Main Help

Welcome to KnotPlot!  Before I describe the Main control panel, let me say a
few words about interacting with knots in the KnotPlot main window.  Use the
following mouse buttons (click down and drag):

   left --- rotate the scene with this button using a `virtual trackball'

   middle --- translate the scene

   right --- scale the scene (move mouse to left to reduce, move mouse to
             right to enlarge)

None of these operations change the knot itself, just how it is viewed.  You 
can undo any of these operations using the `untran' button described below. 

Macintosh users may want to purchase a three button mouse (which works nicely
in MacOSX), or try SHIFT or CTRL.  

Now for the Main control panel.  At the very top of the control panel are two
rows of tabs that can be used to set KnotPlot to its other control panels. 
Below the tabs is a set of buttons that are also found on most of the control 
panels.

   undo --- often can be used to undo an operation.  clicking in quick 
           succession (less than about 1 second between clicks) restores to 
           earlier and earlier states.

   reset --- useful to get KnotPlot into its initial state.  if things ever 
           seem messed up, this button is your friend.

   help --- you've already used this button!  Each control panel has its own
           customized help.

   quit --- quit KnotPlot.  you can also use the ESC key at any point.   

Next are various buttons that load knots from the standard catalogues included
with KnotPlot.

   All --- loads a knot chosen randomly from the entire `basic' knot and
           link catalogue.  this is essentially Appendix C from Dale Rolfsen's
           classic book `Knot and Links' (reference below)

   1  2  3  4 --- loads a knot/link chosen randomly from the basic catalogue
           with 1, 2, 3, or 4 components, resp.

   spec coll --- loads a knot chosen randomly from the `Special Collection'.
           these are knots that are `special' for some reason (they have a 
           name, they are mathematically interesting, they look neat, etc.)

The next row of buttons load knots from basic catalogue, but displays them in
a `zoo' where you can choose them interactively.

   Rand --- selections are random chosen

   A  B  C  D  E  F --- the entire basic knot and link catelogue, in the same
           order they appear in `Knots and Links'

   Torus --- a zoo of torus knots and links, in order of increasing crossing
           number.  if you click on the button repeatedly, you get more and
           more complex torus knots and links.

   RandT --- a selection of torus knots and links, chosen randomly


Display Section

Knots are display either as `smooth tubes' (the default), or as `beads & cyls',
which are the vertices and edges representing the knot.  It is these beads and
cylinders which are how the knots are internally represented, the smooth tubes
are for display purposes only.  Use the radio buttons to choose how you want
the knot displayed:

   smooth  cylinders --- choose one or the other, but KnotPlot lets you display
           both if you wish (it might look strange)

   beads  Beads  points --- the beads (vertices) can be displayed either in a
           `cheapo mode' (beads) or in `luxo mode' (Beads), or in `super cheapo
           mode' (points).  

   forces --- this control is really misplaced, since it's doesn't control how
           the knot is displayed, but whether the forces acting on the beads is
           displayed or not.

Two convenience buttons `smooth tubes' and `beads & cyls' are provided which
set several options simultaneously (including the value of `cyl-rad').

Three buttons which are gathered together for no good reason are next:

   twfix --- fixes the (possibly) ugly deficit angle.  more information about
           this can be found in the KnotPlot manual.

   untran --- resets the virtual trackball to the unrotated state and resets
           and translations to zero (that is anything you may have done to 
           the scene using the left or middle mouse buttons).

   centre --- translates the knot (not the scene) so that its bounding box is
           centered at the origin.  this button is actually misplaced, since
           it changes the internal data and doesn't affect the viewing 
           parameters

Some radio buttons can be used to selectively display various things that are
not the knot:

   xyz axes --- the coordinate axes

   Grid --- the xy plane

   Backdrop --- a coloured background

   Labels --- bead and component labels

   Orientation --- KnotPlot implicitly orients all its knots, but doesn't 
           display the orientation unless this is selected. 

   Sphere --- the `utility sphere'

A set of rollers is next:

   scale --- alternate method for scaling the scene, can also use middle mouse
      
   cyl-rad --- radius of the smooth tube or cylinder

   bead-rad --- radius of beads or Beads

   ncur --- number of refinements along the path of the knot, only applicable
            to smooth tubes

   nseg --- number of refinements along the circumference of a tube or cylinder

To see the effect of ncur and nseg, first load a knot, then click on `smooth
tubes' and click `flat'.  Now try adjusting the rollers. 



Dynamics Section

This is a subset of what is displayed on the `Dyna' control panel.  Click on
the `Dyna' tab and read the help provided there. 



REFERENCES

The basic catalogue is essentially the same as Appendix C in Dale Rolfsen's 
classic book `Knot and Links', AMS Chelsea Publishing, 2003.  This is a reprint
of the original 1976 Publish or Perish Press edition.  The data was graciously
supplied by Professor Rolfsen in the very earliest days of KnotPlot and then
(in most cases) relaxed slightly.  
