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-.TH XScreenSaver 1 "" "X Version 11"
-.SH NAME
-hypertorus \- Draws a hypertorus that rotates in 4d
-.SH SYNOPSIS
-.B hypertorus
-[\-display \fIhost:display.screen\fP]
-[\-install]
-[\-visual \fIvisual\fP]
-[\-window]
-[\-root]
-[\-delay \fIusecs\fP]
-[\-fps]
-[\-wireframe]
-[\-surface]
-[\-transparent]
-[\-solid]
-[\-bands]
-[\-spirals-{1,2,4,8,16}]
-[\-onesided]
-[\-twosided]
-[\-colorwheel]
-[\-change-colors]
-[\-perspective-3d]
-[\-orthographic-3d]
-[\-perspective-4d]
-[\-orthographic-4d]
-[\-speed-wx \fIfloat\fP]
-[\-speed-wy \fIfloat\fP]
-[\-speed-wz \fIfloat\fP]
-[\-speed-xy \fIfloat\fP]
-[\-speed-xz \fIfloat\fP]
-[\-speed-yz \fIfloat\fP]
-.SH DESCRIPTION
-The \fIhypertorus\fP program shows the Clifford torus as it rotates in
-4d.  The Clifford torus is a torus lies on the "surface" of the
-hypersphere in 4d.  The program projects the 4d torus to 3d using
-either a perspective or an orthographic projection.  Of the two
-alternatives, the perspective projection looks much more appealing.
-In orthographic projections the torus degenerates into a doubly
-covered cylinder for some angles.  The projected 3d torus can then be
-projected to the screen either perspectively or orthographically.
-.PP
-There are three display modes for the torus: mesh (wireframe), solid,
-or transparent.  Furthermore, the appearance of the torus can be as a
-solid object or as a set of see-through bands or see-through spirals.
-Finally, the colors with with the torus is drawn can be set to
-one-sided, two-sided, or to a color wheel.  The colors can be static
-or changing dynamically.  In one-sided color mode, the torus is drawn
-with the same color on the inside and the outside.  In two-sided color
-mode, the torus is drawn with red on the outside and green on the
-inside if static colors are used.  If changing colors are used,
-dynamically varying complementary colors are used for the two sides.
-This mode enables you to see that the 3d projection of the torus turns
-inside-out as it rotates in 4d.  The color wheel mode draws the torus
-with a fully saturated color wheel.  If changing colors are used, the
-colors of the color wheel are varying dynamically.  The color wheel
-mode gives a very nice effect when combined with the see-through bands
-or see-through spirals mode.
-.PP
-Finally, the rotation speed for each of the six planes around which
-the torus rotates can be chosen.
-.PP
-This program is inspired by Thomas Banchoff's book "Beyond the Third
-Dimension: Geometry, Computer Graphics, and Higher Dimensions",
-Scientific American Library, 1990.
-.SH OPTIONS
-.I hypertorus
-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 25000, or 1/40th second.
-.PP
-The following three options are mutually exclusive.  They determine
-how the torus is displayed.
-.TP 8
-.B \-wireframe
-Display the torus as a wireframe mesh.
-.TP 8
-.B \-surface
-Display the torus as a solid surface (default).
-.TP 8
-.B \-transparent
-Display the torus as a transparent surface.
-.PP
-The following seven options are mutually exclusive.  They determine the
-appearance of the torus.
-.TP 8
-.B \-solid
-Display the torus as a solid object.
-.TP 8
-.B \-bands
-Display the torus as see-through bands (default).
-.TP 8
-.B \-spirals-1, \-spirals-2, \-spirals-4, \-spirals-8, \-spirals-16
-Display the torus as see-through spirals with the indicated number of
-spirals.
-.PP
-The following three options are mutually exclusive.  They determine
-how to color the torus.
-.TP 8
-.B \-onesided
-Display the torus with a single color.
-.TP 8
-.B \-twosided
-Display the torus with two colors: one color on the outside and the
-complementary on the inside.  For static colors, the colors are red
-and green.
-.TP 8
-.B \-colorwheel
-Display the torus with a fully saturated color wheel (default).  If
-the torus is displayed as see-through bands, each band will be
-displayed with a different color.  Likewise, if the torus is displayed
-as see-through spirals, each spiral will receive a different color.
-.PP
-The following options determine whether the colors with which the
-torus is displayed are static or are changing dynamically.
-.TP 8
-.B \-change-colors
-Change the colors with which the torus is displayed dynamically.
-.TP 8
-.B \-no-change-colors
-Use static colors to display the torus (default).
-.PP
-The following two options are mutually exclusive.  They determine how
-the torus is projected from 3d to 2d (i.e., to the screen).
-.TP 8
-.B \-perspective-3d
-Project the torus from 3d to 2d using a perspective projection
-(default).
-.TP 8
-.B \-orthographic-3d
-Project the torus from 3d to 2d using an orthographic projection.
-.PP
-The following two options are mutually exclusive.  They determine how
-the torus is projected from 4d to 3d.
-.TP 8
-.B \-perspective-4d
-Project the torus from 4d to 3d using a perspective projection
-(default).
-.TP 8
-.B \-orthographic-4d
-Project the torus from 4d to 3d using an orthographic projection.
-.PP
-The following six options determine the rotation speed of the torus
-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.
-.TP 8
-.B \-speed-wx \fIfloat\fP
-Rotation speed around the wx plane (default: 1.1).
-.TP 8
-.B \-speed-wy \fIfloat\fP
-Rotation speed around the wy plane (default: 1.3).
-.TP 8
-.B \-speed-wz \fIfloat\fP
-Rotation speed around the wz plane (default: 1.5).
-.TP 8
-.B \-speed-xy \fIfloat\fP
-Rotation speed around the xy plane (default: 1.7).
-.TP 8
-.B \-speed-xz \fIfloat\fP
-Rotation speed around the xz plane (default: 1.9).
-.TP 8
-.B \-speed-yz \fIfloat\fP
-Rotation speed around the yz plane (default: 2.1).
-.TP 8
-.B \-fps
-Display the current frame rate, CPU load, and polygon count.
-.SH INTERACTION
-If you run this program in standalone mode you can rotate the
-hypertorus by dragging the mouse while pressing the left mouse button.
-This rotates the hypertorus 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 hypertorus is rotated in 4d, i.e., around the
-xy, xz, and yz planes.  To examine the hypertorus at your leisure, it
-is best to set all speeds to 0.  Otherwise, the hypertorus 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 2003-2020 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>, 11-jan-2020.