## Miters and spirals: visualizing, charting (and more) 2

Visualizing the shapes (using charts in Mac Numbers)

A spiral gore is the first or second half of a miter gore, conversely a miter gore has 2 consecutive  spiral gores, knit in mirror image.

GOING ROUND: numbers 1-12 represent knitting sequence for wedges, thicker lines at segment edges = rows across knit width at end of each sequence, 2 rows or many more depending on planned design shape

Previous posts on related topics:

http://alessandrina.com/2011/06/18/knitting-math-and-pies1/

http://alessandrina.com/2011/06/24/taking-it-to-a-garment/

http://alessandrina.com/2011/03/29/the-doilies/

http://alessandrina.com/2013/12/28/short-rows_-balls-tams-3d-rounds/

## Miters and spirals: visualizing, charting (and more) 1

Getting my thoughts together on topic I searched for any of my previous posts that may be related, here is a list

http://alessandrina.com/2013/12/18/holding-stitches-short-rows/

http://alessandrina.com/2014/02/24/holdingshort-rows-hand-tech-to-chart-to-automating-with-slip-stitch-1/

http://alessandrina.com/2013/12/28/short-rows_-balls-tams-3d-rounds/

http://alessandrina.com/2013/01/21/automating-pleating/

Even in my earliest days as a hand knitter, I liked charting out my sweater shapes ie sleeves, necklines, etc on graph paper and tracking my place by marking appropriate row or every other row on the charted image. Many of the formulas for charting math in garment shaping may be emulated by drawing a line on chart where each square represents a stitch and a row, connecting points, and filling in squares. Averaging out grid shifts is also the guideline to increasing and decreasing for shaping on pixel charts. Though this may be a bit of egg before the chicken, I got sidetracked playing with software yet again.

GIMP

Working premise: using holding to shape a wedge over 36 rows. Stitch multiples  are brought into hold opposite the carriage (floats will be created if they are brought into hold on carriage side), in the instances below each graph row represents 2 rows knit, my fabric width at the start is 100 sts

Set image size _ pixels equal stitches and rows required

Magnify X 1000 (this is what I prefer for viewing and editing, less magnification may be used)

Activate 1 stitch grid/ show grid/ snap to grid

Make certain whole image is within your window view

Using line shape: click on upper left corner, press shift key_a drawing line will appear with a + symbol at its bottom right_click on first square on the bottom right , a line will appear where black squares represent  # of stitches to be held each row

bucket fill in appropriate side of wedge to represent knit stitches

create a new, larger canvas that will accommodate desired multiple stacked repeats and possible knit rows in between shapes in new window; copy image from the first window, paste  into new window, move it and place in desired location on your  screen

return to first window, flip image vertically (image menu/ select transform and direction)

again copy, paste, move into desired location and insert knit or (patterned) rows (green) when and if desired. On electronic machines the final image would have to be doubled in length, so those “knit row” pixels/squares would have to be adjusted accordingly to half the desired number

Row by row charting for double height to represent each row of actual knitting: the process

starting with a repeat 6X6

convert image to bitmapped (repeat at upper right below is a different one, should match the one being resized)

scale image: click on locked symbol in turn to alter aspect ratio, change both pertinent numbers

the repeat twice as long, 6 X 12

going 3D, possible spiral

eliminating squares

shifting things around in order to add “automatic wraps”, begin knit with COL

in further progress

stacked repeat

save in image in format for downloading to machines via cable and knitting using slip stitch setting, or export or screen grab for printing and knitting from chart visually as hand technique. If printing images colored cues may be added for carriage/lock setting or color changes, etc.

the question: what about numbers and excel?

NUMBERS

using the line tool (shapes) will get the line in place, shaping is “eyeballed”

knit squares are filled in

so you want to double the height only? Apple for some reason when they  “upgraded” to the latest version of the program (3.2) has eliminated the split table feature, so the only way I can see is through using table: add rows above or below in the chart, new row will be a copy of selected row

EXCEL

the insert row option will add rows only below selected ones, I have not found a tool equal to the line shape in Numbers

## Holding/short rows: hand tech to chart to automating with slip stitch 1

These directions apply to Brother Machines; designs could be used as they are and programmed into Passaps, other brands would require some adjustments. In these samples the holes resulting from holding for 2 row sequences are considered part of the design. Vertical strips in different colors could be knit and later joined. The final result is a “zig zag” pattern. Written directions may read: to begin, cast on and knit 2 rows. **COR: set machine for holding. Place in hold all except the first 2 needles on the right (carriage side). Knit 2 rows. Return to work  the next group of 2 needles on the left to work, knit 2 rows. Repeat until only 2 needles on the far left are in hold, return them to work, knit one row (color 1 in chart below). COL: pull  first 2 needles at far right to hold, knit 2 rows, repeat until last 2 are left in hold, knit 2 rows (color 2). COL: bring next 2 needles into work, knit 2 rows, continue until the last 2 stitches are returned to work on the right, knit one row (color 3). COR: pull first 2 needles on left into hold, knit 2 rows; repeat until last 4 stitches at right are put back into work, knit 2 rows**, and repeat from **. Knit 2 rows at end of desired number of repeats, bind off.

the sorting out hand tech sequences to achieve shapes sample

When producing my charts for using slip stitch to automate holding I like to draw what I would actually be knitting for each row, each stitch and row being a filled square, so the colored areas below represent knit stitches/rows on each row, the blank squares the stitches in holding. I test the repeat as a hand technique first, before in my case marking the mylar, then essentially fill in the knit stitches with color, keeping in mind the location of the knit carriage and the direction of the knitting. The colored squares are then programmed as punched holes, black squares or pixels, and the pattern may be knit using slip stitch <—>. Needle selection needs to be cancelled, otherwise the yarn will be knit on the side of non selected needles on that last stitch, creating a long float. The selection row needs to be toward the first 2 knit rows sequence. Here they are knit beginning on the right for 2 rows, so selection row is made from left to right.  Odd rows move, knitting, from right to left, even rows from left to right. At this point I prefer mac numbers for charting.

the final repeat, working chart

the mylar

the swatch

the  above repeat could be considered composed of 2 pairs of stacked, mirrored triangles, here is an instance of playing single “triangles”

the mylar

and accompanying swatch

## Short rows_ balls, tams, 3D rounds

These forms involve bilateral shaping. 3/4/16 Note: the charts below were produced using the program Intwined, which has been unsupported or updated for Mac since June 2013. At that time I encountered major problems using it, and after being restored the program has remained unpredictable, missing functions that influenced my choice to originally purchase it. The first row knit needs to be toward the first 2 row sequence in the design.

16 stitches, 6 rows, 8 repeats

28 stitches, 12 rows, 8 repeats

17 stitches, 8 rows, 12 repeats

28 stitches, 10 rows, 12 repeats

The samples were knit in “waste” yarns, and seamed on the machine;  if turned purl side out the latter is acceptable, or work could be flipped over and joined on the machine, bringing the join to the purl side; of course kitchener stitch is always the least visible but most time consuming option.  The green forms in the photo were knit using 8 repeats, the white ones 12)

Back to charting in Excel: knitting tams

tam 1: 6.5 sts and 9 rows per inch, 12 inch diameter, 12 gores, 38L, 30R

adjust for gauge:  mine below on bulky machine tension 3, ap 5 sts , 5.72 rs per inch, 10 gores, 26L, 20R

test swatch, if fewer rows are needed for head circumference formed on rt, first 2 rows may be skipped every third round or as needed, extra red rows on top may be added if additional width is needed to fit head comfortably

my hats in 2 different fibers, sizes M and L

going bulkier for an “urchin”: 2.5 sts, 5 rs per inch, 8 gores

step 1, HK, W = wrapped st

a way to size up, adding rows and sts

gauge may be hard to match even eon on bulky. HK version, flipped so as to knit increasing angle, no wrapping required with any of my yarns in this series, test swatches suggested

looking at it another way

in the above, the black represents knit stitches, arrows indicate direction of knit/ reading the chart, the yellow the unworked stitches in each row, no wraps; my sample was knit in garter stitch on size 11 needles, brim circumference = 21 inches

Programming for use of repeats on knitting machines (there are limitations based on gauge and machine model): black/colored squares represent knit stitches. When the machine is set to slip, those squares/punched holes will knit, while blank areas/non selected pattern needles will not, emulating holding techniques. Knit rows need to happen toward 2 row sections of charts, so that needles are “brought to hold” opposite the carriage;  KC (II, no end needle selection) row needs to start the carriage on the side opposite to the first such sequence. For example: in the charts for the balls the KC row would be from left to right, the first knit row from right to left, with the first set of needles to be “held” opposite the carriage on the second knit row. The principle is considered throughout, and the last row knit across all stitches will get the carriage back to the required position for beginning the sequence for the next segment. When knitting on the machine, if row counter tripper is turned off, the RC may be advanced manually as each wedge is finished. Tracing on the charts for such stitches, pretending to be knitting and following with a writing instrument the direction / movement of the carriage to each side helps to clarify the process and find possible errors or more needed rows prior to actual knitting.

If kitchener stitched together, finished hats will be reversible, may be worn in a variety of ways, and takes on a slightly different shape depending on which side is worn on the outside. An excellent series on kitchener stitch may be found on the TECHknitting blog

http://techknitting.blogspot.com/2007/05/easier-way-to-kitchener-stitch-also.html

http://techknitting.blogspot.com/2012/11/step-by-step-kitchener-stitching-with.html

http://techknitting.blogspot.com/2012/11/kitchener-stitching-grafting-with.html

http://techknitting.blogspot.com/2012/12/shaping-in-kitchener-row-useful-for.html

garter grafting video

if blocking of hat forms is required, plates may actually come in handy

if brim is too loose, work one or 2 rows of crochet or of knit rib to gather it in a bit

## Garter bar/ short row trim

A recent MK forum request for a HK trim look alike led me to the following experiment :

the hand knit trim

There are multiple ways to achieve knit and purl combinations on the KM. Brother garter carriage will do so “automatically” albeit slowly, ribbers may be used in combination with main beds, ladders may be latched up by hand, or one may use the garter bars to turn work over. When large widths are required the options are to use multiple panels, or to knit the fabric sideways letting the width become the length. Some HK fabrics are impractical if not impossible to duplicate on standard home knitting machines, and compromises are chosen. I tried to create a distant relative of the proposed trim, with a bit of family resemblance.

Below the  short section to my garter bar is pictured. I mark every 10 eyelets with nail polish on my GBs to help with tracking stitch counts (do same with centers of ribber combs). The photo shows it in the position in which it needs to be held to take stitches off the machine prior to turning them over. The hollows under the eyelets (1) provide room for the needle hooks to slip under the yarn and catch the stitches when work is flipped over. Hollows under eyelets occur on the side with the convex ridge (2). There are many online sources for using the bars, now available in multiple gauges, including an article by Susan Guagliumi.

my working graph

I worked my edging on multiple of 12 stitches. The purl/knit symbols represent how the knit will appear when viewed on side where held shape is convex. Work begins by knitting foundation rows, and using waste yarn at the start with open stitches on first row of knit if the ruffle is to be seamed/joined at its ends upon completion. The magenta/green rows represent respective whole rows to be turned to reverse side using the garter bar after each knitting sequence is completed. Testing first is required to establish the optimum stitch size for gauge that will allow for easy stitch movement in transferring stitches on and off the garter bar:

arrows on blue ground indicate position of KC at beginning of sequences

end knitting of first “purl” section COR, turn work over (magenta)

COL: knit one row across all stitches, carriage moves to right (pink). I find it easier after holding starts to move the carriage to opposite side by taking it physically off the machine and leaving settings alone, results in fewer yarn tangles and problems for me.

COR: set machine for hold except for first 2 stitches on right. I tried one stitch at a time first, but the wedge was too deep, so I began working bringing stitches to hold 2 at a time, carriage side first. Stitches could be held opposite the carriage as well, but that created a set of additional holes when one returns to knitting those stitches in the opposite direction, and a pointy edge  (segment marked with dot #2, more on a later post on miters and spirals). The number of stitches brought to hold can be varied as needed, the goal here is a symmetrical result.

COR: when only 2 needles at left are left in hold opposite carriage, knit an even number of rows (orange area, I chose to knit 4, then 6 rows in my test)

COR: when last 2 stitches on right have been knit for 2 rows (green) transfer all the stitches to garter bar

Get carriage to left, COL: return stitches to needles, knit for an odd number of rows (magenta,COR), turn work over

COL: knit one row across all stitches to right (pink)

COR: begin holding sequence again

I began the sample with 5 rows in between the mitered shapes, and then tried 11. This is labor intensive if produced in significant lengths, so a choice can be made depending on personal taste and patience. Though it could be attached as one knits the item it is intended to trim, there is enough going on I would probably estimate the length, take it off on waste yarn, and hang it onto the larger item. If longer, the trim may be unraveled to suit. If an addition is required it may be added on but at least working with the much larger bulk of materials will not be for the duration. Holding lever may be set to knit for single passes prior to turning work over in sections using holding, or stitches may be pushed into work by hand.

dot 1 rests on “killed acrylic”  repeat test, the remaining sample in knit in wool: dot 2 marks the extra holes when the holding sequence is changed   as described above

with five “purl” rows between turning and holding

11 “purl” rows between turning and holding

the reverse side

about half the wool portion of the ruffle was pressed, the knit became smoother, the edges less rolled. Those are properties that can become a design choice/decision

If an all stocking stitch ruffle serves the purpose this could be the start of the working repeat for using slip stitch to knit programmed needles selected to patterning position; here the black dots represent areas that knit, white squares stitches in holding. The repeat must be an even number of rows, using it as drawn starting side depends on whether one is using a punchcard machine or electronics

## Pleats: automating “pleating”, single bed

This post was originally written in 2013. I found myself reviewing it in 2018, and editing it with the intent to attempt a pleat sample using the Ayab interface. In those days I was using Intwined for some of my charts. The program has since been unsupported for Mac, without upgrades and a series of problems that led to my switching over to excel completely for my charts, and now to Numbers in the latest Mac OS.

I work primarily on multiple model Brother machines, in this instance the 910. Some of the information provided below may need tweaking for use in other brand KMs. “Automation” of some holding functions may be achieved using slip setting to knit required stitches. Below is the mylar sheet repeat used for my samples swatches. The setup is on working needles 21L, 19R, program for color reverse and twice the height; KCII (cancel end needle selection); first row needle selection from left to right, and with carriage ending on the right the first set of needles selected will be those that knit, the remaining bed will slip. This is opposite to the configuration familiar in holding, where needles out to E are held, those in B or D will knit (Brother needle position jumped the letter C, they are  A,B,D,E). In this type of knitting all needles in use on the bed should be cleared with each pass of the carriage.

I have gotten used to keeping programming numbers for  locations on mylar around a square to correspond to the lights surrounding the house icon on the 910, and worked with the following 2 options for my test swatches

In the samples below the first set of every other stitch/ black square in the increasing/decreasing angles were slipped on the non selected needles to create/mark the inner purl fold , the second set in the area that does straight knitting tucked on non selected needles to create/mark the knit outer fold. For the latter to occur, the cam buttons need to be switched to tuck <-> for 2 rows, and then back to slip <-> for the remaining knit repeat. Small holes are created at edges of slipped areas as miters are created, as would appear were the fabric created tthrough holding.

A: the alternate fold areas as they appear on the machine during knitting

the fabric after some casual steaming shown on the knit side, the pleating just about doubling on itself

B: with the added knit rows, the swatch before steaming

here is the purl side after some steaming showing the change in overlap

its knit side

both fabrics allowed to “hang”

The look may be varied considerably by changing the sequencing of the number of knit stitches, and the number of plain knit rows between the EON slipped or tucked ones. Electronics facilitate that, and with machines capable of accepting programming of the whole needle bed, there is even greater freedom. The sample above was knit loosely in acrylic, the holes would be less apparent in a tighter knit. If bothersome, they may in theory be “avoided” by factoring in “wrapping” if every row of the repeat is drawn rather than every other. With only 60 squares available on the mylar it is possible to go twice as wide and produce fabric width that may suffice for a skirt’s length. With software that allows for programming the width of the needle bed, possibilities expand even more. When going double wide with a repeat such as the one above, some  problems result not so much in the inner fold slipped rows, but in the outer fold of the tuck ones. As in nearly any knitting when needles have 2 side by side loops resting on them, these loops will create a float/ ladder, so the tuck rows will essentially behave like the slipped ones as the double loops are dropped rather than anchored on the subsequent pass of the carriage. In the configuration here if the double wide button is used, one way to solve that issue would be to bring consistently the same of either of the 2 non selected needles out to D or E position (still faster than hand selecting repeats by hand for holding), resulting in knit stitches and single tuck loops.

5/18/18  Working out the kinks: the same repeat redrawn to factor in reduction of the eyelets at edges of slipped areas: a partial graph showing “automatic wrap”. However, the “wrap” will fail with color reverse, and that first row would have only one stitch knitting. If double wide is used, then the wrap will happen around 2 needles, creating yet another “float”.

its color reverse

Plain knit rows (blanks on mylar) may be added at the bottom or top of the repeat to change pleat depth. Here is an amended repeat, discarding the “automatic wrap” idea, first prior to color reverse, then after

Those all blank rows would result in no stitches being knit, essentially a 2 row “free” carriage pass, and are removed. The repeat is  now also capable of being knit twice as wide if desired, adding the hand technique on tuck folds

Below the edited repeat begins design using one pixel per stitch and per row. “Automatic” wrap happens as one row is knit, while the next preselects an extra needle. The yarn travels under the extra needle prior to its being knit on the next pass from the opposite side. There will still be an eyelet, a bit larger than hand wrapping, but smaller than without any wrap at all. The EON pixels in the center of the shape are tucked. For that to happen the knit carriage needs to have the cam buttons switched from slip to tuck, and back to slip after the 2 row sequence. The fabric fold out to the knit side. The EON (every other needle) set at the top of the shape are knit is slip stitch setting, resulting in the fabric folding in to the purl side. Process could be reversed to have each fold to the opposite side of the knit.

The carriage needs to be on the opposite side of increases in the number of stitches worked. Here the first preselection row should be from left to right, with carriage traveling to and from right for the subsequent pairs of rows.

More variations: the slip stitch configuration below is changed to the same EON selection for 2 rows. The same could be done for the tuck fold. For this repeat, the first preselection row should be from right to left, making that the side the knit carriage returns to after each pair of rows knit. The sample was knit in a too thin acrylic. Both eyelets and their “wraps are visible, as well as the direction of folds.

These are pleats in a skirt made eons ago, that have retained the fold over the course of many a year

An added alternative for fold lines: create outside crease transferring EON to make a row of eyelets, create inside crease by knitting the desired row double row of  with 2 strands of  garment yarn. “Automatic” repeat must be adjusted accordingly, whether by re drawing or punching, or using cam settings for the correct stitch formation.

Seaming should be planned on the inner fold of the fabric, depending on whether the purl or knit side is used as the “public” side, the least visible join being one that is grafted ie with kitchener stitch.

The same principles may be applied to punchcard knitting but because the repeat size is 24 stitches the resulting fabric is one suitable for portions of garments/ accessories, in details such as ruffles and edgings. Punched holes would match the black squares in the color reversed repeats.  “Air” knitting helps determine exact needle location required , and to decide which side the first row must be selected prior to actual knitting. The image below shows the start of only one possible partial repeat based on the last one above

I usually sample my repeats by using hand selection and holding before committing to drawing on mylar or punching holes. The former are hard to get, the latter time consuming to punch, and “repairs” are more difficult when there are that many holes side by side. An even number of rows is required in this technique.

## Back to that pie: a bit of holding

Holding/ short rowing is used to knit each wedge. The basic rule for holding is followed: stitches are brought into work on the carriage side, and into hold opposite the carriage to avoid floats. The greater the number of sections, for either the full circle or a donut, the smoother the curves at the outer circumference, as can be imagined in the form below, which divided into more sections than those 5 in our original calculation.

The “pie slices” begin and end on open stitches, ultimately requiring a join where the radii meet, using whatever method is preferred by the knitter. Assuming the knit carriage is on left and set for hold in the diagrams below, if all stitches are brought into hold except 1 on the carriage side (or number required by calculations for the individual piece), 2 rows are knit, and action is repeated until all needles are in work, the following shape starts to fill in and a miter with pointed edges is created.

If all the needles are in work, and one begins to bring them into hold opposite the carriage, one begins to fill in the shape creating the form below, and a spiral is created, with circumference edges more rounded.

Like shapes may be stacked sequentially. If shaping at the top of the initial triangle wedge is reversed however,  the following begins to occur.

Knit rows in between the triangles begin to create larger holes in center of pie, and a donut occurs. The donut center can be varied, the knit rows between triangles increased to suit. The illustration below shows some of the variables. The plain knit rows are another factor in smoothing that outer circumference.

## Knitting math and pies

Math is non always fun, and is downright dreaded by some. One instance in knitting wherein basic calculations are required is in obtaining stitch and row gauges. I have known one hand knitter who would purchase yarn (not necessarily the one used in pattern), knit happily away, and try the finished product on everyone she knew until she found an accommodating body shape and size. If the large number of family and friends did not oblige, sweaters were stored until such a correct body appeared. Predictable results require careful measurements and some basic formula calculations.

Using home knitting machines to produce circular forms one resorts to breaking down the round object into pie wedges, which in turn are knit as triangles with straight line outer edges. The outer final circumference curve is controlled in a number of ways, one is by creating a far greater number of pie slices. For this exercise I will work with 5 segments.

There are some math constants. One example: to find the circumference of a circle its diameter is multiplied by pi = 3.14. If the diameter of our knit is 44 inches, its circumference will measure 44 X 3.14 = 138.16 inches. Using the rule of 5 or less than 5, this measurement is rounded to 138 inches.

The radius becomes the width of the pie wedge. In this instance, it would measure 22 inches. Let us assume our gauge is 4 stitches and 6 rows per inch. The radius is converted to stitches: 22 X 4 = 88 sts. The circumference becomes rows:  138 X 6 = 828 rs.  If subdivided into 5 slices, each slice would be composed of 166 rows.

To knit the pie slice, short row are used ; since they happen every 2 rows, our row number for outer edge is divided by 2, yielding the total of now 83, which in this exercise I will round off to the even # 84.