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Diffstat (limited to 'hacks/glx/hypertorus.man')
| -rw-r--r-- | hacks/glx/hypertorus.man | 76 |
1 files changed, 51 insertions, 25 deletions
diff --git a/hacks/glx/hypertorus.man b/hacks/glx/hypertorus.man index 8c7075f..8f0837e 100644 --- a/hacks/glx/hypertorus.man +++ b/hacks/glx/hypertorus.man @@ -16,8 +16,10 @@ hypertorus - Draws a hypertorus that rotates in 4d [\-solid] [\-bands] [\-spirals-{1,2,4,8,16}] +[\-onesided] [\-twosided] [\-colorwheel] +[\-change-colors] [\-perspective-3d] [\-orthographic-3d] [\-perspective-4d] @@ -37,18 +39,28 @@ 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 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 +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 @@ -97,18 +109,31 @@ Display the torus as see-through bands (default). 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. +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: red on the outside and green on -the inside. +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 +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. +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). @@ -158,9 +183,9 @@ 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 +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 +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. @@ -177,12 +202,13 @@ stored in the RESOURCE_MANAGER property. .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. +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>, 28-sep-2005. +Carsten Steger <carsten@mirsanmir.org>, 11-jan-2020. |