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// Spirograph simulator for MPCNC used as plotter |
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// Ed Nisley KE4ZNU – 2017-12-23 |
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// Adapted for Guillioche plots with ball point pens – 2018-09-25 |
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// Spirograph equations: |
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// https://en.wikipedia.org/wiki/Spirograph |
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// Loosely based on GCMC cycloids.gcmc demo: |
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// https://gitlab.com/gcmc/gcmc/tree/master/example/cycloids.gcmc |
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// Required command line parameters: |
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// -D Pen=n pen selection, 0 = no legend, 1 = current pen |
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// -D PaperSize=[x,y] overall sheet size: [17in,11in] |
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// -D PRNG_Seed=i non-zero random number seed |
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include("tracepath.inc.gcmc"); |
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include("engrave.inc.gcmc"); |
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//—– |
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// Greatest Common Divisor |
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// https://en.wikipedia.org/wiki/Greatest_common_divisor#Using_Euclid's_algorithm |
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// Inputs = integers without units |
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function gcd(a,b) { |
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if (!isnone(a) || isfloat(a) || !isnone(b) || isfloat(b)) { |
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warning("GCD params must be dimensionless integers:",a,b); |
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} |
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local d = 0; // power-of-two counter |
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while (!((a | b) & 1)) { // remove and tally common factors of two |
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a >>= 1; |
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b >>= 1; |
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d++; |
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} |
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while (a != b) { |
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if (!(a & 1)) {a >>= 1;} // discard non-common factor of 2 |
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elif (!(b & 1)) {b >>= 1;} // … likewise |
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elif (a > b) {a = (a – b) >> 1;} // gcd(a,b) also divides a-b |
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else {b = (b – a) >> 1;} // … likewise |
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} |
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local GCD = a*(1 << d); // form gcd |
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// message("GCD: ",GCD); |
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return GCD; |
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} |
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//—– |
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// Max and min functions |
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function max(x,y) { |
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return (x > y) ? x : y; |
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} |
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function min(x,y) { |
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return (x < y) ? x : y; |
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} |
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//—– |
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// Pseudo-random number generator |
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// Based on xorshift: |
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// https://en.wikipedia.org/wiki/Xorshift |
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// http://www.jstatsoft.org/v08/i14/paper |
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// Requires initial state from calling script |
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// -D "PRNG_Seed=whatever" |
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// You can get nine reasonably random digits from $(date +%N) |
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function XORshift() { |
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local x = PRNG_State; |
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x ^= x << 13; |
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x ^= x >> 17; |
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x ^= x << 5; |
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PRNG_State = x; |
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return x; |
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} |
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//—– |
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// Spirograph tooth counts mooched from: |
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// http://nathanfriend.io/inspirograph/ |
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// Stators includes both inside and outside counts, because we're not fussy |
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Stators = [96, 105, 144, 150]; |
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Rotors = [24, 30, 32, 36, 40, 45, 48, 50, 52, 56, 60, 63, 64, 72, 75, 80, 84]; |
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//—– |
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// Start drawing things |
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// Set initial parameters from command line! |
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comment("PRNG seed: ",PRNG_Seed); |
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PRNG_State = PRNG_Seed; |
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// Define some useful constants |
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AngleStep = 2.0deg; |
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Margins = [12mm,12mm] * 2; |
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comment("Paper size: ",PaperSize); |
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PlotSize = PaperSize – Margins; |
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comment("PlotSize: ",PlotSize); |
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//—– |
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// Set up gearing |
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s = (XORshift() & 0xffff) % count(Stators); |
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StatorTeeth = Stators[s]; |
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comment("Stator ",s,": ",StatorTeeth); |
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r = (XORshift() & 0xffff) % count(Rotors); |
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RotorTeeth = Rotors[r]; |
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comment("Rotor ",r,": ",RotorTeeth); |
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GCD = gcd(StatorTeeth,RotorTeeth); // reduce teeth to ratio of least integers |
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comment("GCD: ",GCD); |
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StatorN = StatorTeeth / GCD; |
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RotorM = RotorTeeth / GCD; |
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L = to_float((XORshift() & 0x3ff) – 512) / 100.0; // normalized pen offset in rotor |
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comment("Offset: ", L); |
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sgn = sign((XORshift() & 0xff) – 128); |
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K = sgn*to_float(RotorM) / to_float(StatorN); // normalized rotor dia |
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comment("Dia ratio: ",K); |
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Lobes = StatorN; // having removed all common factors |
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Turns = RotorM; |
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comment("Lobes: ", Lobes); |
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comment("Turns: ", Turns); |
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//—– |
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// Crank out a list of points in normalized coordinates |
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Path = {}; |
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Xmax = 0.0; |
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Xmin = 0.0; |
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Ymax = 0.0; |
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Ymin = 0.0; |
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for (a = 0.0deg ; a <= Turns*360deg ; a += AngleStep) { |
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x = (1 – K)*cos(a) + L*K*cos(a*(1 – K)/K); |
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if (x > Xmax) {Xmax = x;} |
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elif (x < Xmin) {Xmin = x;} |
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y = (1 – K)*sin(a) – L*K*sin(a*(1 – K)/K); |
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if (y > Ymax) {Ymax = y;} |
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elif (y < Ymin) {Ymin = y;} |
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Path += {[x,y]}; |
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} |
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//message("Max X: ", Xmax, " Y: ", Ymax); |
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//message("Min X: ", Xmin, " Y: ", Ymin); // min will always be negative |
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Xmax = max(Xmax,-Xmin); // odd lobes can cause min != max |
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Ymax = max(Ymax,-Ymin); // … need really truly absolute maximum |
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//—– |
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// Scale points to actual plot size |
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PlotScale = [PlotSize.x / (2*Xmax), PlotSize.y / (2*Ymax)]; |
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comment("Plot scale: ", PlotScale); |
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Points = scale(Path,PlotScale); // fill page, origin at center |
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//—– |
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// Start drawing lines |
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feedrate(1500.0mm); |
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TravelZ = 1.5mm; |
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PlotZ = -1.0mm; |
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//—– |
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// Box the outline for camera alignment |
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goto([-,-,TravelZ]); |
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goto([-PaperSize.x/2,-PaperSize.y/2,-]); |
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goto([-,-,PlotZ]); |
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foreach ( {[-1,1], [1,1], [1,-1], [-1,-1]} ; pt) { |
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move([pt.x*PaperSize.x/2,pt.y*PaperSize.y/2,-]); |
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} |
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goto([-,-,TravelZ]); |
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//—– |
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// Draw the plot |
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tracepath(Points, PlotZ); |
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//—– |
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// Add legends |
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// … only for nonzero Pen |
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if (Pen) { |
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feedrate(250mm); |
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TextFont = FONT_HSANS_1_RS; |
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TextSize = [2.5mm,2.5mm]; |
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TextLeading = 1.5; // line spacing as multiple of nominal text height |
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line1 = typeset("Seed: " + PRNG_Seed + " Stator: " + StatorTeeth + " Rotor: " + RotorTeeth,TextFont); |
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line2 = typeset("Offset: " + L + " GCD: " + GCD + " Lobes: " + Lobes + " Turns: " + Turns,TextFont); |
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maxlength = TextSize.x * max(line1[-1].x,line2[-1].x); |
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textpath = line1 + (line2 – [-, TextLeading, -]); // undef – n -> undef to preserve coordinates |
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textorg = [-maxlength/2,PaperSize.y/2 – 0*Margins.y/2 – 2*TextLeading*TextSize.y/2]; |
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placepath = scale(textpath,TextSize) + textorg; |
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comment("Legend begins"); |
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engrave(placepath,TravelZ,PlotZ); |
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attrpath = typeset("Ed Nisley – KE4ZNU – softsolder.com",TextFont); |
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attrorg = [-(TextSize.x * attrpath[-1].x)/2,-(PaperSize.y/2 – Margins.y/2 + 2*TextLeading*TextSize.y)]; |
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placepath = scale(attrpath,TextSize) + attrorg; |
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comment("Attribution begins"); |
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engrave(placepath,TravelZ,PlotZ); |
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} |
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goto([PaperSize.x/2,PaperSize.y/2,25.0mm]); // done, so get out of the way |
The Smell of Molten Projects in the Morning 