X-Git-Url: http://git.hungrycats.org/cgi-bin/gitweb.cgi?p=xscreensaver;a=blobdiff_plain;f=hacks%2Fglx%2Fklein.man;h=de4fd4807a4ddbc05852c89a636fe22b38ebb786;hp=c5c52d6c51f7c2712c86856fb129d08a69409c75;hb=f0261d8acab611f3433160e4f07367b870439739;hpb=7b34ef992563d7bcbb64cc5597dc45fa24470b05 diff --git a/hacks/glx/klein.man b/hacks/glx/klein.man index c5c52d6c..de4fd480 100644 --- a/hacks/glx/klein.man +++ b/hacks/glx/klein.man @@ -1,25 +1,98 @@ .TH XScreenSaver 1 "" "X Version 11" .SH NAME -klein - A Klein Bottle (and other parametric surfaces) visualization. +kleinbottle - Draws a 4d Klein bottle. .SH SYNOPSIS -.B klein +.B kleinbottle [\-display \fIhost:display.screen\fP] +[\-install] [\-visual \fIvisual\fP] [\-window] [\-root] -[\-speed \fInumber\fP] -[\-rand] -[\-spin] -[\-wander] +[\-delay \fIusecs\fP] [\-fps] +[\-klein-bottle \fIbottle-name\fP] +[-figure-8] +[-lawson] +[\-mode \fIdisplay-mode\fP] +[\-wireframe] +[\-surface] +[\-transparent] +[\-appearance \fIappearance\fP] +[\-solid] +[\-bands] +[\-colors \fIcolor-scheme\fP] +[\-twosided] +[\-rainbow] +[\-depth] +[\-view-mode \fIview-mode\fP] +[\-walk] +[\-turn] +[\-walk-turn] +[\-orientation-marks] +[\-projection-3d \fImode\fP] +[\-perspective-3d] +[\-orthographic-3d] +[\-projection-4d \fImode\fP] +[\-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] +[\-walk-direction \fIfloat\fP] +[\-walk-speed \fIfloat\fP] .SH DESCRIPTION -This draws a three dimensional visualization of a Klein Bottle parametric -surface (the three dimensional equivalent of the Moebious strip). +The \fIkleinbottle\fP program shows two different Klein bottles in 4d: +the figure-8 Klein bottle or the Lawson Klein bottle. You can walk on +the Klein bottle, see it turn in 4d, or walk on it while it turns in +4d. The figure-8 Klein bottle is well known in its 3d form. The 4d +form used in this program is an extension of the 3d form to 4d that +does not intersect itself in 4d (which can be seen in the depth colors +mode). The Lawson Klein bottle, on the other hand, does intersect +itself in 4d. Its primary use is that it has a nice appearance for +walking and for turning in 3d. The Klein bottle 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 Klein bottle. While walking on the +Klein bottle, you will notice that the orientation of the curling +arrows changes (which it must because the Klein bottle is +non-orientable). The program projects the 4d Klein bottle to 3d using +either a perspective or an orthographic projection. Which of the two +alternatives looks more appealing depends on the viewing mode and the +Klein bottle. For example, the Lawson Klein bottle looks nicest when +projected perspectively. The figure-8 Klein bottle, on the other +hand, looks nicer while walking when projected orthographically from +4d. The projected Klein bottle can then be projected to the screen +either perspectively or orthographically. When using the walking +modes, perspective projection to the screen should be used. There are +three display modes for the Klein bottle: mesh (wireframe), solid, or +transparent. Furthermore, the appearance of the Klein bottle can be +as a solid object or as a set of see-through bands. Finally, the +colors with with the Klein bottle is drawn can be set to two-sided, +rainbow, or depth. In the first case, the Klein bottle is drawn with +red on one "side" and green on the "other side". Of course, the Klein +bottle only has one side, so the color jumps from red to green along a +curve on the surface of the Klein bottle. This mode enables you to +see that the Klein bottle is non-orientable. The second mode draws +the Klein bottle with fully saturated rainbow colors. This gives a +very nice effect when combined with the see-through bands mode or with +the orientation markers drawn. The third mode draws the Klein bottle +with colors that are chosen according to the 4d "depth" of the points. +This mode enables you to see that the figure-8 Klein bottle does not +intersect itself in 4d, while the Lawson Klein bottle does intersect +itself. The rotation speed for each of the six planes around which +the Klein bottle rotates can be chosen. For the walk-and-turn more, +only the rotation speeds around the true 4d planes are used (the xy, +xz, and yz planes). Furthermore, in the walking modes the walking +direction in the 2d base square of the Klein bottle and the walking +speed can be chosen. This program is somewhat inspired by Thomas +Banchoff's book "Beyond the Third Dimension: Geometry, Computer +Graphics, and Higher Dimensions", Scientific American Library, 1990. .SH OPTIONS -.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. +.I kleinbottle +accepts the following options: .TP 8 .B \-window Draw on a newly-created window. This is the default. @@ -27,22 +100,180 @@ Draw on a newly-created window. This is the default. .B \-root Draw on the root window. .TP 8 -.B \-delay \fInumber\fP -Per-frame delay, in microseconds. Default: 20000 (0.02 seconds.). +.B \-install +Install a private colormap for the window. .TP 8 -.B \-speed \fInumber\fP -Number of frames before changing shape. Default: 150. +.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 \-rand -Randomize the parametric surfaces displayed. Use random OpenGL primitives -too. -.B \-wander | \-no-wander -Whether to wander around the screen. -.B \-spin | \no-spin -Whether to rotate around the centre of the figure. +.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 +which Klein bottle is displayed. +.TP 8 +.B \-klein-bottle random +Display a random Klein bottle (default). +.TP 8 +.B \-klein-bottle figure-8 \fP(Shortcut: \fB\-figure-8\fP) +Display the figure-8 Klein bottle. +.TP 8 +.B \-klein-bottle lawson \fP(Shortcut: \fB\-lawson\fP) +Display the Lawson Klein bottle. +.PP +The following four options are mutually exclusive. They determine +how the Klein bottle is displayed. +.TP 8 +.B \-mode random +Display the Klein bottle in a random display mode (default). +.TP 8 +.B \-mode wireframe \fP(Shortcut: \fB\-wireframe\fP) +Display the Klein bottle as a wireframe mesh. +.TP 8 +.B \-mode surface \fP(Shortcut: \fB\-surface\fP) +Display the Klein bottle as a solid surface. +.TP 8 +.B \-mode transparent \fP(Shortcut: \fB\-transparent\fP) +Display the Klein bottle as a transparent surface. +.PP +The following three options are mutually exclusive. They determine the +appearance of the Klein bottle. +.TP 8 +.B \-appearance random +Display the Klein bottle with a random appearance (default). +.TP 8 +.B \-appearance solid \fP(Shortcut: \fB\-solid\fP) +Display the Klein bottle as a solid object. +.TP 8 +.B \-appearance bands \fP(Shortcut: \fB\-bands\fP) +Display the Klein bottle as see-through bands. +.PP +The following four options are mutually exclusive. They determine +how to color the Klein bottle. +.TP 8 +.B \-colors random +Display the Klein bottle with a random color scheme (default). +.TP 8 +.B \-colors twosided \fP(Shortcut: \fB\-twosided\fP) +Display the Klein bottle with two colors: red on one "side" and green +on the "other side". +.TP 8 +.B \-colors rainbow \fP(Shortcut: \fB\-rainbow\fP) +Display the Klein bottle with fully saturated rainbow colors. If the +Klein bottle is displayed as see-through bands, each band will be +displayed with a different color. +.TP 8 +.B \-colors depth \fP(Shortcut: \fB\-depth\fP) +Display the Klein bottle with colors chosen depending on the 4d +"depth" of the points. +.PP +The following four options are mutually exclusive. They determine +how to view the Klein bottle. +.TP 8 +.B \-view-mode random +View the Klein bottle in a random view mode (default). +.TP 8 +.B \-view-mode walk \fP(Shortcut: \fB\-walk\fP) +View the Klein bottle as if walking on its surface. +.TP 8 +.B \-view-mode turn \fP(Shortcut: \fB\-turn\fP) +View the Klein bottle while it turns in 4d. +.TP 8 +.B \-view-mode walk-turn \fP(Shortcut: \fB\-walk-turn\fP) +View the Klein bottle as if walking on its surface. Additionally, the +Klein bottle turns around the true 4d planes (the xy, xz, and yz +planes). +.PP +The following options determine whether orientation marks are shown on +the Klein bottle. +.TP 8 +.B \-orientation-marks +Display orientation marks on the Klein bottle. +.TP 8 +.B \-no-orientation-marks +Don't display orientation marks on the Klein bottle (default). +.PP +The following three options are mutually exclusive. They determine +how the Klein bottle is projected from 3d to 2d (i.e., to the screen). +.TP 8 +.B \-projection-3d random +Project the Klein bottle from 3d to 2d using a random projection mode +(default). +.TP 8 +.B \-projection-3d perspective \fP(Shortcut: \fB\-perspective-3d\fP) +Project the Klein bottle from 3d to 2d using a perspective projection. +.TP 8 +.B \-projection-3d orthographic \fP(Shortcut: \fB\-orthographic-3d\fP) +Project the Klein bottle from 3d to 2d using an orthographic +projection. +.PP +The following three options are mutually exclusive. They determine +how the Klein bottle is projected from 4d to 3d. +.TP 8 +.B \-projection-4d random +Project the Klein bottle from 4d to 3d using a random projection mode +(default). +.TP 8 +.B \-projection-4d perspective \fP(Shortcut: \fB\-perspective-4d\fP) +Project the Klein bottle from 4d to 3d using a perspective projection. +.TP 8 +.B \-projection-4d orthographic \fP(Shortcut: \fB\-orthographic-4d\fP) +Project the Klein bottle from 4d to 3d using an orthographic +projection. +.PP +The following six options determine the rotation speed of the Klein +bottle 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. In walk mode, all +speeds are ignored. In walk-and-turn mode, the 3d rotation speeds are +ignored (i.e., the wx, wy, and wz speeds). In walk-and-turn mode, +smaller speeds must be used than in the turn mode to achieve a nice +visualization. Therefore, in walk-and-turn mode the speeds you have +selected are divided by 5 internally. +.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). +.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 Klein +bottle (default: 7.0). +.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 Klein bottle by dragging the mouse while pressing the left +mouse button. This rotates the Klein bottle 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 Klein bottle is rotated in 4D, +i.e., around the xy, xz, and yz planes. To examine the Klein bottle +at your leisure, it is best to set all speeds to 0. Otherwise, the +Klein bottle will rotate while the left mouse button is not pressed. +This kind of interaction is not available in the two walk modes. .SH ENVIRONMENT .PP .TP 8 @@ -55,5 +286,14 @@ stored in the RESOURCE_MANAGER property. .SH SEE ALSO .BR X (1), .BR xscreensaver (1) +.SH COPYRIGHT +Copyright \(co 2005-2009 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 -Andrey Mirtchovski. +Carsten Steger , 03-aug-2009.