polytopes(6x) XScreenSaver manual polytopes(6x)
NAME
polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
SYNOPSIS
polytopes [-display host:display.screen] [-install] [-visual visual]
[-window] [-root] [-delay usecs] [-fps] [-5-cell] [-8-cell] [-16-cell]
[-24-cell] [-120-cell] [-600-cell] [-wireframe] [-surface] [-transpar-
ent] [-single-color] [-depth-colors] [-perspective-3d] [-ortho-
graphic-3d] [-perspective-4d] [-orthographic-4d] [-speed-wx float]
[-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz float]
[-speed-yz float]
DESCRIPTION
The polytopes program shows one of the six regular 4d polytopes
(5-cell, 8-cell, 16-cell, 24-cell, 120-cell, or 600-cell) rotating in
4d. The program projects the 4d polytope to 3d using either a perspec-
tive or an orthographic projection. The projected 3d polytope can then
be projected to the screen either perspectively or orthographically.
There are three display modes for the polytope: mesh (wireframe),
solid, or transparent. Furthermore, the colors with which the polytope
is drawn can be set to either single color or to a coloring according
to the 4d "depth" (the w coordinate) of the polytope in its unrotated
position. In the first case, the polytope is drawn in red. This col-
oring combined with transparency gives a nice visual effect of the
structure of the polytope. The second mode draws the polytope with a
fully saturated color wheel in which the edges or faces are colored ac-
cording to their average 4d "depth". This mode is best combined with
the wireframe mode, where it allows you to see how different parts of
the polytope are moved to the "inside" of the projected polytope in 3d.
Of course, in 4d the cells, faces, and edges of the polytope all have
the same distance from the center of the polytope. Only the projection
creates the appearance that some of the cells lie "inside" the figure
in 3d.
OPTIONS
polytopes accepts the following options:
-window Draw on a newly-created window. This is the default.
-root Draw on the root window.
-install
Install a private colormap for the window.
-visual visual
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.
-delay microseconds
How much of a delay should be introduced between steps of the
animation. Default 25000, or 1/40th second.
The following six options are mutually exclusive. They determine which
polytope is displayed.
-5-cell Display the 5-cell. The 5-cell is the 4d analogon of a regular
tetrahedron in 3d. It has 5 regular tetrahedra as its cells,
10 equilateral triangles as faces, 10 edges, and 5 vertices.
-8-cell Display the 8-cell (a.k.a. hypercube or tessaract). The 8-cell
is the 4d analogon of a cube in 3d. It has 8 cubes as its
cells, 24 squares as faces, 32 edges, and 16 vertices.
-16-cell
Display the 16-cell. The 16-cell is the 4d analogon of an oc-
tahedron in 3d. It has 16 regular tetrahedra as its cells, 32
equilateral triangles as faces, 24 edges, and 8 vertices.
-24-cell
Display the 24-cell. The 24-cell has no 3d analogon. It has
24 regular octahedra as its cells, 96 equilateral triangles as
faces, 96 edges, and 24 vertices.
-120-cell
Display the 120-cell. The 120-cell has no 3d analogon. It has
120 regular dodecahedra as its cells, 720 regular pentagons as
faces, 1200 edges, and 600 vertices.
-600-cell
Display the 600-cell. The 600-cell has no 3d analogon. It has
600 regular tetrahedra as its cells, 1200 equilateral triangles
as faces, 720 edges, and 120 vertices.
The following three options are mutually exclusive. They determine how
the polytope is displayed.
-wireframe
Display the polytope as a wireframe mesh.
-surface
Display the polytope as a solid object.
-transparent
Display the polytope as a transparent object (default).
The following two options are mutually exclusive. They determine how
to color the polytope.
-single-color
Display the polytope in red.
-depth-colors
Display the polytope with a fully saturated color wheel in
which the edges or faces are colored according to their average
4d "depth", i.e., the w coordinate of the polytope in its unro-
tated position (default).
The following two options are mutually exclusive. They determine how
the polytope is projected from 3d to 2d (i.e., to the screen).
-perspective-3d
Project the polytope from 3d to 2d using a perspective projec-
tion (default).
-orthographic-3d
Project the polytope from 3d to 2d using an orthographic pro-
jection.
The following two options are mutually exclusive. They determine how
the polytope is projected from 4d to 3d.
-perspective-4d
Project the polytope from 4d to 3d using a perspective projec-
tion (default).
-orthographic-4d
Project the polytope from 4d to 3d using an orthographic pro-
jection.
The following six options determine the rotation speed of the polytope
around the six possible hyperplanes. The rotation speed is measured in
degrees per frame. The speeds should be set to relatively small val-
ues, e.g., less than 4 in magnitude.
-speed-wx float
Rotation speed around the wx plane (default: 1.1).
-speed-wy float
Rotation speed around the wy plane (default: 1.3).
-speed-wz float
Rotation speed around the wz plane (default: 1.5).
-speed-xy float
Rotation speed around the xy plane (default: 1.7).
-speed-xz float
Rotation speed around the xz plane (default: 1.9).
-speed-yz float
Rotation speed around the yz plane (default: 2.1).
INTERACTION
If you run this program in standalone mode you can rotate the polytope
by dragging the mouse while pressing the left mouse button. This ro-
tates the polytope 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 polytope is rotated in 4D, i.e., around the xy, xz, and yz
planes. To examine the polytope at your leisure, it is best to set all
speeds to 0. Otherwise, the polytope will rotate while the left mouse
button is not pressed. -fps Display the current frame rate, CPU load,
and polygon count.
ENVIRONMENT
DISPLAY to get the default host and display number.
XENVIRONMENT
to get the name of a resource file that overrides the global
resources stored in the RESOURCE_MANAGER property.
SEE ALSO
X(1), xscreensaver(1)
COPYRIGHT
Copyright © 2003-2005 by Carsten Steger. Permission to use, copy, mod-
ify, distribute, and sell this software and its documentation for any
purpose is hereby granted without fee, provided that the above copy-
right notice appear in all copies and that both that copyright notice
and this permission notice appear in supporting documentation. No rep-
resentations are made about the suitability of this software for any
purpose. It is provided "as is" without express or implied warranty.
AUTHOR
Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
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