☆ [`PostsAndLintel`, `Arch`](#PostsAndLintel_Arch) 

☆ [Columns and rows](#Sides_Rows) 

★ [`Array`](#Array) 

★ [Related parameters](#Related_parameters) 

★ [Code extracts](#Code_extracts)

The user specifies an array, `PackingStyles`, which is a list of generic packing styles.

In turn each style from the list is taken, and each allowed variation is tested.

If the element of `PackingStyles` is just the style, it doesn’t need to be in an array.

But the elements of `PackingStyles` can have constraints and variations.

```

This code has enough generality that it often finds the best, and when it can’t, its radius is not much smaller than the mathematical optimum.

E.g., for 14 glasses on `/A3` see discussion in [issue 151](http://github.com/jdaw1/placemat/issues/151).

For many possible tastings, `PackingStyles` can be left at its default value.

For example, if there are 24 different Madeiras over four `/A4` pages, the defaults work (though, of course, very important, don’t forget to invite [me](http://www.jdawiseman.com/author.html)).

But if table space were tight, it could be better to have fifteen on an `/A3`, six on an `/A4`, and three on the right side of an `/A4`, so lessening usage of table space from 4 × 210mm = 840mm per person to ≈ 3½ × 210mm = 735mm.

That would require changing [`GlassesOnSheets`](page_level.md#glassesonsheets-and-glassesontastingnotepages), and also changing the subject of this page, `PackingStyles`.

There follow descriptions and pictures of the various styles allowable in `PackingStyles`.

<a name="Efficient"></a>

<a name="RectangularDislocation"></a>

<div align="center">

`/SquareGrid` can be similar to `/RectangularDislocation`.

In `/SquareGrid` there is no dislocation, and by default the vertical and horizontal distances are the same and equal to the diameter.

Obviously either `/Justify` can allow distances to differ.

<div align="center">

<a name="DiamondsPlus"></a>

It is the best packing of seven or ten glasses on several paper sizes.

There is a generalisation of `/DiamondsPlus` over any number of rows (columns), [not yet coded](http://github.com/jdaw1/placemat/issues/38).

`/RectangularAlternateNudge`: in this rectangular variant, alternate rows (or columns) are slightly nudged, better to fill the space.

Thus `/RectangularAlternateNudge` is a small deviation away from greater symmetry, about which the the author is unenthusiastic.

This imposes an additional requirement: this packing style is chosen only if it is an improvement on the previous best radius of &ge;&nbsp;2pt &asymp;&nbsp;0.7mm &asymp;&nbsp;0.028&Prime;.

The next table of examples shows six glasses on `/USL` = 8&frac12;&Prime;&times;11&Prime; and on `/A4` = 210mm&times;297mm, in all cases with margins of 24pt = &#8531;&Prime; &asymp; 8.5mm, and space of 6pt &asymp; 2.1mm for the header.

<a name="RectangularAlternateSplitNudge"></a>

<div align="center">

`/Temple` is an intricate pattern, that has the largest radius for 10 glasses on `/USL`, and for 13 glasses on either `/USLegal` or `/Tabloid`.

<div align="center">

<a name="Sides_Rows"></a>

`/RightSide` (and, *mutatis mutandis*, `/LeftSide`) have a particular use.

Consider a tasting with 17 glasses.

The code then chooses the radius and separately scales the *x* and *y* directions such that things fit as snugly as possible, obviously subject to the other upper bounds on the radius.

The glass ordering is that given in the array: there is no subsequent sorting or ordering.

The first two elements are used, as before, and fix the radius and the canvas.

The circle at (*x*,*y*) is then moved in a straight line towards (*x'*,*y'*).

A circle stops moving if it collides with another circle (a tangential touch not being a collision); if it collides with the edge of the page; or it arrives at (*x'*,*y'*).

The difference is the movement of the circles at (2,2) and (4,2), both towards (3,2).

For the author&rsquo;s taste, the closer relationship of the two B0 circles (same wine in single and magnum) means they should be touching, rather than equally spaced between A0 and C0.

* `/Mirror`: the alternate chirality.

If there isn&rsquo;t a sensible meaning to this, ignored.

* `/ShoveLeft` and `/ShoveRight`: if there is spare space between the circles, probably because the radius has been shrunk to that on another sheet, the circles are shoved leftwards (or rightwards) against that margin.

But not heeded in every base style.

If these are in the front row, it is more fiddly to lower subsequent older vintages into place.

Adding `/PackingNestingColumnMajor true` fixes this.

* `/ProhibitVerticalNudging` or `/ProhibitHorizontalNudging`: have the obvious effect in base styles `/RectangularAlternateNudge` and `/RectangularAlternateSplitNudge`.

* `/TempleExtraColsToLeftOrRowsBelow int` chooses the position of the &lsquo;hole&rsquo; in `/Temple`.

* `/RowsNumMin int`, `/RowsNumMax int`: minimum or maximum number of rows permitted.

Relevant in the `/Diamonds`, `/RectangularDislocation`, `/SquareGrid`, `/RectangularAlternateNudge`, and `/PostsAndLintel` packing styles.

* `/GlassesDeemedAtLeast int`: the number of glasses is deemed to be the greater of this and <code>GlassesOnSheets&nbsp;<i>SheetNum</i>&nbsp;get&nbsp;length</code>. Say there are 17 glasses, to be spread over three `/A4` sheets 6:6:5.

* `/OnlyIfGlassesNumMin int`, `/OnlyIfGlassesNumMax int`: permitted number of glasses.

If breaching constraint, this packing specification not used.

* `/OnlyIfSheetNumMin int`, `/OnlyIfSheetNumMax int`: specifying permitted values for the internal variable `SheetNum`, which is `0` on the first sheet, `1` on the second, etc.

If `Orientation` not agreeing, this packing specification not used.

* `/ImprovementPointsMin num`, `/ImprovementProportionMin num`: this specification used only if beating previous best radius by the required amount, either absolute (e.g., `2`&nbsp;points) or as a proportion (e.g., `0.01`&nbsp;=&nbsp;1%).