Drawing a Knot Diagram

 

When this utility was first conceived, it was thought that it would be used to create diagrams of existing knots so that the diagram could be communicated using the cypher file and allowing the diagram to be reliably and unambiguously re-created by some other user.

 

Since then, use of the utility has changed quite markedly and now includes drawing out a knot diagram in an attempt to identify the knot by looking up its Binary Signature in The Library of Knots.  The utility has also been put to work to help experiment with knot structures, design new knots and even help in developing wasy of tying those new knots.

 

If your intention is to create a diagram of a physical knot, then a little preparation work will make the job of diagramming the knot a little easier.  Here are some tips on preparing the knot for diagramming:-

 

Tie the knot in a fairly thick (6mm) braided cord.  Dress the knot to its working structure but do not tighten the knot to set it, in fact, it may be advantageous to do the opposite, i.e. loosen it slightly, but retain its dressed shape.  Next, take a cork or polystyrene tile and lay the knot onto it.  Use 'bobby' pins to hold the cords  in place so that you are able to see through the knot and so that cords only cross one at a time.  If your knot has a junction where for example, three cords cross one above the other, either rotate the knot for a perspective which does not require to depict three cords crossing, or displace one of the cords slightly so its crossings can be shown to the side of the other two cords crossings.

 

Some find it advantageous to sketch the knot first onto paper, but with practice it becomes easy to create the diagram straight into the utility.  One word of advice though - having created a diagram, tie a copy of the knot using only the diagram for guidance, then compare the copy with the original to ensure that the diagram truly represents the target knot.

 

 

One cord

 

From experience, you will find that one of the hardest things is to judge how much room to leave for all the turns and crossings, so perhaps one of the easiest places to start the knot diagram is in the middle of the knot and in the middle of the grid.  You do not have to draw the knot in any particular order, nor do you have to draw the knot continuously as you trace the cord path through it, you can draw bits of the knot piecemeal and then connect them up later, although this will probably lead to you deciding to tidy up your diagram in a second attempt.  A handy way to do this is to keep the first rough diagram open, then open another copy of FCB42 alongside and use the rough diagram to guide the layout of the second, tidier, diagram.

 

To start with though, try drawing a simple knot such as the overhand knot.  Tie the knot in thick cord and pin it out on a cork tile to keep it in place as you make its diagram.

 

Start by clicking one of the cord end tiles in the green pallet area, choose the one which has the same orientation as your sample knot.  Then click one of the empty cells in the drawing area, the 'end' or 'Working end' tile will be drawn in the square that you clicked.  Then take note of how the working end enters the knot - is it first passage over or under the first cord it encounters?  Click on one of the two crossing pallet tiles to select the one which matches your knot characteristics and then click in the square next to the 'end' drawing.  If you have chosen the Overhand knot as your starting example, the diagram might now look like this -

 

  the 'end' tile alongside a top crossing tile.  In the Overhand knot, the cord then passes under a cord, so the next tile would be an under crossing and  the diagram would look like this -

 

  an 'under' crossing following the 'over' crossing.  The path of the cord in the OH knot then turns back on itself, so use two of the quarter turn tiles like this -

 

  Now another 'over' crossing tile is needed -

 

  and another quarter turn, to join back to the crossing tile we started off with -

 

  Now the cord turns again to connect up with the second crossing tile we placed and finishes with an arrow indicating 'the rest of the cord' like this -

 

 

While you have been putting these tiles into the grid, you may have noticed that the Overs Index and the signature boxes kept changing and now the knot is finished, they look like this -

 

 

If you now click the 'Find' button, the utility will attempt to look up the signature '101010' in the Knot Library Wiki and display the page with information regarding that knot (if it has already been indexed into the library).

 

If the Library did not recognise your particular knots signature, it might be because that knot has yet to be stored in the library or it might just be that your knot is brand new to the knotting records of today.  Either way, it would be valuable to the Knotting World for you to post your knots .cyp file onto the IGKT forum to see if anyone can recognise it and for them to then include the knot into the Library with you as its discoverer (if it is new of course).

 

 

 

Two / three cords

 

There  are a great number of 'joining' knots which are tied using two cords, one example is the Reef knot -

 

 

 

It is very easy to draw a two cord knot using the utility but a little care is needed to put the crossing tiles onto the right cord in order to depict the knot correctly.

 

First, start by drawing out the blue cord from start to end. 

 

 

Then click in the Cord #2 text field, this will select cord #2 for the next tiles to be painted into.

Click on the first end tile, i.e. the one which points West, then click on the grid to start the second cord which will be drawn in red -

 

the red cord goes under its first crossing and then over its second crossing.  The important thing to remember here is that all 'over' crossings need to be in the colour of that cord.  So, leave the first under crossing in blue, select the horizontal 'over crossing from the tiles panel (the left hand side one) and click into teh horizontal crossing cell - it will be added to the red cord, so it will turn red.  At the same time, the 'under' parts of the crossing just right of it will automatically be coloured red to show that the red cord has passed behind the blue one.  Next draw in a curve to connect to the next crossing, notice that again it automatically colours the 'behind' cord as red -

 

  fill in the gap with a vertical line and again the 'behind' cord is correctly coloured, then add two quarter curves to return the cord to the 'above' crossing.  Notice that the crossing stays blue.  Now select the vertical 'over' crossing tile and click to replace the blue tile with a red one -

 

  Now finish the diagram with a quarter bend and a finish arrow.

 

 

The Overs Index will also show the correct value of 6:10 and the Binary Signature will have been calculated.

 

 

 

Flipping handedness

 

With the previous drawing, select Tools  --  Swap Hand (or press Ctrl + w) and every crossing will be reversed - 

 

  This has effectively shanged a 'right hand knot' into its 'left hand' version.  You might also notice that the two binary signatures of these versions are exact compliments of oneanother.

 

Nudging tools

 

Started a little too close to the edge and need a bit more room to draw in ?  Use the Nudge tools to move the drawing around the grid space.  But be careful, if you move any of the drawing off the grid either off the top or off the left, them it will be wiped off, however, the grid continues to the right and downwards, so if you move the diagram in those directions it is still there and can be moved back into the viewing area later.

 

Spars for Hitches

 

Hitches are knots tied around some static object.  To depict a cord going behind a spar, use the dotted horizontal or vertical lines and a representation of a fixing spar will automatically be added  -

 

  as in this representation of a Marlinspike hitch.

 

If you need to move the spars, use the spar direction arrows just beneath the tiles pallet.

 

 

 

Saving and Loading tools

 

Once you have drawn a diagram, click File - Save As to open a save dialogue box, choose a directory and a name and click Save to save the diagram into a .cyp file format.

 

To Load a .cyp file simply choose File -- Open, navigate to the selected .cyp file and click Open.