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IsoGridTRACER© USER’s TIPS REGULAR KNOTS (RK)
== knots made on a Turk’s head (THK) cordage route (or shadow - topological term-. The shadow is the knot diagram *without* any indication of the nature of the crossing existing in it ). When the nature (OVER / UNDER) of the crossing is added then “the coding” of the knot is added. THK are but only one very special type of RK with a strictly alternating coding OVER-UNDER ( respectively UNDER-OVER ). Any knot *not* having this coding even if using a THK cordage route is NOT A * THK.(this essential point is ignored by 99.999999% ;-( of the knot tyers roving Net forums so this may be a ‘to be ignored’ point. * Essential as in ‘essence’ , the deep ‘what is ‘. RKBuilder©, Claude HOCHET’s program does REGULAR KNOTS of any TYPE of CODING and in any number of LEAD and BIGHT But IsoGridTracer© also provides for NON-REGULAR or MULTISTRAND knots made on a THK cordage route. PRE-REQUISITE: - Knowing all about the different TYPE OF CODING and what that entails. - Making no confusion between a THK and other knots made on a THK cordage route but using another coding that the strict O1 – U1 (or U1 – O1) of the THK, you know those knots and the particularities that make each quite different from the other. - Making no confusion between the two different frames of reference: vertical cylinder or horizontal mandrel and the consequences of this choice upon the appellation of the TYPE OF CODING in each frame of reference. If you happen not to be quite clear about that then please read SCHAAKE or shorter see the Turk’s Head pages at http://tinyurl.com/38mrcp or if you are shy of using a tiny url directly at http://preview.tinyurl.com/38mrcp - Knowing what PIN-STEPS are and how to use the PIN NUMBER when making a knot. - Having no trouble making a knot using the coding for each of the HALF-PERIOD (HP ) in it. LAUNCH THE IsoGRidTracer SCRIPT -----------------------------------------------------A panel open offering ONE pair of slider-scale and TWO sets ( or groups) of what is called radio-buttons. Usage of slider is pretty immediately intuitive. In any given set one radio-button and only one may be activated. The panel opens with pre-set choices so as to avoid crashes due to missing
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options.
SLIDERS and SCALES is on the upper left corner, Using them you may chose width ( thickness) and the length of the line figuring the crossing. Default choice is 10 for width and 11 for length. I would advise not to go over 13 for thickness and 17 or 18 for length but that is a matter of personal choice.
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FIRST SET of button is in the mid of the right side column. TWO radio-buttons with which you will be able to chose SINGLE STRAND ( GCD==1) or MULTISTRAND ( GCD>1). Default choice is set to GDC=1 or SINGLE STRAND. KEEP SOUND ‘ON’ to get the warnings. SECOND SET of button is in lower right corner. FIVE radio-buttons with which you will chose the TYPE OF CODING to be used: *** THK automated: you will just need to enter the Number of LEAD and the Number of BIGHT, the rest is taken care of by the program. *** COLumn-coded. *** ROW-coded. *** NEITHER Row coded NOR Column-coded . *** FREE manual entry by user (that is the default setting) : the grid with L & B asked for will be traced devoid of any crossing and user will add the crossing using MOUSE BUTTONS. RIGHT mouse click = for the UNDER or ‘0’ (that is LEFT mouse click = for the OVER or ‘1’ crossing.
digit zero and not letter ‘O’) crossing.
You will have an ERASER IsoGridTracer© USER’s TIPS
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Old version was Using LEFT ARROW to erase a Or RIGHT ARROW to erase a
\ an UNDER of “going upward to the left” crossing.
/ an OVER of “going upward to the right” crossing.
Whether putting in or erasing a crossing you need to position the extreme point of the MOUSE CURSOR smack on the intersection where the crossing is to be traced. THIS version IS: Using LEFT ARROW or RIGHT ARROW will erase the crossing whatever it type a
\ an
/
of “going upward to the left” crossing or erase a an OVER of “going upward to the right” crossing as the program ‘read’ a memory of the crossings made :erasing from the last made prior to use of eraser to those back in time. If you need to erase just one particular crossing that is not the last made and you don’t want to erase a whole backward sequence then you may also = trace it again and then use the eraser once. UNDER
In both cases, this immediately following here under apply: The quality of erasing depends on having put the mouse cursor in EXACTLY the same position it was in at the moment of tracing (the upper band of the panel will give you the coordinate- in panel coordinate not in screen or in program coordinates) Old version was This works *only* for the very last traced crossing. One way to by-pass that limitation is to trace again a faulty crossing and erase it then trace it correctly. THIS version IS: You will erase without the need to position again the cursor the crossing in reverse Sequence. DO NOT attempt to erase beyond the last crossing existing. In all cases of TYPE OF CODING ( left side bottom corner set of radio buttons ) except the THK automated choice you will be led to ENTRY of Number of LEAD and ENTRY of Number of BIGHT using SCALES AND SLIDERS.
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LEAD number MUST BE BETWEEN 1 and 41 BIGHT number MUST BE BETWEEN 1 and 26 This is for reason of “room available” on the screen ; the use of scrolling was not practical and anyway as it is this allows for a grid large enough for most practical purposes to be traced : 41L 26B. That leads to a ‘handful’ of crossings ( 40 * 26 = 1040 ) NOTE = you may not use ANYTHING beyond the buttons and sliders and still get what you want. NO ENTRY with the keyboard please.
The entries made were both POSITIVE INTEGER, depending on the choice made the GDC = 1 rule will be tested or not . If choice was SINGLE STRAND then entries not complying with the GDC=1 will be rejected and a beep will sound. Once the LEAD and BIGHT are accepted : --- if choice of TYPE OF CODING == THK automated then you will get directly the grid all made up in a panel ( see just above ) --- if choice of coding = FREE entry by user you will be led to a panel with a virginal grid, you just have to play with the mouse. --- if choice of coding = COLumn-coded OR ROW-coded then you will be led to an entry panel (same for both BUT the constraints hidden behind depend on the ROW or COL option) Note that there is NO text cursor positioned in the entry field : that is because pasting or keying in this field is not permitted. It is not permitted because that was leading to a great number of potential mistaken entries.
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Still entries are needed hence the push-buttons. Note the textual reminder of the length of the entry to be made depending on the COL or ROW option. When you are done verifying your entry just use CONFIRM entry. That close the windows if the entry is acceptable. THERE IS NO WARNING MESSAGE GIVEN : AN ENTRY NOT COMPLIANT WITH RULES IS REJECTED WITH NO WARNING AND SILENTLY. In the right side illustration you see that Add ONE has been pushed twice, followed by one add ZERO, followed by one add ONE, Followed by one add ZERO. What you cannot see is that The last three entries done were erased using the ERASE rightmost digit button.
CASE= COLUMN-CODED You need to enter ( L- 1 ) crossings. Those crossing are those “read” LEFT to RIGHT in a finished knot/diagram by an ODDnumbered Half-Period (HP ; HP-1 being the most often used)
Here are shown two ODD-numbered HP just to show that in a COLUMN-CODED ANY ODD-numbered HP will read the same code sequence LEFT TO RIGHT. Here the red one is the HP-1 as chosen in IsoGridTracer©. The sequence is read LEFT to RIGHT by the ODD-numbered HP going from the LEFT side BIGHT RIM to the RIGHT side BIGHT RIM OVER – UNDER – OVER – OVER – OVER- UNDER – UNDER – UNDER- OVER- OVER – UNDER – UNDER 1 0 1 1 1 0 0 0 1 1 0 0
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OVER – OVER – UNDER - OVER 1 1 0 1
That will have to be entered, using the push-buttons as 1011100011001101 But on a paper prepared prior to entering the code it will be easier to read if entered as 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 or
1
0
1
1
1
1
0
0
0
1
1
0
0 1
1
0 1
Use whatever takes your fancy and makes your task easier.
CASE= ROW-CODED You need to enter ( 2*B ) crossings. Those crossing are those “read” in a finished knot/diagram in a special manner : going from ROW ZERO to ROW ( 2 * B - 1) you tale the LEFTMOST CROSSING ON EACH ROW.
CASE NEITHER ROW-CODED NOR COLUMN-CODED: --- if choice of coding = NEITHER row-coded NOR column-coded then you will be led to an entry panel as here under:
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Note that there is NO text cursor positioned in the entry field: that is because pasting or keying in this field is not permitted. It is not permitted because that would be leading to a great number of potential mistaken entries. Still entries are needed hence the push-buttons. There is ABSOLUTELY NO CONTROL done on the VALIDITY of your entries only on their LENGTH. Note the reminder about the entries to be done : B * 2 ROW numbered ZERO to ( 2 * B – 1 ) each row will be (L-1) long in characters (see annexe about the justification for using ‘9’ as place holder.)
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When you are done verifying your entry just use CONFIRM entry.
Here under a ROW-coded of my fashion traced by IsoGridTracer© and on its left the HP coding as done by RKBuilder© the program Claude HOCHET wrote that can do ANY TYPE OF CODING and even ANY ENLARGEMENT ( UP stream and DOWN stream from the THK entered )
To understand the numbering remember that the two “end” top and bottom meet in a cylinder, this is illustrated in the picture above.
A SECOND FLAVOUR OF THIS PROGRAM EXISTS, a stand alone that draws the grids HALF-PERIOD AFTER HALF-PERIOD ( mouse click command ) Its name is HPparHP.:;for now it is WITHELD AND WILL BE GIVEN ONLY TO THOSE ASKING FOR IT. You just need to rename the .000 file to .EXE and to put it in the same folder as GRID.EXE
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USING THE SCRIPT UNZIP ( the very best tool for that IMO is the freeware 7ZIP ) the file I gave for download in a folder of your choice. No install process, Nothing written forcibly in your Windows register. If the downloaded file is SomeName.000 rename it to SomeName.ZIP For me it was IsoGridTracer See illustration under the folder containing the set of files
Double-click on GRID.exe (it may be another name but beside w9xpopen.exe it will be the only .EXE file ) so as to open a session. I made it run on VISTA PRO 32 bits and on an old early 2005 XP Home SP2 without doing anything special. You must have those .DLL in your windows/system32 folder for the .exe not to crash.
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You may get them downloading from Microsoft the vcredist_x86.exe http://www.microsoft.com/downloads/details.aspx?FamilyId=32BC1BEE-A3F94C13-9C99-220B62A191EE&displaylang=en NOT repeat NOT THE SP1 version as it will not work. Put the .dll in the same folder as the GRID.EXE first. DO NOT MESS WITH YOUR WINDOWS INSTALL AND DO NOT REPLACE A NEWER .DLL BY AN OLDER ONE ! I put a DLLWIN folder in the download zone that contains those .dll (OWNED by Microsoft) .
ANNEXE 1 . The FRAME OF REFERENCE for the appellation of the TYPE is Schaake’s : the HORIZONTAL MANDREL with a Bight Rim (or border, or frontier) on the LEFT side and a Bight Rim on the RIGHT side such as in this diagram taken from Schaake. Note the HP1 in yellow ; all ODD-numbered HP go from LEFT to RIGHT and the HP2 in blue ( EVEN-numbered HP go from RIGHT to LEFT ).
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Choice Column-Coded --------------------------------------------------------------------------Enter the sequence of crossings seen on the HP1 of the finished knot (or on the complete grid diagram of thereof ) as read by the SPart-Wend vector (Working End / Courant ). (a vector is a line with a direction, think arrow and read from feathers to point). An ODD-numbered HP ( HP 1 being the usual reference ) starts on the LOWER LEFT side (of the horizontal mandrel diagram for Schaake), at the crossing between SPart ( Standing Part / Dormant ) and goes UPPER RIGHT to the other bight rim or frontier. There are (L – 1) crossings to be noted. The type of crossing is as ‘read’ by the *vector* or ODD numbered HP (HP-1 being one) directional arrow. Don’t make too short an entry as it will be rejected, the program will not allow you to make a too long sequence. YOU MAY NOT MAKE AN ENTRY BY ANY OTHER MEAN THAN THE BUTTONS
Choice Row-Coded In the same conditions that you entered the HP ODD numbered crossings ( ‘0’, ‘1’ only and complying this time with the adequate length of 2*B characters) you need to enter the Row-Coding. The Row-Coding is the coding of EACH row in the finished knot.
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As in a Row-coded ALL the crossings in a given row are of the same type (either Over or Under) the whole row is easily represented by only one of its crossings : the very first one on this row, the leftmost one that is. (see diagram just above) Note = The *entry* starts at row ZERO ( Modulus oblige ) and goes DOWNWARD continually till row numbered (2*B) *BUT ON THE DIAGRAM AND ALSO FOR THE ROW-CODING* the rows entry begins at ROW ZERO which is the one in direct alignment with the crossing (on the left side bight rim ) made by the SPart (Standing Part) and the Wend (Working End) ( Dormant-Courant ). In the general case of grids : First go UPWARD till no row are left (here last row up is 9) and , ‘MODULUS oblige’, start again at the very bottom of the diagram (here Row 10) and go UPWARD toward row ZERO When ALL the rows have been noted, ONCE and ONCE ONLY EACH, please verify your entries once again before validating the whole matrix. In IsoGridTracer© the lowermost ROW is ROW ZERO and the last row which is the topmost is ROW (2*B – 1) so your task is made easier. Each crossing in this upward zig-zag is “as read” by an ODD numbered HP and *not* in succession by ODD and EVEN numbered HP. This is *very* important as for example a \ is an UNDER when read by ODD-numbered HP *but* is an OVER when read by an EVEN-numbered HP (vice versa for a
/
OVER==ODD)
Choice Neither-Nor YOU MUST
make the entries in this manner:
Important note: each row is ‘read’ from LEFT to RIGHT to get the order of the crossings and ‘as read’ by an ODD-numbered HP for the nature of each crossing.
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- With L EVEN (L-1) is ODD so you need one ODD Row and one EVEN Row ; first Row entered being ODD ( with L ODD then (L-1) is EVEN you get ROWS of equal LENGTH and they are all EVEN of course).
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SHORT REVIEW
TYPE OF CODING AND FRAME OF REFERENCE (IsoGridTracer follows SCHAAKE’s choice of the HORIZONTAL MANDREL frame of reference )
Note: the SHADOW of a THK is the cordage route of a THK but without any indication of the nature of the crossings. Adding the coding of the crossings allow a strict and logical differentiation of knots
Note that the ROW and COLUMN coded appellation are QUITE MYOPIC and change drastically with the frame of reference. It is *never* a good idea to keep a frame dependant point of view. A point of view INDEPENDENT of the frame of reference because it is INTRINSIC to the object is much, much better hence my INTER-BIGHT and PARALLEL BIGHT coded appellation that does NOT vary with Horizontal Mandrel versus Vertical Cylinder but stay unchanged because they belong to the knots themselves. Anyway the ‘parti pris’ adopted in the IsoGridTracer© application is Schaake’s horizontal mandrel ---- In a ROW AND COLUMN-CODED knot in a GIVEN column ALL the crossings are of the SAME TYPE ( either OVER or UNDER ) and in a GIVEN row ALL the crossings are of the same type. ---- In a COLUMN-CODED knot in a GIVEN column ALL the crossings are of the SAME TYPE ( either OVER or UNDER ). ---- In a ROW-CODED knot in a GIVEN row ALL the crossings are of the SAME TYPE ( either OVER or UNDER ). ---- In a Neither Column Nor Row –coded Columns AND Row may be with Crossings of different type = a mix of OVER and UNDER.
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Now take also note of the FACT that there are STRICT RULES governing the classification of those Regular or Standard Knots. In particular you MAY NOT extend in an arbitrary way, say a GAUCHO and still call it a GAUCHO. The main ‘basic coding’ are given in page turksheads_22.html in http://preview.tinyurl.com/38mrcp for those wishing to understand things a bit more.
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This under to show the influence of going “COLumn coded” or “ROW-coded”. The very same sequence of code 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 is entered but in one case it is read as a ROW-coding and in the other as a COLUMN-coding
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