The New Hotness

An improved version of my GCMC Spirograph pattern generator, now with better annotation and tool changes:

Spirograph pattern - overview — Spirograph pattern – overview

The GCMC code sets the stator and rotor gear tooth counts, the rotor diameter, and the pen offset using a pseudo-random number generator. This requires randomizing the PRNG seed, which I do in the calling script with the nanosecond of the current second: rnd=$(date +%N).

The G-Code file name also comes from the timestamp:

ts=$(date +%Y%m%d-%H%M%S)
fn='Spiro_'${ts}'.ngc'
# blank line to make the underscore visible

Which means you must call the Bash script slowly to generate a pile o’ plots:

for i in {1..60} ; do sh /mnt/bulkdata/Project\ Files/Mostly\ Printed\ CNC/Patterns/spiro.sh ; sleep 1 ; done

Sift through the heap with drag-n-drop action using an online G-Code previewer. There seems no clean way to convert G-Code to a bitmap on the command line, although you can do it manually, of course.

The GCMC program spits out the G-code for one plot at a time, so the Bash script calls it four times to fill a sheet of paper with random patterns:

for p in $(seq 4)
do
  rnd=$(date +%N)
  gcmc -D Pen=$p -D $Paper -D PRNG_Seed=$rnd $Flags $LibPath -q "$Spirograph" >> $fn
done

The -q parameter tells GCMC to not include the prolog and epilog files, because the calling script glues those onto the lump of G-Code for all four plots.

The -D Pen=$p parameter tells the GCMC program which “tool” to select with a Tn M6 tool change command before starting the plot. Although plotter pens have a well-defined position in the holder and a pretty nearly constant length, you must have a tool length probe installed and configured:

MPCNC Tool Length Probe - Plotter Pen — MPCNC Tool Length Probe – Plotter Pen

Set the overall sheet size in inches or millimeters to get a plot centered in the middle of the page with half-inch margins all around:

Paper='PaperSize=[16.5in,14in]

With all that in hand, those good old black ceramic-tip pens give impeccable results:

Spirograph pattern - black ceramic pen - detail — Spirograph pattern – black ceramic pen – detail

The surviving ones, anyhow. I must apply my collection of Sakura Micron pens to this task.

The other three colors come from fiber pens with reasonably good tips:

Spirograph pattern - central details — Spirograph pattern – central details

They’re a lot like diatoms: all different and all alike.

The GCMC and Bash source code as a GitHub Gist:

	# Spirograph G-Code Generator
	# Ed Nisley KE4ZNU – December 2017

	Paper='PaperSize=[16.5in,14in]'

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

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

	ts=$(date +%Y%m%d-%H%M%S)
	fn='Spiro_'${ts}'.ngc'
	echo Output: $fn

	rm -f $fn

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

	for p in $(seq 4)
	do
	rnd=$(date +%N)
	gcmc -D Pen=$p -D $Paper -D PRNG_Seed=$rnd $Flags $LibPath -q "$Spirograph" >> $fn
	done

	cat $Epilog >> $fn

view raw spiro.sh hosted with ❤ by GitHub

	// Spirograph simulator for MPCNC used as plotter
	// Ed Nisley KE4ZNU – 2017-12-23

	// 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 for tool change and legend position
	// -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) {
	local d=0;

	if (!isnone(a) \|\| isfloat(a) \|\| !isnone(b) \|\| isfloat(b)) {
	warning("Values must be dimensionless integers");
	}

	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=$(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 has 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 these variables from command line

	comment("PRNG seed: ",PRNG_Seed);

	PRNG_State = PRNG_Seed;

	// Define some useful constants

	AngleStep = 2.0deg;

	Margins = [0.5in,0.5in] * 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

	//—–
	// Set up pen

	if (Pen > 0) {
	comment("Tool change: ",Pen);
	toolchange(Pen);
	}

	//—–
	// Plot the curve

	feedrate(3000.0mm);

	safe_z = 1.0mm;
	plot_z = -1.0mm;

	tracepath(Points, plot_z);

	//—–
	// Put legend in proper location

	feedrate(500mm);
	TextSize = [3.0mm,3.0mm];
	TextLeading = 1.5; // line spacing as multiple of nominal text height
	MaxPen = 4;

	line1 = typeset("Seed: " + PRNG_Seed + " Stator: " + StatorTeeth + " Rotor: " + RotorTeeth,FONT_HSANS_1);
	line2 = typeset("Offset: " + L + " GCD: " + GCD + " Lobes: " + Lobes + " Turns: " + Turns,FONT_HSANS_1);

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

	textpath = line1 + (line2 – [-, TextLeading, -]); // undef – n -> undef to preserve coordinates

	if (Pen == 1 \|\| Pen > MaxPen ) { // catch and fix obviously bogus pen selections
	textorg = [PlotSize.x/2 – maxlength,-(PlotSize.y/2 – TextLeading*TextSize.y)];
	}
	elif (Pen == 2) {
	textorg = [-PlotSize.x/2,-(PlotSize.y/2 – TextLeading*TextSize.y)];
	}
	elif (Pen == 3) {
	textorg = [PlotSize.x/2 – maxlength, PlotSize.y/2 – TextSize.y];
	}
	elif (Pen == 4) {
	textorg = [-PlotSize.x/2, PlotSize.y/2 – TextSize.y];
	}
	else {
	Pen = 0; // squelch truly bogus pens
	textorg = [0mm,0mm]; // just to define it
	}

	if (Pen) { // Pen = 0 suppresses legend
	placepath = scale(textpath,TextSize) + textorg;
	comment("Legend begins");
	engrave(placepath,safe_z,plot_z);
	}

	if (Pen == 1) { // add attribution along right margin
	attrpath = typeset("Ed Nisley – KE4ZNU – softsolder.com",FONT_HSANS_1);
	attrpath = rotate_xy(attrpath,90deg);
	attrorg = [PlotSize.x/2,5TextLeadingTextSize.y – PlotSize.y/2];
	placepath = scale(attrpath,TextSize) + attrorg;
	comment("Attribution begins");
	engrave(placepath,safe_z,plot_z);
	}

	goto([-,-,25.0mm]);

view raw Spirograph.gcmc hosted with ❤ by GitHub

The New Hotness

MPCNC: Spirograph Generator with Tool Changes