Celtic Knots Help

This control panel implements a method of constructing Celtic knots that I
learned from the beautiful books of Aidan Meehan.  I won't fully describe 
the method here, please refer to his books to find out more (references at 
end).  

The method works by first creating a regular grid of (not-necessarily) 
square cells.  This is called the primary grid (you can see it easiest if
you unselect everything else in the Show: radio button section).  Another
grid, the secondary grid is created by subdividing this primary grid, and
yet a third grid, the tertiary grid created from the secondary (hidden by
default in KnotPlot).  It is along the tertiary grid that the knot path
will follow.  Try clicking on the `diagram' button to see the knot.

Here is how stuff works:

   Show:  --- you can turn on and off the primary and secondary grids.
              note that primary and secondary breaklines can only be 
              placed or removed if the corresponding grid is visible. 

   diagram  --- click on this button to draw the knot path 

   auto diagram --- if checked, draw the knot diagram every time the 
                    grid or breakline pattern changes

   place a breakline --- hover over the spot where you want the breakline
                         and click.  if you have `auto diagram' checked
                         you should see a new knot appear. 

   clear a breakline --- hover over an existing breakline and click
  
The two sets of sliders allow you to create various sorts of grids.
Select `auto create' to have the grids created and displayed as you change
the sliders.  It's funnest to have both `auto create' and `auto diagram'
checked and have the `Knot interlace' shown. 

Other things to try:

   turn off primary cells --- do this by first making sure that the view
                              window has mouse focus (click in an empty
                              region).  then press and hold down the `A'
                              key and move the mouse over a primary grid
                              cell (the primary grid needs to be visible).
                             
                              when hovering over a primary grid cell, you 
                              should see that cell highlighted.  if you 
                              then click the mouse, that cell will be
                              turned off and not used in the interlace
                              creation.  you can turn that cell on again
                              by clicking it a second time.

                              NOTE: there is a bug in KnotPlot in that it
                              allows you to turn off a primary cell that
                              contains a secondary breakline.  if you do
                              that you get a `Bad path found' error.

   copy to arena --- KnotPlot uses a very lightweight drawing method when
                     showing the Celtic knotting.  nothing is actually 
                     copied to the KnotPlot `arena' (the main location 
                     where stuff in KnotPlot happens) until you click on
                     this button.  You have to exit the Celtic Knotting 
                     panel to see what's in the arena. 

   scale the drawing space --- use the right mouse


Although this control panel only allows you to create regular and circular
grids, KnotPlot allows for arbitrary Celtic knot grids, which can consist
of any collection of quads embedded in various ways in 3D.  To see a some
examples, try the `splaits' and `star/box' demos on DemoA.

If you've laboured long to create a beautiful Celtic knot grid and would
like to save it, just use KnotPlot's `save' command.  The grid is saved
along with the knot in the arena (if any).  You can load the knot back 
with the `load' command (see the manual for more information). 

Another good reference for Celtic knotting, which describes a method at
first glance different from Meehan's, is Iain Bain's `Celtic Knotwork'. 
The method is mathematically equivalent to the Meehan method. 

Several Celtic grids constructed from examples in the references are 
included with the KnotPlot distribution. 

Bugs

The Celtic knotting tool is somewhat unpolished.  There are a few bugs:

   --- allows you to turn off primary cells that contain a secondary 
       breakline.  well, at least KnotPlot detects the bad path.

   --- if you click on `reset', KnotPlot returns to its default mode, and
       the Celtic knotting features are no longer enabled.  to get back,
       simply go to some other control panel and then return to the Celtic
       knotting control panel.

   --- when loading a Celtic grid from a file and `auto diagram' is 
       selected, doesn't draw the diagram.  you have to click `diagram'
       yourself. 


REFERENCES

Even the quickest look through any of the following excellent books will
make it obvious that there is much more to Celtic Knotting than what
KnotPlot can offer. 

Bain, George    `Celtic Art: The Methods of Construction'
                Dover Publications Inc., 1973, (ppbk edition)
                A classic and a must-have for those interested in Celtic Art.

Bain, Iain      `Celtic Knotwork'
                Constable and Company Limited, 1990 (ppbk edition)
                A beautiful book and my favourite on Celtic knotting.  Has 
                many illustrations of the great masterpieces of Celtic Art.
                

Meehan, Aidan   `Knotwork - The Secret Method of the Scribes', 
                Thames and Hudson, 1991
                Part of a series of delightful books on Celtic Art by Meehan.

                `Celtic Knots - Mastering the Traditional Patters'
                Thames & Hudson, 2003
                This book has a huge number of illustrations, 2843 in fact,
                and is a delight to flip thru for many interesting breakline
                patterns.

