is selected, the surface order
-is changed each time an eversion has been completed.
-.PP
-The colors with with the sphere is drawn can be set to two-sided,
-parallel, meridian, or random.  In two-sided mode, the sphere is drawn
-with red on one side and green on the other side.  In parallel mode,
-the sphere is displayed with colors that run from red to cyan on one
-side of the surface and from green to violet on the other side.  The
-colors are aligned with the parallels of the sphere in this mode.  In
-meridian mode, the the sphere is displayed with colors that run from
-red to white to cyan to black and back to red on one side of the
-surface and from green to white to violet to black and back to green
-on the other side.  The colors are aligned with the meridians of the
-sphere in this mode. If random mode is selected, the color scheme is
-changed each time an eversion has been completed.
-.PP
-By default, the sphere is rotated to a new viewing position each time
-an eversion has been completed.  In addition, it is possible to rotate
-the sphere while it is deforming.  The rotation speed for each of the
-three coordinate axes around which the sphere rotates can be chosen
-arbitrarily.  For best effects, however, it is suggested to rotate
-only around the z axis while the sphere is deforming.
-.PP
-This program is inspired by the following paper: Adam Bednorz, Witold
-Bednorz: "Analytic sphere eversion using ruled surfaces", Differential
-Geometry and its Applications 64:59-79, 2019.
-.SH OPTIONS
-.I sphereeversion
-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 three options are mutually exclusive.  They determine
-how the deformed sphere is displayed.
-.TP 8
-.B \-mode random
-Display the sphere in a random display mode (default).
-.TP 8
-.B \-mode surface \fP(Shortcut: \fB\-surface\fP)
-Display the sphere as a solid surface.
-.TP 8
-.B \-mode transparent \fP(Shortcut: \fB\-transparent\fP)
-Display the sphere as a transparent surface.
-.PP
-The following four options are mutually exclusive.  They determine the
-appearance of the deformed sphere.
-.TP 8
-.B \-appearance random
-Display the sphere with a random appearance (default).
-.TP 8
-.B \-appearance solid \fP(Shortcut: \fB\-solid\fP)
-Display the sphere as a solid object.
-.TP 8
-.B \-appearance parallel-bands \fP(Shortcut: \fB\-parallel-bands\fP)
-Display the sphere as see-through bands that lie along the parallels
-of the sphere.
-.TP 8
-.B \-appearance meridian-bands \fP(Shortcut: \fB\-meridian-bands\fP)
-Display the sphere as see-through bands that lie along the meridians
-of the sphere.
-.PP
-The following three options are mutually exclusive.  They determine
-whether a graticule is displayed on top of the sphere.
-.TP 8
-.B \-graticule random
-Randomly choose whether to display a graticule (default).
-.TP 8
-.B \-graticule on
-Display a graticule.
-.TP 8
-.B \-graticule off
-Do not display a graticule.
-.PP
-The following option determines the order of the surface to be
-displayed.
-.TP 8
-.B \-surface-order \fIorder\fP
-The surface order can be set to random or to a value between 2 and 5
-(default: random).  This determines the the complexity of the
-deformation.
-.PP
-The following four options are mutually exclusive.  They determine how
-to color the deformed sphere.
-.TP 8
-.B \-colors random
-Display the sphere with a random color scheme (default).
-.TP 8
-.B \-colors twosided \fP(Shortcut: \fB\-twosided-colors\fP)
-Display the sphere with two colors: red on one side and green on the
-other side.
-.TP 8
-.B \-colors parallel \fP(Shortcut: \fB\-parallel-colors\fP)
-Display the sphere with colors that run from red to cyan on one side
-of the surface and from green to violet on the other side.  The colors
-are aligned with the parallels of the sphere.  If the sphere is
-displayed as parallel bands, each band will be displayed with a
-different color.
-.TP 8
-.B \-colors meridian \fP(Shortcut: \fB\-meridian-colors\fP)
-Display the sphere with colors that run from red to white to cyan to
-black and back to red on one side of the surface and from green to
-white to violet to black and back to green on the other side.  The
-colors are aligned with the meridians of the sphere.  If the sphere is
-displayed as meridian bands, each band will be displayed with a
-different color.
-.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 three options are mutually exclusive.  They determine
-how the deformed sphere is projected from 3d to 2d (i.e., to the
-screen).
-.TP 8
-.B \-projection random
-Project the sphere from 3d to 2d using a random projection mode
-(default).
-.TP 8
-.B \-projection perspective \fP(Shortcut: \fB\-perspective\fP)
-Project the sphere from 3d to 2d using a perspective projection.
-.TP 8
-.B \-projection orthographic \fP(Shortcut: \fB\-orthographic\fP)
-Project the sphere from 3d to 2d using an orthographic projection.
-.PP
-The following three options determine the rotation speed of the
-deformed sphere 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.
-.TP 8
-.B \-speed-x \fIfloat\fP
-Rotation speed around the x axis (default: 0.0).
-.TP 8
-.B \-speed-y \fIfloat\fP
-Rotation speed around the y axis (default: 0.0).
-.TP 8
-.B \-speed-z \fIfloat\fP
-Rotation speed around the z axis (default: 0.0).
-.SH INTERACTION
-If you run this program in standalone mode, you can rotate the
-deformed sphere by dragging the mouse while pressing the left mouse
-button.  This rotates the sphere in 3d.  To examine the deformed
-sphere at your leisure, it is best to set all speeds to 0.  Otherwise,
-the deformed sphere will rotate while the left mouse button is not
-pressed.
-.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 2020 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>, 01-jun-2020.