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GCMC source code: Guilloche / Spirograph pattern generator with layer colors for laser cuttery
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// Spirograph simulator | |
// Ed Nisley KE4ZNU - 2017-12-23 | |
// Adapted for Guillioche plots with ball point pens - 2018-09-25 | |
// 2019-06 Text on circular arcs | |
// 2019-08 Coordinate pruning | |
// 2019-09 Allow L > 1.0, proper scale to fit disk | |
// 2023-11 Strip down for SVG output, add layer colors for LightBurn | |
// 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 | |
//----- | |
// Library routines | |
include("tracepath.inc.gcmc"); | |
include("engrave.inc.gcmc"); | |
// SVG layers map to LightBurn colors | |
layerstack("Engrave","Mark","Cut","Dot","Tool2"); // 1-base index! | |
LBColors = [0x000000,0x0000ff,0xff0000,0xa00000,0x0c9609]; // LightBurn layers, 0-base index | |
//----- | |
// Define useful constants | |
AngleStep = 0.1deg; | |
Snuggly = 0.25mm; // prune coordinates when closer | |
TextFont = FONT_HSANS_1_RS; | |
TextSize = [1.5mm,1.5mm]; | |
//----- | |
// Command line parameters | |
// -D DiskType="string" | |
if (!isdefined("DiskType")) { | |
DiskType = "CD"; | |
} | |
if (DiskType != "CD" && // list all possible types | |
DiskType != "3.5" && | |
DiskType != "TrimCD" | |
) { | |
error("Unknown disk type: ",DiskType); | |
} | |
message("Disk type: ",DiskType); // default is "CD" | |
Margin = 1.5mm; // clamping margin around disk OD | |
DiskDia = (DiskType == "3.5") ? 95.0mm : | |
(DiskType == "TrimCD") ? 95.0mm : | |
120.0mm; | |
OuterDia = DiskDia - 2*Margin; | |
OuterRad = OuterDia / 2; | |
message("Outer Diameter: ",OuterDia); | |
message(" Radius: ",OuterRad); | |
InnerDia = (DiskType == "3.5") ? 33.0mm : | |
(DiskType == "TrimCD") ? 38.0mm : | |
38.0mm; | |
InnerDia = InnerDia; | |
InnerRad = InnerDia / 2; | |
message("Inner Diameter: ",InnerDia); | |
message(" Radius: ",InnerRad); | |
MidDia = (InnerDia + OuterDia) / 2; | |
MidRad = MidDia / 2; | |
message("Mid Diameter: ",MidDia); | |
message(" Radius: ",MidRad); | |
LegendDia = (DiskType == "3.5") ? 31.0mm : | |
(DiskType == "TrimCD") ? 31.0mm : | |
30.0mm; | |
LegendDia = LegendDia; | |
LegendRad = LegendDia / 2; | |
message("Legend Diameter: ",LegendDia); | |
message(" Radius: ",LegendRad); | |
// -D PRNG_Seed=integer non-zero random number seed | |
if (isdefined("PRNG_Seed")) { // did we get a seed? | |
if (!PRNG_Seed) { // .. it must not be zero | |
PRNG_Seed = 347221084; | |
warning("Zero PRNG_Seed, forced to: ",PRNG_Seed); | |
} | |
} | |
else { // no incoming seed, so use a constant | |
PRNG_Seed = 674203941; | |
warning("No PRNG_Seed, forced to: ",PRNG_Seed); | |
} | |
message("PRNG seed: ",PRNG_Seed); | |
PRNG_State = PRNG_Seed; // set initial state | |
// -D various other useful tidbits | |
if (!isdefined("Legend")) { | |
Legend = "Ed Nisley - KE4ZNU - softsolder.com"; | |
} | |
PlotZ = 0.0mm; // dummy for SVG output | |
TravelZ = 1.0mm; | |
//----- | |
// Spirograph tooth counts mooched from: | |
// http://nathanfriend.io/inspirograph/ | |
// Stators includes both inside and outside counts, because we're not fussy | |
// Stator with prime tooth count will always produce that number of lobes | |
// Prime numbers: | |
// https://en.wikipedia.org/wiki/Prime_number | |
// Table of primes: | |
// https://www.factmonster.com/math/numbers/prime-numbers-facts-examples-table-all-1000 | |
// Must be sorted and should not exceed 127 teeth, which will make plenty of lobes | |
Stators = [37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127]; | |
// Rotor tooth count is picked randomly within some constraints | |
// This remains for historic interest | |
//Rotors = [24, 30, 32, 36, 40, 45, 48, 50, 52, 56, 60, 63, 64, 72, 75, 80, 84]; | |
//----- | |
// 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)) { | |
error("GCD params must be dimensionless integers. a: ",a," b: ",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 | |
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 | |
// www.jstatsoft.org/v08/i14/paper | |
// Requires initial state from calling script | |
// -D "PRNG_Seed=whatever" | |
// Bash (et. al.) supplies nine reasonably random digits from $(date +%N) | |
function XORshift() { | |
local x = PRNG_State; // fetch current state | |
x ^= x << 13; | |
x ^= x >> 17; | |
x ^= x << 5; | |
PRNG_State = x; // save state for next invocation | |
return x; | |
} | |
//----- | |
// Bend text around an arc | |
function ArcText(TextPath,Center,Radius,BaseAngle,Align) { | |
PathLength = TextPath[-1].x; | |
Circumf = 2*pi()*Radius; | |
TextAngle = to_deg(360 * PathLength / Circumf); | |
AlignAngle = BaseAngle + (Align == "Left" ? 0 : | |
Align == "Center" ? -TextAngle / 2 : | |
Align == "Right" ? -TextAngle : | |
0); | |
ArcPath = {}; | |
foreach(TextPath; pt) { | |
if (!isundef(pt.x) && !isundef(pt.y) && isundef(pt.z)) { // XY motion, no Z | |
r = Radius - pt.y; | |
a = 360deg * (pt.x / Circumf) + AlignAngle; | |
ArcPath += {[r*cos(a) + Center.x, r*sin(a) + Center.y,-]}; | |
} | |
elif (isundef(pt.x) && isundef(pt.y) && !isundef(pt.z)) { // no XY, Z up/down | |
ArcPath += {pt}; | |
} | |
else { | |
error("Point is not pure XY or pure Z: " + to_string(pt)); | |
} | |
} | |
return ArcPath; | |
} | |
//----- | |
// Set up gearing | |
s = (XORshift() & 0xffff) % count(Stators); | |
StatorTeeth = Stators[s]; | |
message("Stator ",s,": ",StatorTeeth); | |
// When Stator has prime teeth, any Rotor will have GCD = 1 | |
// Iterate to get random Rotor tooth count producing a nice pattern | |
RotorTeeth = Stators[-1]; | |
n = 0; | |
while (RotorTeeth >= floor(0.95 * StatorTeeth) || RotorTeeth < 5) { | |
RotorTeeth = (XORshift() & 0x007f); // this is why Stator can't have more than 127 teeth | |
n++; | |
} | |
message("Rotor: ",RotorTeeth," in ",n," iterations"); | |
K = to_float(RotorTeeth) / to_float(StatorTeeth); // find normalized rotor dia | |
message("Dia ratio K: ",K," 1/K: ",1.0/K); | |
GCD = gcd(StatorTeeth,RotorTeeth); // reduce teeth to ratio of least integers | |
message("GCD: ",GCD); | |
Lobes = StatorTeeth / GCD; // compute useful values | |
message("Lobes: ", Lobes); | |
Turns = RotorTeeth / GCD; | |
message("Turns: ", Turns); | |
// Find normalized pen offset to never cross Stator center | |
n = 0; | |
do { | |
L = (to_float((XORshift() & 0x1f) + 1) / 32.0) * (1.0/K - 1.0); // allow L > 1.0 | |
n++; | |
} while (L >= (1.0/K - 1.0) || L < 0.01); | |
message("Offset L: ", L," in ",n," iterations"); | |
//----- | |
// Crank out a list of points in normalized coordinates | |
Path = {}; | |
for (a = 0.0deg ; a <= Turns*360deg ; a += AngleStep) { | |
x = (1 - K)*cos(a) + L*K*cos(a*(1 - K)/K); | |
y = (1 - K)*sin(a) - L*K*sin(a*(1 - K)/K); | |
Path += {[x,y]}; | |
} | |
//----- | |
// Calculate normalized limits for band traced by pen in rotor at offset L | |
// L was chosen to produce a band around the rotor center point | |
RotorMin = 1.0 - 2*K; | |
message("Rotor Min: ",RotorMin); | |
BandCtr = 1.0 - K; // band center radius | |
BandMin = BandCtr - L*K; // ... min radius | |
BandMax = BandCtr + L*K; // ... max radius | |
BandAmpl = BandMax - BandCtr; | |
message("Band Min: ",BandMin," Ctr: ",BandCtr," Max: ",BandMax); | |
//----- | |
// Scale normalized band to fill physical limits centered at mid-disk radius | |
FillPath = {}; | |
foreach (Path; pt) { | |
a = atan_xy(pt); // recover angle to point | |
r = length(pt); // ... radius to point | |
br = (r - BandCtr) / BandAmpl; // remove center bias, rescale to 1.0 amplitude | |
dr = br * (OuterRad - MidRad); // rescale to fill disk | |
pr = dr + MidRad; // set at disk centerline | |
x = pr * cos(a); // find new XY coords | |
y = pr * sin(a); | |
FillPath += {[x,y]}; | |
} | |
message("Path has ",count(FillPath)," points"); | |
//----- | |
// Prune too-snuggly physical coordinates | |
PointList = {FillPath[0]}; // must include first point | |
lp = FillPath[0]; | |
n = 0; | |
foreach (FillPath; pt) { | |
if (length(pt - lp) <= Snuggly) { // discard too-snuggly point | |
n++; | |
} | |
else { | |
PointList += {pt}; // otherwise, add it to output | |
lp = pt; | |
} | |
} | |
PointList += {FillPath[-1]}; // ensure closure at last point | |
message("Pruned ",n," points, ",count(PointList)," remaining"); | |
//----- | |
// Convert coordinate list to SVG | |
layer("Mark"); | |
linecolor(LBColors[layer() - 1]); | |
message("Pattern begins"); | |
tracepath(PointList, PlotZ); | |
//----- | |
// Draw the legend | |
layer("Dot"); | |
linecolor(LBColors[layer() - 1]); | |
message("Legend begins"); | |
if (Legend) { | |
tp = scale(typeset(Legend,TextFont),TextSize); | |
tpa = ArcText(tp,[0mm,0mm],LegendRad,0deg,"Center"); | |
engrave(tpa,TravelZ,PlotZ); | |
} | |
tp = scale(typeset(to_string(PRNG_Seed),TextFont),TextSize); | |
tpa = ArcText(tp,[0mm,0mm],LegendRad,180deg,"Center"); | |
engrave(tpa,TravelZ,PlotZ); | |
message("Disk ends"); |
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#!/bin/bash | |
# Guilloche and Legend Generator | |
# Ed Nisley KE4ZNU - 2019-06 | |
# 2022-03-14 stripped for SVG ouput | |
Disk='DiskType="CD"' | |
Flags='-P 3 --pedantic --svg --svg-no-movelayer --svg-toolwidth=0.2 --svg-opacity=1.0' | |
# Set these to match your file layout | |
LibPath='/opt/gcmc/library' | |
Script='/mnt/bulkdata/Project Files/Laser Cutter/Platters/Code/Platter Engraving.gcmc' | |
# get date for filename | |
ts=$(date +%Y%m%d-%H%M%S) | |
if [ -n "$1" ] # if random seed parameter exists | |
then | |
rnd=$1 # .. use it | |
else | |
rnd=$(date +%N) # .. otherwise use nanoseconds | |
fi | |
fn="Disk_${ts}_${rnd}.svg" | |
echo Output: $fn | |
Seed="PRNG_Seed=$rnd" | |
rm -f $fn | |
gcmc -D "$Disk" -D "$Seed" -D "$Legend" $Flags \ | |
--include "$LibPath" \ | |
"$Script" >> "$fn" | |
viewnior "$fn" & |
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More details on my blog at https://softsolder.com/2023/11/08/guilloche-generator-now-with-layers-colors/