Provided by: xscreensaver-gl_5.08-0ubuntu3_i386 bug
 

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
        accoring 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
                octahedron  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 accoring 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
        rotates 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.
        X(1), xscreensaver(1)
 

COPYRIGHT

        Copyright  (C)  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 war-
        ranty.
 

AUTHOR

        Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.