The New Hotness

It turns out the Spirograph patterns I’d been using to wring out the MPCNC are also known as Guilloché, perhaps after the guy who invented a lathe-turning machine to engrave them. Sounds pretentious, but they still look nice:

Guilloche 591991062 - scanned — Guilloche 591991062 – scanned

With the ballpoint pen / knife collet holder in mind, I stripped the tool changes out of the Spirograph generator GCMC source code, set the “paper size” to a convenient 100 mm square, and tidied up the code a bit.

As with Spirograph patterns, changing the random number seed produces entirely different results. A collection differing in the last digit, previewed online:

Seed = 213478836:

Seed = 213478837:

Seed = 213478838:

Seed = 213478839:

They’re such unique snowflakes …

The Bash script now accepts a single parameter to force the PRNG seed to a value you presumably want to plot again, rather than just accept whatever the Gods of Cosmic Jest will pick for you.

The GCMC source code and Bash (or whatever) script feeding it as a GitHub Gist:

	// Spirograph simulator for MPCNC used as plotter
	// Ed Nisley KE4ZNU – 2017-12-23
	// Adapted for Guillioche plots with ball point pens – 2018-09-25

	// Spirograph equations:
	// https://en.wikipedia.org/wiki/Spirograph
	// Loosely based on GCMC cycloids.gcmc demo:
	// https://gitlab.com/gcmc/gcmc/tree/master/example/cycloids.gcmc

	// Required command line parameters:

	// -D Pen=n pen selection, 0 = no legend, 1 = current pen
	// -D PaperSize=[x,y] overall sheet size: [17in,11in]
	// -D PRNG_Seed=i non-zero random number seed

	include("tracepath.inc.gcmc");
	include("engrave.inc.gcmc");

	//—–
	// Greatest Common Divisor
	// https://en.wikipedia.org/wiki/Greatest_common_divisor#Using_Euclid's_algorithm
	// Inputs = integers without units

	function gcd(a,b) {
	if (!isnone(a) \|\| isfloat(a) \|\| !isnone(b) \|\| isfloat(b)) {
	warning("GCD params must be dimensionless integers:",a,b);
	}

	local d = 0; // power-of-two counter

	while (!((a \| b) & 1)) { // remove and tally common factors of two
	a >>= 1;
	b >>= 1;
	d++;
	}

	while (a != b) {
	if (!(a & 1)) {a >>= 1;} // discard non-common factor of 2
	elif (!(b & 1)) {b >>= 1;} // … likewise
	elif (a > b) {a = (a – b) >> 1;} // gcd(a,b) also divides a-b
	else {b = (b – a) >> 1;} // … likewise
	}

	local GCD = a*(1 << d); // form gcd

	// message("GCD: ",GCD);
	return GCD;

	}

	//—–
	// Max and min functions

	function max(x,y) {
	return (x > y) ? x : y;
	}

	function min(x,y) {
	return (x < y) ? x : y;
	}

	//—–
	// Pseudo-random number generator
	// Based on xorshift:
	// https://en.wikipedia.org/wiki/Xorshift
	// http://www.jstatsoft.org/v08/i14/paper
	// Requires initial state from calling script
	// -D "PRNG_Seed=whatever"
	// You can get nine reasonably random digits from $(date +%N)

	function XORshift() {

	local x = PRNG_State;

	x ^= x << 13;
	x ^= x >> 17;
	x ^= x << 5;

	PRNG_State = x;
	return x;
	}

	//—–
	// Spirograph tooth counts mooched from:
	// http://nathanfriend.io/inspirograph/
	// Stators includes both inside and outside counts, because we're not fussy

	Stators = [96, 105, 144, 150];
	Rotors = [24, 30, 32, 36, 40, 45, 48, 50, 52, 56, 60, 63, 64, 72, 75, 80, 84];

	//—–
	// Start drawing things
	// Set initial parameters from command line!

	comment("PRNG seed: ",PRNG_Seed);
	PRNG_State = PRNG_Seed;

	// Define some useful constants

	AngleStep = 2.0deg;

	Margins = [12mm,12mm] * 2;

	comment("Paper size: ",PaperSize);

	PlotSize = PaperSize – Margins;
	comment("PlotSize: ",PlotSize);

	//—–
	// Set up gearing

	s = (XORshift() & 0xffff) % count(Stators);
	StatorTeeth = Stators[s];
	comment("Stator ",s,": ",StatorTeeth);

	r = (XORshift() & 0xffff) % count(Rotors);
	RotorTeeth = Rotors[r];
	comment("Rotor ",r,": ",RotorTeeth);

	GCD = gcd(StatorTeeth,RotorTeeth); // reduce teeth to ratio of least integers
	comment("GCD: ",GCD);
	StatorN = StatorTeeth / GCD;
	RotorM = RotorTeeth / GCD;

	L = to_float((XORshift() & 0x3ff) – 512) / 100.0; // normalized pen offset in rotor
	comment("Offset: ", L);

	sgn = sign((XORshift() & 0xff) – 128);
	K = sgn*to_float(RotorM) / to_float(StatorN); // normalized rotor dia
	comment("Dia ratio: ",K);

	Lobes = StatorN; // having removed all common factors
	Turns = RotorM;

	comment("Lobes: ", Lobes);
	comment("Turns: ", Turns);

	//—–
	// Crank out a list of points in normalized coordinates

	Path = {};
	Xmax = 0.0;
	Xmin = 0.0;
	Ymax = 0.0;
	Ymin = 0.0;

	for (a = 0.0deg ; a <= Turns*360deg ; a += AngleStep) {
	x = (1 – K)cos(a) + LKcos(a(1 – K)/K);
	if (x > Xmax) {Xmax = x;}
	elif (x < Xmin) {Xmin = x;}

	y = (1 – K)sin(a) – LKsin(a(1 – K)/K);
	if (y > Ymax) {Ymax = y;}
	elif (y < Ymin) {Ymin = y;}

	Path += {[x,y]};
	}

	//message("Max X: ", Xmax, " Y: ", Ymax);
	//message("Min X: ", Xmin, " Y: ", Ymin); // min will always be negative

	Xmax = max(Xmax,-Xmin); // odd lobes can cause min != max
	Ymax = max(Ymax,-Ymin); // … need really truly absolute maximum

	//—–
	// Scale points to actual plot size

	PlotScale = [PlotSize.x / (2Xmax), PlotSize.y / (2Ymax)];
	comment("Plot scale: ", PlotScale);

	Points = scale(Path,PlotScale); // fill page, origin at center

	//—–
	// Start drawing lines

	feedrate(1500.0mm);

	TravelZ = 1.5mm;
	PlotZ = -1.0mm;

	//—–
	// Box the outline for camera alignment

	goto([-,-,TravelZ]);
	goto([-PaperSize.x/2,-PaperSize.y/2,-]);
	goto([-,-,PlotZ]);

	foreach ( {[-1,1], [1,1], [1,-1], [-1,-1]} ; pt) {
	move([pt.xPaperSize.x/2,pt.yPaperSize.y/2,-]);
	}

	goto([-,-,TravelZ]);

	//—–
	// Draw the plot

	tracepath(Points, PlotZ);

	//—–
	// Add legends
	// … only for nonzero Pen

	if (Pen) {
	feedrate(250mm);

	TextFont = FONT_HSANS_1_RS;
	TextSize = [2.5mm,2.5mm];
	TextLeading = 1.5; // line spacing as multiple of nominal text height

	line1 = typeset("Seed: " + PRNG_Seed + " Stator: " + StatorTeeth + " Rotor: " + RotorTeeth,TextFont);
	line2 = typeset("Offset: " + L + " GCD: " + GCD + " Lobes: " + Lobes + " Turns: " + Turns,TextFont);

	maxlength = TextSize.x * max(line1[-1].x,line2[-1].x);

	textpath = line1 + (line2 – [-, TextLeading, -]); // undef – n -> undef to preserve coordinates
	textorg = [-maxlength/2,PaperSize.y/2 – 0Margins.y/2 – 2TextLeading*TextSize.y/2];

	placepath = scale(textpath,TextSize) + textorg;
	comment("Legend begins");
	engrave(placepath,TravelZ,PlotZ);

	attrpath = typeset("Ed Nisley – KE4ZNU – softsolder.com",TextFont);
	attrorg = [-(TextSize.x * attrpath[-1].x)/2,-(PaperSize.y/2 – Margins.y/2 + 2TextLeadingTextSize.y)];
	placepath = scale(attrpath,TextSize) + attrorg;
	comment("Attribution begins");
	engrave(placepath,TravelZ,PlotZ);
	}

	goto([PaperSize.x/2,PaperSize.y/2,25.0mm]); // done, so get out of the way

view raw Guilloche.gcmc hosted with ❤ by GitHub

	# Guilloche G-Code Generator
	# Ed Nisley KE4ZNU – September 2018

	Paper='PaperSize=[100mm,100mm]'

	Flags="-P 2"
	LibPath="-I /opt/gcmc/library"
	Spirograph='/mnt/bulkdata/Project Files/Mostly Printed CNC/Patterns/Guilloche.gcmc'

	Prolog="/home/ed/.config/gcmc/prolog.gcmc"
	Epilog="/home/ed/.config/gcmc/epilog.gcmc"

	ts=$(date +%Y%m%d-%H%M%S)

	if [ -n "$1" ] # if parameter
	then
	rnd=$1 # .. use it
	else
	rnd=$(date +%N) # .. otherwise use nanoseconds
	fi

	fn='Guilloche_'${ts}_$rnd'.ngc'
	echo Output: $fn

	p=1

	rm -f $fn

	echo "(File: "$fn")" > $fn
	#cat $Prolog >> $fn

	gcmc -D Pen=$p -D $Paper -D PRNG_Seed=$rnd $Flags $LibPath -G $Prolog -g $Epilog "$Spirograph" >> $fn

	#cat $Epilog >> $fn

view raw guilloche.sh hosted with ❤ by GitHub

The New Hotness

GCMC Guilloche Plot Generator