X-Git-Url: http://git.hungrycats.org/cgi-bin/gitweb.cgi?p=xscreensaver;a=blobdiff_plain;f=hacks%2Fglx%2Fhypertorus.man;fp=hacks%2Fglx%2Fhypertorus.man;h=8c7075f7821c48a6030d8fa112cb82489b9e66e0;hp=0000000000000000000000000000000000000000;hb=ffcd2e7e3da122dbba5c4188e05d3a63d0ede26e;hpb=019de959b265701cd0c3fccbb61f2b69f06bf9ee diff --git a/hacks/glx/hypertorus.man b/hacks/glx/hypertorus.man new file mode 100644 index 00000000..8c7075f7 --- /dev/null +++ b/hacks/glx/hypertorus.man @@ -0,0 +1,188 @@ +.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}] +[\-twosided] +[\-colorwheel] +[\-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. +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 either +two-sided or to a color wheel. In the first case, the torus is drawn +with red on the outside and green on the inside. This mode enables +you to see that the torus turns inside-out as it rotates in 4d. The +second mode draws the torus with a fully saturated color wheel. This +gives a very nice effect when combined with the see-through bands or +see-through spirals mode. The rotation speed for each of the six +planes around which the torus rotates can be chosen. This program is +very much 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 two options are mutually exclusive. They determine how +to color the torus. +.TP 8 +.B \-twosided +Display the torus with two colors: red on the outside and green on +the inside. +.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 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 2003-2005 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 , 28-sep-2005.