In the above, the 1963 over Ck and Mz are clearly smaller than those over G and D; perhaps some form of proportion since the Mz and Ck are in a smaller font than G and D (being maximised to fit within circles), but it would look better if all the 1963s were the same size font. I don't know how the font size decision for the over-print of the year was determined (I haven't looked, to be fair); perhaps some additional form of control might already provide the capability to enforce a common font size for the 1963s since they are all the same and in the same size area, but if not then perhaps it might be a worthwhile addition.
Software that makes placemats
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- Dalva Golden White Colheita 1952
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Re: Software that makes placemats
In the latest placemats, why are the "1963" over the shipper different sizes?
Re: RE: Re: Software that makes placemats
It was wrong. I will investigate whether it was a user error or a programmer failure (same person; different roles) and suggest a plan, or just effect it.PhilW wrote:In the above, the 1963 over Ck and Mz are clearly smaller than those over G and D; perhaps some form of proportion since the Mz and Ck are in a smaller font than G and D (being maximised to fit within circles), but it would look better if all the 1963s were the same size font. I don't know how the font size decision for the over-print of the year was determined (I haven't looked, to be fair); perhaps some additional form of control might already provide the capability to enforce a common font size for the 1963s since they are all the same and in the same size area, but if not then perhaps it might be a worthwhile addition.
Re: Software that makes placemats
Instead ofit would have been better to do So it could be a user error.
But I think a change of default for FontSizesRatioAboveBelowOverMin would be advisable, fromtoSo it could be a programmer error.
A reminder: if font sizes are closer in ratio than FontSizesRatioAboveBelowOverMin (or, mutatis mutandis, FontSizesRatioTitlesMin, then they are set to be the same. It is, in ratio terms, the minimum difference in font size. These two parameters prevent there being many font sizes that differ only slightly.
Objections?
Code: Select all
/OvertitleMaxFontSizeProportionTitles 0.125 def
Code: Select all
/OvertitleMaxFontSizeProportionTitles 0.166666666 def
/FontSizesRatioAboveBelowOverMin 999 def
But I think a change of default for FontSizesRatioAboveBelowOverMin would be advisable, from
Code: Select all
/FontSizesRatioAboveBelowOverMin 2 sqrt sqrt def
Code: Select all
/FontSizesRatioAboveBelowOverMin 999 def
A reminder: if font sizes are closer in ratio than FontSizesRatioAboveBelowOverMin (or, mutatis mutandis, FontSizesRatioTitlesMin, then they are set to be the same. It is, in ratio terms, the minimum difference in font size. These two parameters prevent there being many font sizes that differ only slightly.
Objections?
Re: Software that makes placemats
Advice wanted on a technical problem, relating to the seed for PostScript’s random numbers, the seed being set with srand.
To fix some bugs and refactor code, each circle’s painting is surrounded by a rrand … srand pair, to put in the stack the current seed, and then to reset the random-number seed to that.
Discussion is happening about a forthcoming Cockburn vertical. The current draft of the placemats has the 1947 and 1967 as:
Observe that the layout of the stars look very similar, with a slight offset. (The eye might start at the top-right of the ‘7’s.) Indeed, relative to the centre of the circle, the stars are identically positioned. Is this:
• Perfection?
• Tolerable?
• Erroneous?
(I admit to dislike—hence this question.)
(Typo fixed.)
To fix some bugs and refactor code, each circle’s painting is surrounded by a rrand … srand pair, to put in the stack the current seed, and then to reset the random-number seed to that.
Discussion is happening about a forthcoming Cockburn vertical. The current draft of the placemats has the 1947 and 1967 as:


Observe that the layout of the stars look very similar, with a slight offset. (The eye might start at the top-right of the ‘7’s.) Indeed, relative to the centre of the circle, the stars are identically positioned. Is this:
• Perfection?
• Tolerable?
• Erroneous?
(I admit to dislike—hence this question.)
(Typo fixed.)
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- Dalva Golden White Colheita 1952
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Re: Software that makes placemats
Tolerable, though less than ideal. Why do you keep get/setting the seed, rather than simply setting it at the start of the script (presumably to a fixed value for determinism) and then just using rand throughout thereafter?
Re: Software that makes placemats
Because sometimes multiple passes of randomness need to be aligned. E.g., in Titles and Overtitles:

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- Dalva Golden White Colheita 1952
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Re: Software that makes placemats
"need"? no. "want"? perhaps - I would likely have compromised this one, and not chosen alignment for this, unless it turned out to look poor. With your chosen method you still should only need to cache and reseed while drawing the multiple aspects of a single circle, then continue (though this would place restrictions on the order in which you need to draw elements, or increase the seed cache-ing to one per circle, and then restore to subsequent afterwards, which might be the better route, depending on the currently implemented order of drawing of elements.
Re: Software that makes placemats
Disagree: this is a need.
Yes. And my question was whether I should. And the answers seems to be ‘yes’.PhilW wrote: ↑13:34 Sat 21 Jul 2018With your chosen method you still should only need to cache and reseed while drawing the multiple aspects of a single circle, then continue (though this would place restrictions on the order in which you need to draw elements, or increase the seed cache-ing to one per circle, and then restore to subsequent afterwards, which might be the better route, depending on the currently implemented order of drawing of elements.
Re: Software that makes placemats
I actually noticed the non-randomness of the 47 and 67 with merely a glance before reading the rest of the original post.
That said, I don't see it as a problem.
(The overtitles example looks bad to me, and not due to alignment. I would not put the pattern in the overtitle as it makes that word too difficult to read. Especially in the busy parts in 'pe' and 'ia'.)
That said, I don't see it as a problem.
(The overtitles example looks bad to me, and not due to alignment. I would not put the pattern in the overtitle as it makes that word too difficult to read. Especially in the busy parts in 'pe' and 'ia'.)
Glenn Elliott
Re: Software that makes placemats
Decision made: fixed.
That the fix has shortened the code by ten lines increases the likelihood that it was the right thing to do.
That the fix has shortened the code by ten lines increases the likelihood that it was the right thing to do.
Re: Software that makes placemats
Julian - Thomas V over on FTLOP has posted that the ps to pdf converter seems to no longer function with a placemat .ps file. Any ideas what's happened? I suspect the converter is doing something different and doesn't like something in the .ps file. The converter at www.ps2pdf.com also seems to have stopped giving a log which is a bit unhelpful for figuring out the issue.
Re: Software that makes placemats
Link to Thomas V’s comment. I’ve asked the PS➝PDF folks for help.
Re: Software that makes placemats
Posted with permission.Mike Hugo wrote:I've sold the ps2pdf.com domain and it is now being run by someone else.
I continue to keep the old service as ps2pdf.org.
I'm not even sure how your email made it to me as the new owner should be receiving email for the dot com domain but perhaps has not updated something.
When I take the document and convert it at ps2pdf.org it does produce a document.
This document also causes my security wrapper to generate a pile of output as this file includes a bunch of code in it that causes the converter to block certain transactions that the file is trying to do. It still creates a final pdf .
Feel free to link to the ps2pdf.org site.
Re: Software that makes placemats
Many thanks Julian.
Re: Software that makes placemats
I agree with this, the pattern in the over label is completely distracting when placed over the vintage stars.
The vintage stars themselves I find a little too cluttered for the overall appearance that I'm distracted with the fill and not the vintage date itself.
Disclosure: Distributor of Quevedo wines and Quinta do Gomariz
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- Dalva Golden White Colheita 1952
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Re: Software that makes placemats
Or just using a different shape from the options available; I think gman was saying he didn't like that particular fill, and I'm sure we all have our preferences and dislikes in that regard (and false is already the default for /ShapesInTitles in the current placemat.ps anyway, for anyone wondering).
In agreement with the above view, though I realise this is in disagreement with author preference.
Note that there is an equivalent /ShapesInOvertitles parameter, and indeed equivalents for /ShapesInAbovetitles, /ShapesInBelowtitles and /ShapesInPlacenames (noting the latter has missing { } brackets in the definition compared with the peer definitions). These currently all default to be the same as /ShapesInOvertitles but can be changed by the user, so those of us who prefer not to have the pattern in the overtitles can easily change this.
Re: Software that makes placemats
Note ‘latter’ of two; ‘last’ of three or more.
Geek note: /ShapesInPlaceNames ShapesInTitles def works naturally if ShapesInTitles is a Boolean constant. But if ShapesInTitles is code referencing the likes of WithinTitles, that would fail if referenced in ShapesInPlaceNames. The absence of brackets causes it to fail earlier, and more traceably. So the absence of {} was deliberate.
Re: Software that makes placemats
As requested:




Re: Software that makes placemats
Fabulous. Thank you.



Re: Software that makes placemats
Anybody else?
Please specify pattern, the number of columns (so far everybody has five), and the number of rows (so far everybody has one).
From the Manual:
Please specify pattern, the number of columns (so far everybody has five), and the number of rows (so far everybody has one).
From the Manual:
/Alternating
/Sideways
/Upright
Re: Software that makes placemats
Yes please, alternating.
Re: Software that makes placemats
From the current code:
Code: Select all
/TastingNotesStarsNameColsRowsArrangement % (ASCIIfied Name) NumCols NumRows /Alternating|/Sideways|/Upright
[
(DRT) 5 1 /Upright (Derek T.) 4 copy pop
(WPS) 5 1 /Sideways (Wolfgang S.) 4 copy pop
(PW) 5 1 /Sideways (Phil W.) 4 copy pop
(DJ) 5 1 /Sideways (Daniel J.) 4 copy pop
(IDJ) 5 1 /Alternating (Ian J.) 4 copy pop
(DRL) 5 1 /Alternating (Dave L.) 4 copy pop
(TC) 5 1 /Alternating (Tony C.) 4 copy pop
(MPM) 5 1 /Alternating (Mike M.) 4 copy pop
] def % /TastingNotesStarsNameColsRowsArrangement
Re: Software that makes placemats
Geeks might be interested in the comp.lang.postscript thread Mathematical functions as a single Bézier cubic, as used in the Spirals feature (which, note to self, I need to document).
Re: Software that makes placemats
For the few who care, HeapSort has been replaced by ShellSort, with gap sequence 1 2 5 11 23 51 113 247 541 1189 2617 5761 12671 27877 61331 134933 296843 653057 1436731 3160811 6953783 15298321 33656309 74043881 162896543 358372411 788419321 1734522497, each being the nearest to 2.2× previous, subject to being coprime to all previous except 1. (Of course, as the maximum array length in most implementations of PostScript is 65535, usually only the bolded gaps are relevant.)
Code for both, and a speed comparison, is in ShellSort_HeapSort.ps. It seems that ShellSort is better for arrays of length ≤ 216−1, but the extent of the advantage diminishes with length. So it may well be that for arrays of length millions or billions, HeapSort is better. But for arrays as short as PostScript’s longest, ShellSort seems to be faster.
Code for both, and a speed comparison, is in ShellSort_HeapSort.ps. It seems that ShellSort is better for arrays of length ≤ 216−1, but the extent of the advantage diminishes with length. So it may well be that for arrays of length millions or billions, HeapSort is better. But for arrays as short as PostScript’s longest, ShellSort seems to be faster.
Re: Software that makes placemats
There have been few instances of old versions being printed, perhaps because of caching problems.
One solution — rejected here — would be to have many separate file names. I dislike that, because I don’t want many versions existing after, and I want a single canonical-seeming file name.
A different technique is something I don’t know how to do. In the PDF, presumably added via pdfmark, could be something like the following pseudocode:
Do any readers of thread 175 know how to implement this in a PDF? Advice and guidance welcomed.
Edit, Aug 2021: also asked in github.com/jdaw1/placemat/issues/152, and on comp.lang.postscript.
One solution — rejected here — would be to have many separate file names. I dislike that, because I don’t want many versions existing after, and I want a single canonical-seeming file name.
A different technique is something I don’t know how to do. In the PDF, presumably added via pdfmark, could be something like the following pseudocode:
Code: Select all
On Open
{
If Today ≤ HardWiredDateConstantBeingDateOfTasting
{
MessageBoxPopUp
string="This version HardWiredStringConstant: check that is latest with a force-reload."
Buttons={"OK, checked"}
}
}
Edit, Aug 2021: also asked in github.com/jdaw1/placemat/issues/152, and on comp.lang.postscript.
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- Warre’s Otima 10 year old Tawny
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Re: Software that makes placemats
I used the placemats last night for a small tasting among a few physicists. Naturally, we decided to have field lines drawn on. I noted in the manual that Julian is displeased by these and whilst they are good for the majority of the page, some of the lines are non-physical (as circled).
Problems i foresee. How on earth do you,
1. Interpolate in PS
2. Differentiate in PS
3. Use PS
For my work I use Mathematica and its fantastic library of simple to use mathematical functions.
We then went on to discuss how we would do it ourselves (and is a similar method to how I create electric field simulations for trapped ions) . We believe the best option would be to treat each circle as a point charge and then create a potential map (i.e calculate the voltage across the sheet as superposition of each charge) for the entire sheet. From this grid, we can then perform some numerical differentiation (ideally if the point like nature is interpolated with a "reasonable order" function) to create a vector field (which would correspond to the electric field lines). As for visualization, the field lines would be the back-most image and the tasting circles would terminate drawing of lines such that the point charge wouldn't been seen. Problems i foresee. How on earth do you,
1. Interpolate in PS
2. Differentiate in PS
3. Use PS
For my work I use Mathematica and its fantastic library of simple to use mathematical functions.
Re: Software that makes placemats
• I dislike the whole Rays algorithm. Despite the previous discussion of it way back in summer 2013.
• You say that each circle should be a “point charge”. I suspect that aesthetically that wouldn’t work with the very strong circle motif. The lines need to leave the bounding circle, not a point charge within it. (But each circle cannot be a perfect conductor, as they touch, so would all be at the same charge.)
• Interpolate in Postscript … Differentiate in Postscript. Ans: do the work in Mathematica. Then output it in PostScript. Doh!(Did you really think that the Temple calculations currently in lines 4918–4950 of the code were written by hand?)
• You say that each circle should be a “point charge”. I suspect that aesthetically that wouldn’t work with the very strong circle motif. The lines need to leave the bounding circle, not a point charge within it. (But each circle cannot be a perfect conductor, as they touch, so would all be at the same charge.)
• Interpolate in Postscript … Differentiate in Postscript. Ans: do the work in Mathematica. Then output it in PostScript. Doh!
Code: Select all
(* PostScriptForm — this version of Jan 2019. *)
(* \
PostScriptForm[] *)
(*
\
http://mathematica.stackexchange.com/questions/101954/postscriptform-\
or-forthform
http://mathematica.stackexchange.com/questions/102894/multi-case-\
function-many-single-case-delayed-assignments-or-one-which
*)
Remove[PostScriptForm];
PostScriptForm[thing_Rational] :=
If[Abs[Denominator[
thing]/(2^IntegerExponent[Denominator[thing], 2])/(5^
IntegerExponent[Denominator[thing], 5])] == 1,
ToString[N[thing, 20], InputForm, NumberMarks -> False],
PostScriptForm[Numerator[thing]] <> " " <>
PostScriptForm[Denominator[thing]] <> " div"];
PostScriptForm[thing_?AtomQ] := ToString[thing];
PostScriptForm[thing_List] :=
StringJoin @@ Riffle[Map[PostScriptForm, thing], "\r\n"];
PostScriptForm[MatrixForm[thing_]] := PostScriptForm[thing];
PostScriptForm[Times[-1, thing_]] :=
StringJoin[PostScriptForm[thing], " neg"];
PostScriptForm[thing_Power] := (
psExponent := Which[
# > 5 && Divisible[#, 3],
psExponent[#/3] <> " dup dup mul mul",
# >= 5 && OddQ[#],
"dup " <> psExponent[(# - 1)/2] <> " dup mul mul" ,
# >= 4 && EvenQ[#], psExponent[#/2] <> " dup mul",
# == 3, "dup dup mul mul",
# == 2, "dup mul",
# == 1/2, "sqrt",
# == 3/2, "dup sqrt mul",
# < 0, psExponent[-#] <> " 1 exch div",
(Rational === Head[#]) && (Log[2, # // Denominator] //
IntegerQ), psExponent[Simplify[2 #]] <> " sqrt",
Not[IntegerQ[#]], PostScriptForm[#] <> " exp",
# == 1, "",
True,
" !!!\[Bullet]\[Bullet]\[Bullet]Error with exponent = " <>
ToString[#] <> "\[Bullet]\[Bullet]\[Bullet]!!! "
] &;
Which[
thing[[2]] > 0 || Not[IntegerQ[thing[[2]]]],
PostScriptForm[thing[[1]]] <> " " <> psExponent[thing[[2]]],
thing[[2]] == -1, "1 " <> PostScriptForm[thing[[1]]] <> " div",
thing[[2]] == 0, "1",
True,
"1 " <> PostScriptForm[thing[[1]]] <> " " <>
psExponent[-thing[[2]]] <> " div"
]);
PostScriptForm[thing_Times] :=
StringJoin@
Riffle[Reap[
If[MatchQ[thing[[1]],
Power[_,
n_Integer /; n < 0]], (Sow[
"1 " <> PostScriptForm[thing[[1, 1]]] <> " div"];), (Sow[
PostScriptForm[thing[[1]]]];)];
Map[(If[MatchQ[#,
Power[_,
n_Integer /; n < 0]], (Sow[
PostScriptForm[#[[1]]^(-#[[2]])] <> " div"];), (Sow[
PostScriptForm[#] <> " mul"]; )]) &,
Drop[List @@ thing, 1]]][[2, 1]], " "];
PostScriptForm[thing_Plus] :=
StringJoin @@ If[FreeQ[thing, _^n_],
(* Simple expression, no powers,
to be summed one item at a time *)
Module[{i},
i =
Position[thing, Except[Times[-1, _] | (_?Negative)], 1,
Heads -> False];
If[Length[i] > 0,
i = i[[1, 1]], (i =
Position[thing, Not[MatchQ[#, Times[-1, _]]] &, 1,
Heads -> False]; i = If[Length[i] > 0, i[[1, 1]], 1])];
Prepend[
Map[(" " <>
Replace[#, {(n_Integer /; n < 0 :>
ToString[-n] <> " sub"), (Times[-1, _] :>
PostScriptForm[Times @@ Drop[#, 1]] <> " sub"), (Times[
n_ /; n < 0, _] :>
PostScriptForm[Times @@ Drop[#, 1]] <> " " <>
ToString[-#[[1]]] <> " mul sub"), (Times[
n_ /; n > 0, _] :>
PostScriptForm[Times @@ Drop[#, 1]] <> " " <>
ToString[#[[1]]] <> " mul add"), (_ :>
PostScriptForm[#] <> " add")}]) &,
Drop[List @@ thing, {i}]],
Replace[thing[[
i]], {Times[-1, _] :>
PostScriptForm[-thing[[i]]] <> " neg", _ :>
PostScriptForm[thing[[i]]]}]] ],
(* Polynomial *)
Module[{vars, exps, v, rcl, i, firstMul},
vars = Variables[thing];
exps = Exponent[thing, vars];
v =
Select[Transpose[{vars, exps}], (#[[2]] == Max @@ exps) &][[1,
1]];
rcl = Reverse[Map[Factor, CoefficientList[thing, v]]];
Reap[
i = 1; firstMul = True;
If[rcl[[1]] =!= 1, Sow[PostScriptForm[rcl[[1]]]]];
Map[
If[# === 0,
i++, (Sow[
If[firstMul && rcl[[1]] === 1, PostScriptForm[v^i] <> " ",
" " <> PostScriptForm[v^i] <> " mul "] <>
If[MatchQ[#, (Times[_?Negative, _] | (_?Negative))],
PostScriptForm[-#] <> " sub",
PostScriptForm[#] <> " add"]]; i = 1;
firstMul = False)] &, Drop[rcl, 1]];
If[i > 1, Sow[" " <> PostScriptForm[v^(i - 1)] <> " mul "]];
][[2, 1]]
]];
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- Warre’s Otima 10 year old Tawny
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Re: Software that makes placemats
So I had a quick play (please ignore the asymmetrical crimes against mathematics) around in mathematica doing a point charge simulation, see below for results. Depending on how the circle is placed over, I think it would look ok?
I like the idea of doing it in Mathematica. I presume this is some sort of language converter?
I like the idea of doing it in Mathematica. I presume this is some sort of language converter?
Re: Software that makes placemats
Interesting. What charge did you give each point? By what algorithm should the charges be chosen? And please post the code that made the diagram.
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Re: Software that makes placemats
Below is the code I used. I've changed things slightly so that it can all be solved analytically. Firstly, we define a series of vectors in circlepos which correspond to x,y and charge respectively. Set these however you please (I'd suggest arranging as a n/quadrupole- only because of the work i do https://en.wikipedia.org/wiki/Quadrupole_ion_trap) . The function pot[] then calculates the potential (analytically). This is then summed over all potentials and differentiated in both x and y to produce the field in said directions. StreamPlot is then used to visualise it.
Code: Select all
circlepos = {{1, 1, 1}, {1, 2, -1}, {2, 1, 1}, {2, 2, -1}};
p1 = ListPlot[circlepos, PlotRange -> {{0, 3}, {0, 3}}];
pot[x_, y_, qx_, qy_, q_] := q/Sqrt[(x - qx)^2 + (y - qy)^2]
potgridx[x_, y_] =
D[Total[Table[
pot[x, y, circlepos[[i, 1]], circlepos[[i, 2]],
circlepos[[i, 3]]], {i, 1, Length[circlepos]}]], x];
potgridy[x_, y_] =
D[Total[Table[
pot[x, y, circlepos[[i, 1]], circlepos[[i, 2]],
circlepos[[i, 3]]], {i, 1, Length[circlepos]}]], y];
p2 = StreamPlot[{potgridx[x, y], potgridy[x, y]}, {x, 0, 2.5}, {y, 0,
2.5}];
Show[p1, p2]
Re: Software that makes placemats
Yes. Converts basic expressions to (slightly) idiomatic PostScript. Typical use case is a polynomial to be solved: it converts the CoefficientList, which is then passed to a PostScript polynomial solver.
E.g.: PostScriptForm[(a + Sqrt[b])^15] ➝ a b sqrt add dup dup mul dup mul mul dup dup mul mul
Your approach is well suited to circles in a rectangular grid. Not so much in a hexagonal grid. E.g.:
Code: Select all
circlepos = {
{0, 1, 1},
{Sqrt[3.]/2, 0.5, -1},
{Sqrt[3.]/2, -0.5, 1},
{0, -1, -1},
{-Sqrt[3.]/2, -0.5, 1},
{-Sqrt[3.]/2, 0.5, -1},
{0, 0, 1}
};
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- Warre’s Otima 10 year old Tawny
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Re: Software that makes placemats
Love it.
Fixed.jdaw1 wrote: ↑20:04 Mon 17 Jun 2019
Your approach is well suited to circles in a rectangular grid. Not so much in a hexagonal grid. E.g.:Code: Select all
circlepos = { {0, 1, 1}, {Sqrt[3.]/2, 0.5, -1}, {Sqrt[3.]/2, -0.5, 1}, {0, -1, -1}, {-Sqrt[3.]/2, -0.5, 1}, {-Sqrt[3.]/2, 0.5, -1}, {0, 0, 1} };
Code: Select all
circlevec = {{0, 1, 1}, {Sqrt[3.]/2, 0.5, -1}, {Sqrt[3.]/2, -0.5,
1}, {0, -1, -1}, {-Sqrt[3.]/2, -0.5, 1}, {-Sqrt[3.]/2,
0.5, -1}, {0, 0, 1}};
circlepos =
Table[{circlevec[[i, 1]], circlevec[[i, 2]]}, {i, 1,
Length[circlevec]}];
p1 = ListPlot[circlepos, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}},
PlotMarkers -> {Automatic, Large}];
pot[x_, y_, qx_, qy_, q_] := q/Sqrt[(x - qx)^2 + (y - qy)^2]
potgridx[x_, y_] =
D[Total[Table[
pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]],
circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], x];
potgridy[x_, y_] =
D[Total[Table[
pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]],
circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], y];
p2 = StreamPlot[{potgridx[x, y], potgridy[x, y]}, {x, -2.5,
2.5}, {y, -2.5, 2.5}];
Show[p1, p2]
Re: Software that makes placemats
So do I, but perhaps more for its wilful stubbornness than its practicality.
Hmm. Bug or feature?
• The points south, east-by-north-east and west-by-north-west relate well to the central circle.
• But the points north, east-by-south-east and west-by-south-west do not connect to the central circle at all.
For my palate, this is an offence to symmetry. There’s no a priori reason for the central circle to exhibit such favouritism. You’re trying to squeeze a 2ⁿ pattern into a shape divisible by three, and I think it doesn’t fit.
Others: please take sides.
Some circle arrangements to consider (ignore the decorations):
- 11 June 2019 (14 on /A3);
- 26 Mar 2019 (15 on /A3);
- 13 Feb 2019 (5 on /A4);
- 01 Dec 2018 (6 on /A4);
- 02 Oct 2018 (13 on /A3);
- 10 Oct 2017 (14 on /A3);
- 01 Feb 2017 (9|11 on /A3);
- 24 Feb 2016 (24 on trimmed /A2).








I repeat:
Display: inside the circles is different to outside. Perhaps it should be shown inside faded 60%; and outside at full strength? Comment and recommendation welcomed.
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- Warre’s Otima 10 year old Tawny
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Re: Software that makes placemats
Obviously a feature.
With the asymmetry, it is bothering me too. I have a suspicion that it's because we're working up against imperfect machine precision. If you plot symmetries in along one plane, you might notice there's a field preference to one side. Perhaps the numbers will have to be adjusted so that they can be positions with exact machine precision? I'll have a play and see what I can muster up.
I'll have a look at some previous placemats soon, see what can be made.
As for the algorithm, I'm really not sure. At least there is a flexibility to have any charge (or even strength of charge for that extra special something).
With the asymmetry, it is bothering me too. I have a suspicion that it's because we're working up against imperfect machine precision. If you plot symmetries in along one plane, you might notice there's a field preference to one side. Perhaps the numbers will have to be adjusted so that they can be positions with exact machine precision? I'll have a play and see what I can muster up.
I'll have a look at some previous placemats soon, see what can be made.
As for the algorithm, I'm really not sure. At least there is a flexibility to have any charge (or even strength of charge for that extra special something).
Re: Software that makes placemats
FYI, the only floating-point precision in PostScript is single: 23-bit mantissa ≈ one part in eight million; 8 bits exponent so maximum value ≈ ±10³⁸.
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- Warre’s Otima 10 year old Tawny
- Posts: 556
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Re: Software that makes placemats
Ok, I will try zeroing at 2^-23.
I also had a little play with some other fun field related plots (whilst trying to diagnose). Whilst just a first attempt, and numbers will have to be fudged to make it look better, Plotted using
Code: Select all
ContourPlot[
Log[Total[
Table[pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]],
circlevec[[i, 3]]], {i, 1, Length[circlevec]}]]], {x, -2.5,
2.5}, {y, -2.5, 2.5}, Contours -> 20]
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- Dalva Golden White Colheita 1952
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Re: Software that makes placemats
From the imagery, would I be correct in thinking that each point represents a certain positive or negative charge, and therefore that the reason some points connect to others while others pairs to not is that essentially we are only seeing lines between points of opposite (or different) charge? If so, some variation from binary charge setting would enable alternate maps with all points connecting, though would be potentially difficult to keep regular and symmetrical for all designs without specific rules.
Based on the above, but varying slightly, would making the centre of all circles could be a positive charge, and then placing negative charges between (either in the spaces or the mid-point between adjacent circles) might provide a more fully-connected and symmetric output, though I can't picture whether that might become too linear.
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- Warre’s Otima 10 year old Tawny
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Re: Software that makes placemats
Good idea. I also changed circlepos to a different hexagonal lattice..PhilW wrote: ↑07:20 Tue 18 Jun 2019 From the imagery, would I be correct in thinking that each point represents a certain positive or negative charge, and therefore that the reason some points connect to others while others pairs to not is that essentially we are only seeing lines between points of opposite (or different) charge? If so, some variation from binary charge setting would enable alternate maps with all points connecting, though would be potentially difficult to keep regular and symmetrical for all designs without specific rules.
Based on the above, but varying slightly, would making the centre of all circles could be a positive charge, and then placing negative charges between (either in the spaces or the mid-point between adjacent circles) might provide a more fully-connected and symmetric output, though I can't picture whether that might become too linear.
Code: Select all
{{0, 2 Sqrt[2], -1}, {Sqrt[2], Sqrt[2], -1}, {-Sqrt[2],
Sqrt[2], -1}, {0, -2 Sqrt[2], -1}, {-Sqrt[2], -Sqrt[2], -1}, {Sqrt[
2], -Sqrt[2], -1}, {0, 0, 1}}
- Attachments
-
- hexclosepacked.png (152.29 KiB) Viewed 50916 times
Re: Software that makes placemats
Charges good. Because circles touch, hexagonal was better.
How to generalise the charges it to fit
For this type of layout, might a triangle tesselation with charges {⅓,⅔,1} be correct?
Code: Select all
circlevec = {
{0, 1, 1},
{Sqrt[3.]/2, 0.5, 1/3},
{Sqrt[3.]/2, -0.5, 1},
{0, -1, 1/3},
{-Sqrt[3.]/2, -0.5, 1},
{-Sqrt[3.]/2, 0.5, 1/3},
{0, 0, 2/3}
};
p1 = Map[Graphics[{Red, Thick, Circle[{#[[1]], #[[2]]}, 0.5]}] &, circlevec[[All, 1 ;; 2]]];
pot[x_, y_, qx_, qy_, q_] := q/Sqrt[(x - qx)^2 + (y - qy)^2];
potgridx[x_, y_] =
D[Total[Table[
pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]],
circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], x];
potgridy[x_, y_] =
D[Total[Table[
pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]],
circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], y];
p2 = StreamPlot[{potgridx[x, y], potgridy[x, y]}, {x, -1.6,
1.6}, {y, -1.6, 1.6}];
Show[p1, p2, AspectRatio -> 1]

(Alas my Mathematica v9 can’t specify StreamMarkers -> "Segment".)
Re: Software that makes placemats
Edited Wed 19th June to rename Dists ➝ Pot. Please, no jokes.
Possible algorithm for assigning charges
Circles either have a charge assigned (hurray!), which is one of {1,2,3}. Or don’t yet, in which case deemed charge is 0.
Repeatedly we’ll compute, for circle i, Poti0, Poti1, Poti2, and Poti3.
Potik ≡ ∑j ( (xi − xj)² + (yi − yj)² )⁻¹ where j≠i and circle j has charge k.
Pick of the i with no assigned charge the largest value of Poti0÷1024 + Poti1 + Poti2 + Poti3
Assign to it the the charge {3,1,2} according to whichever is smallest of Poti3, Poti1, Poti2, with ties being resolved in that order.
Repeat until all charges assigned.
Observe: easy to code; O(n³) which is acceptable with n≤24; effectively maximises distance between similar charges; starts in centre and chooses circles adjacent to those with known charge, working outwards.
Good? Bad? Improvements?
(But I still have no idea how to compute the streams. Help!)
Possible algorithm for assigning charges
Circles either have a charge assigned (hurray!), which is one of {1,2,3}. Or don’t yet, in which case deemed charge is 0.
Repeatedly we’ll compute, for circle i, Poti0, Poti1, Poti2, and Poti3.
Potik ≡ ∑j ( (xi − xj)² + (yi − yj)² )⁻¹ where j≠i and circle j has charge k.
Pick of the i with no assigned charge the largest value of Poti0÷1024 + Poti1 + Poti2 + Poti3
Assign to it the the charge {3,1,2} according to whichever is smallest of Poti3, Poti1, Poti2, with ties being resolved in that order.
Repeat until all charges assigned.
Observe: easy to code; O(n³) which is acceptable with n≤24; effectively maximises distance between similar charges; starts in centre and chooses circles adjacent to those with known charge, working outwards.
Good? Bad? Improvements?
(But I still have no idea how to compute the streams. Help!)
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- Warre’s Otima 10 year old Tawny
- Posts: 556
- Joined: 20:42 Tue 13 Nov 2018
- Location: Three Bridges
Re: Software that makes placemats
I never said it was an efficient packing

As for you algorithm, it seems good. I think seeing it in action will let us know how well it looks.
For manually making a StreamPlot (I think this is what you meant?) I imagine that will be tougher. What I suggest is that we...
1. Create field seed spots at the edges of the circles (at whatever density we decide).
2. At that point, we have a vector (from potgridx and potgridy) telling us where the field goes next.
3. Follow that on some small distance (there is definitely a mathematical way of determining how small this distance is - I cant' remember however).
4. Return back to step 2 until you're off the mat or in another circle.
5. Fit a curve to each trace.
I'm a touch busy atm with pesky thesis writing (we'll forget about a week in Provence coming soon) but if I get some time, I can try have a play with it.
Re: Software that makes placemats
I am absolutely sure it will be very tricky.
Or choose seed points in a small circle around a charge, perhaps every 15°. Flow uphill. But those won’t arrive at even angles at other charges, nor at even distances at edge. Then what? I don’t know.
Also, can the flow uphill be ‘locally’ analytic? If it could be known quite well over a moderate distance, that could be converted to a single Bézier cubic using ApproximatingCurve.
- Alex Bridgeman
- Fonseca 1966
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- Joined: 12:41 Mon 25 Jun 2007
- Location: Berkshire, UK
Re: Software that makes placemats
Sorry? Did someone say something?
Wake me up when it's over and someone can explain in English what just happened...
Top Ports in 2023: Taylor 1896 Colheita, b. 2021. A perfect Port.
2024: Niepoort 1900 Colheita, b.1971. A near perfect Port.
2024: Niepoort 1900 Colheita, b.1971. A near perfect Port.
Re: Software that makes placemats
Test implementation of the charge assignment: output looks good — nearby circles have different charges; PostScript code follows.jdaw1 wrote: ↑22:17 Tue 18 Jun 2019Possible algorithm for assigning charges
Circles either have a charge assigned (hurray!), which is one of {1,2,3}. Or don’t yet, in which case deemed charge is 0.
Repeatedly we’ll compute, for circle i, Poti0, Poti1, Poti2, and Poti3.
Potik ≡ ∑j ( (xi − xj)² + (yi − yj)² )⁻¹ where j≠i and circle j has charge k.
Pick of the i with no assigned charge the largest value of Poti0÷1024 + Poti1 + Poti2 + Poti3
Assign to it the the charge {3,1,2} according to whichever is smallest of Poti3, Poti1, Poti2, with ties being resolved in that order.
Repeat until all charges assigned.
Code: Select all
/ParametersVersionDateTimeAdobeFormat (D:201906202330) def
/Circlearrays [ [/lozenge] 15 {dup} repeat pop ] def
/Titles [ ( ) 15 {dup} repeat pop ] def
/Belowtitles [ Titles length {()} repeat ] def
/Names [
(JDAW)
] def
/HeadersLeft [
0 [(Assigning charges: a test)]
] def % /HeadersLeft
/HeadersCenter [
] def % /HeadersCenter
/HeadersRight [
0
{ExternalLinks 2 get}
] def % /HeadersRight
/ExternalLinks [ % Array, length a multiple of three: indented0-boolean, (Descriptor0), (http://URL0), indented1-boolean, (Descriptor1), (http://URL1), ...
false (Thread on ThePortForum.com) (http://www.theportforum.com/viewtopic.php?t=175&start=1136#p112232)
false (Algorithm on ThePortForum.com) (http://www.theportforum.com/viewtopic.php?p=112250#p112250)
false (Latest version this placemat) (http://www.jdawiseman.com/papers/2019/20190620_Charges.pdf)
] def % /ExternalLinks
/VoteRecorders false def
/CorkDisplayNumCopies 0 def
/NeckTagsNumCopies 0 def
/DecantingNotesNumCopies 0 def
/TastingNotePagesNumCopies 0 def
/PaperType { [ /A3 /A4 dup dup dup /A3 dup dup dup] SheetNum get } def
/Orientation {SheetNum 1 eq SheetNum 2 eq or {/Portrait} {/Landscape} ifelse} def % /Landscape /Portrait
/GlassesOnSheets [
[ 7 5 6 5 7 11 13 14 15 ]
{ [ exch 0 exch 1 exch 1 sub {} for ] }
forall
] def % /GlassesOnSheets
/ShrinkRadii /NotAtAll def % /NotAtAll | /ToSmallest | /ToSmallestSamePageOrdering | array denoting equivalence classes
/PackingStyles [
[ /RectangularDislocation /OnlyIfSheetNumMin 1 ]
[ /Diamonds /OnlyIfSheetNumMin 1 ]
[ /DiamondsAndRectangular /OnlyIfSheetNumMin 1 ]
[ /Bespoke5 /OnlyIfOrientation /Landscape /OnlyIfSheetNumMin 1 ]
[ /Bespoke7 /OnlyIfOrientation /Landscape/OnlyIfSheetNumMin 1 ]
[ /RectangularAlternateSplitNudge /OnlyIfSheetNumMin 1 /ImprovementPointsMin 2 ]
[ /DiamondsPlus /OnlyIfOrientation /Portrait /OnlyIfSheetNumMin 1 ]
[ /DiamondsPlus /OnlyIfOrientation /Landscape /OnlyIfSheetNumMin 1 /ImprovementPointsMin 2 ]
[ /RectangularAlternateNudge /OnlyIfSheetNumMin 1 /ImprovementPointsMin 2 ]
[ /Arch /CentralGlasses 1 /GlassesNumMin 6 /OnlyIfOrientation /Landscape ]
] def % /PackingStyles
/PaintBackgroundCode
{
% Done properly, the computations would be in PrologueCode, and only the painting in PaintBackgroundCode.
/Glasses TypeOfPagesBeingRendered eq
{
10 dict begin
/N1s GlassPositions SheetNum get length 1 sub def
/Xs [ GlassPositions SheetNum get {0 get} forall ] def
/Ys [ GlassPositions SheetNum get {1 get} forall ] def
/Charges [ 0 N1s {dup} repeat ] def
/Title 1 string def Title 0 65 put
N1s 1 add
{
/Pot [ 4 { [ 0 N1s {dup} repeat ] } repeat ] def
0 1 N1s
{
/i exch def
0 1 N1s
{
/j exch def
i j ne
{
Pot Charges j get get i 2 copy get 1 Xs i get Xs j get sub dup mul Ys i get Ys j get sub dup mul add div add put
} if % i j ne
} for % j
} for % i
/PotMax -1 def
/iBest -1 def
0 1 N1s
{
/i exch def
Charges i get 0 eq
{
Pot 0 get i get 1024 div Pot 1 get i get add Pot 2 get i get add Pot 3 get i get add
dup PotMax gt {/PotMax exch def /iBest i def} {pop} ifelse
} if % Charges i get 0 eq
} for % i
Charges iBest
Pot 3 get iBest get Pot 1 get iBest get le
{Pot 3 get iBest get Pot 2 get iBest get le {3} {2} ifelse}
{Pot 1 get iBest get Pot 2 get iBest get le {1} {2} ifelse}
ifelse put
TitlesFont RadiiCirclearrayInside SheetNum get 1.9 mul selectfont
GlassPositions SheetNum get iBest get aload pop moveto
GSave nulldevice 0 0 moveto Title false CharPathRecursive PathBBox GRestore exch 4 -1 roll add -2 div 3 1 roll add -2 div rmoveto
[ {/Error} {0.8 setgray} {0.4 0.4 0.5 setrgbcolor} {0.6 0 0 setrgbcolor} ] Charges iBest get get exec
Title ShowRecursive
Title 0 2 copy get 1 add put
} repeat
end
} if
} bind def
Re: Software that makes placemats
More realistic example at jdawiseman.com/2019/20190623_Rays_A4.nb.
In the picture green numbers are the charges.

If only StreamPlot weren’t so fiercely difficult to re-code.
Code: Select all
h = 297 (360/127) - 30 - 24;
w = 210 (360/127) - 24 - 24;
r = w/4;
Clear["yy"]; yy = yy /. Solve[(yy - r)^2 == (h - r - yy)^2 + (w/2 - r)^2, yy][[1]];
Print["h=", h, " w=", w, " r=", r, " yy=", yy];
Print[N[circlevec = {
{w/2, h - r, 2},
{r, yy, 3},
{w - r, yy, 1},
{r, r, 2},
{w - r, r, 3}
}] // MatrixForm];
p1 = Map[Graphics[{Red, Thick, Circle[{#[[1]], #[[2]]}, r]}] &, circlevec[[All, 1 ;; 2]]];
p2 = Graphics[Map[Text[Style[#[[3]], FontSize -> 60, Bold, Green], {#[[1]], #[[2]]}, {0, 0}] &, circlevec]];
pot[x_, y_, qx_, qy_, q_] := q/Sqrt[(x - qx)^2 + (y - qy)^2];
potgridx[x_, y_] = D[Total[Table[pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]], circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], x];
potgridy[x_, y_] = D[Total[Table[pot[x, y, circlevec[[i, 1]], circlevec[[i, 2]], circlevec[[i, 3]]], {i, 1, Length[circlevec]}]], y];
p3 = StreamPlot[{potgridx[x, y], potgridy[x, y]}, {x, 0, w}, {y, 0, h}];
Show[p1, p2, p3, AspectRatio -> h/w]

If only StreamPlot weren’t so fiercely difficult to re-code.
-
- Dalva Golden White Colheita 1952
- Posts: 3633
- Joined: 13:22 Wed 15 Dec 2010
- Location: Near Cambridge, UK
Re: Software that makes placemats
A suggestion for alternate charge-plan to try and regularise:
- For every circle, inscribe a hexagon (possibly slightly smaller diameter).
- Assign charge to hexagon points (instead of circle centres), all with +1 at top point, then alternating -1/+1 around the hexagon.
In any square or hexagonal arrangement of circles, that should avoid like charges bring close, allowing good connectivity between, while also being regular/simple charge definition for all layouts.
- For every circle, inscribe a hexagon (possibly slightly smaller diameter).
- Assign charge to hexagon points (instead of circle centres), all with +1 at top point, then alternating -1/+1 around the hexagon.
In any square or hexagonal arrangement of circles, that should avoid like charges bring close, allowing good connectivity between, while also being regular/simple charge definition for all layouts.
-
- Dalva Golden White Colheita 1952
- Posts: 3633
- Joined: 13:22 Wed 15 Dec 2010
- Location: Near Cambridge, UK
Re: Software that makes placemats
Do you have a pseudo-code algorithm?If only StreamPlot weren’t so fiercely difficult to re-code.
Re: Software that makes placemats
Interesting. I will test. Might the mesh of points be too fine — points too close — such that it loses the macro structure?PhilW wrote: ↑20:23 Sun 23 Jun 2019A suggestion for alternate charge-plan to try and regularise:
- For every circle, inscribe a hexagon (possibly slightly smaller diameter).
- Assign charge to hexagon points (instead of circle centres), all with +1 at top point, then alternating -1/+1 around the hexagon.
In any square or hexagonal arrangement of circles, that should avoid like charges bring close, allowing good connectivity between, while also being regular/simple charge definition for all layouts.
No.