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Glasses placemat: choosing a page size

Julian D. A. Wiseman

Publication history: only at Usual disclaimer and copyright terms apply. Also see the main documentation at; the PostScript program itself; the documentation on how to use code in parameters; and, for PostScript programmers, the list of re-usable routines.


When creating a placemat, a page size and the page orientation must be chosen.

Before being clever, there is a question that is both basic and important: how competent is the person doing the printing? If not known to be competent, use the geographically appropriate of /A4 or /USL, spreading glasses over as many sheets as required. Otherwise you might arrive at the tasting and find your /A3 or /USLegal placemats shrunk down to A4 or US Letter. If the glasses are bigger than thimbles, this won’t work. (If the glasses are not bigger than thimbles, the tasting won’t work for a different reason!) So, before making an aesthetic decision, make the practical decision about the competence of the person doing the printing. Twice the author has been caught out by this: you be less trusting. Henceforth in this page it is assumed that the person doing the printing has the required basic competence.

Next, my answers. Is table space tight? If not, just use /A4: that’s 1×A4 up to six glasses; 2×A4 up to twelve; and 3×A4 up to eighteen. But it is trickier if table space is tight. In that case use /A3 for 13 or 14; and use a variant of that used on 9 March 2017 for 7 to 9, or for 15. If you have access to /USLegal = 14″×8½″, as I do, then use that for 7 or 8.

Or your choose for yourself. The following five diagrams show, for the five main page sizes with margins of 24pt = ⅓″ ≈ 8.5mm , the pattern that allows the largest circle. In faint grey on each image is, for easy comparison to glass sizes, the diameter in inches and millimetres. Choose a paper size to which you have access; measure the diameter of the glasses and add some finger space; compare to images; make a judgement about the number of glasses per page.

/A3 (420mm×297mm)
/A3 /Landscape, best arrangements
/USL2 (11″×17″)
/USL2 /Landscape, best arrangements
/USLegal (8½″×14″)
/USLegal /Portrait, best arrangements
/USL (8½″×11″)
/USL /Portrait, best arrangements
/A4 (210mm×297mm)
/A4 /Portrait, best arrangements


In the code paper size and orientation are specified thus:

/PaperType /A4 def  % /A4 /A3 /USL = 8.5"x11", /USLegal = 8.5"x14", /USL2 = 11"x17", [SmallerPts LargerPts]
/Orientation /Portrait def  % /Landscape /Portrait

Various page sizes are allowed including /A4, /A3, /USL (8½″×11″), /USLegal (8½″×14″), and /USL2 (11″×17″). PaperType can also be an array of length two, [a b], with 0 < a ≤ b, being paper of size a×b, measured in points (1 pt = 172″ = 0.01388″ = 127360 mm = 0.35277 mm) . Which of these page sizes should be chosen? That depends primarily on what paper sizes are available (North American or ISO), how many glasses there will be on each page, and how big are the glasses to be used.

The chart below shows the computed circle sizes, for the various pages sizes and possible classes of elements of PermittedPackingStyles. The left axis is the radius in points. On the right are written diameters, in millimetres and inches. All page sizes are assumed to have margins of 30 points = 512″ ≈ 0.42″ ≈ 10.6 mm. On the chart colours are pages sizes: — A4 in dark blue —; — A3 in light blue —; — US Letter = 8½″×11″ in red —; — US Legal = 8½″×14″ in brown —; and — US Ledger = 11″×17″ in orange —. The various marker shapes are the classes of elements of PermittedPackingStyles. The thick lines show the largest for each page size, these being reached or almost reached by the default value of PermittedPackingStyles. The thin lines are the values for /PostsAndLintel, assuming that the flag /CentralGlasses is at the default of 0.

In shades of grey are the boundaries for various glass sizes. The author owns many of the INAO/ISO 3591 tasting glass (excellent for port, Madeira, sherry, whisky), which has a radius of 30mm ≈ 85pt, so the diameter ≈ 2.36″. Other port enthusiasts own the IVDP glass designed by Álvaro Siza Vieira, which is of very similar shape and size except that the foot has a diameter of 72mm, so the radius is ≈ 102pt. But a circle radius of 85pt packs INAO glasses rather tightly, making it very awkward for fingers to extract a glass. So a recommended minimum radius is a little over a hundred points. Obviously larger glasses require a larger radius: measure, and add 15 to 20 points for fingers.

Radius as a function of number of glasses for several page sizes

Ready reckoner

— Julian D. A. Wiseman

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