The New Hotness

A few more attempts at layered paper construction, done with plain white Art Paper of various vintages:

The middle one comes from a version of the original GCMC marquetry shape generator, tweaked to produce just the frame SVG, called by a Bash script to change the sash width, and imported into LightBurn for laser control:

LightBurn - Marq-6-0.6-0.0mm — LightBurn – Marq-6-0.6-0.0mm

I generated the plain disk for the bottom by deleting all the inner shapes.

The left and right coasters use LightBurn’s Offset tool to reduce the size of the interior holes on successive layers:

LightBurn - Marq-8-0.40-20.0mm-Layers — LightBurn – Marq-8-0.40-20.0mm-Layers

Although the GCMC version turned out OK, you’ll note it lacks the central disk, as I was unwilling to tweak the code enough to make the disk diameter vary with the kerf width.

Applying the LB Offset tool requires selecting only the inner shapes (it has an option to ignore the inner shapes) and applying the appropriate offset. Because the tool remembers its previous settings, it’s straightforward to step the offset from 1.0 mm to 7.0 mm on successive patterns.

Applying glue (from a glue stick!) to the bottom of each disk, aligning them atop each other, and pressing them together becomes tedious in short order. If I had to do a lot of these, I’d be tempted to add three wings (not at 120° angles!) around the perimeter with holes for pegs, then stacking the layers in a fixture to ensure good alignment. A polygonal perimeter would simplify trimming the tabs.

Spray adhesive might be faster, but each layer would have sticky edges and the finished coaster would become a dust collector par excellence.

I like the overall effect, but …

The OpenSCAD source code as a GitHub Gist:

	#!/bin/bash
	# Layering paper cutouts
	# Ed Nisley KE4ZNU – 2022-08-21

	Flags='-P 4 –pedantic' # quote to avoid leading hyphen gotcha

	SVGFlags='–svg –svg-no-movelayer –svg-opacity=1.0 –svg-toolwidth=0.2'

	# Set these to match your file layout

	ProjPath='/mnt/bulkdata/Project Files/Laser Cutter/Coasters/Source Code'

	LibPath='/opt/gcmc/library'

	ScriptPath=$ProjPath
	Script='Marquetry Layers.gcmc'


	[ -z "$1" ] && leaves="6" \|\| leaves="$1"
	[ -z "$2" ] && aspect="0.50" \|\| aspect="$2"
	[ -z "$3" ] && center="0.0mm" \|\| center="$3"

	numlayers=8
	sashmin=2.0
	sashstep=2.0
	sashmax=$(echo "$sashmin+$sashstep*($numlayers-1)" \| bc)

	echo min: $sashmin step: $sashstep max: $sashmax

	for sash in $(seq $sashmin $sashstep $sashmax) ; do

	fn=Marq-$leaves-$aspect-$center-S$sash.svg
	echo Output: $fn

	gcmc $Flags $SVGFlags –include "$LibPath" \
	-D "NumLeaves=$leaves" -D "LeafAspect=$aspect" -D "CenterDia=$center" \
	-D "Sash=${sash}mm" \
	"$ScriptPath"/"$Script" > "$fn"

	done

view raw layers.sh hosted with ❤ by GitHub

	// Marquetry Layers
	// Ed Nisley KE4ZNU
	// 2022-08-21 layered paper test piece

	layerstack("Frame","Leaves","Rim","Base","Center","Tool1"); // SVG layers map to LightBurn colors

	//—–
	// Library routines

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

	FALSE = 0;
	TRUE = !FALSE;

	//—–
	// Command line parameters

	// -D various useful tidbits
	// add unit to speeds and depths: 2000mm / -3.00mm / etc

	if (!isdefined("OuterDia")) {
	OuterDia = 120.0mm;
	}

	if (!isdefined("CenterDia")) {
	CenterDia = 20.0mm;
	}

	if (!isdefined("NumLeaves")) {
	NumLeaves = 8;
	}

	if (!isdefined("Sash")) {
	Sash = 4.0mm;
	}

	if (!isdefined("LeafAspect")) {
	LeafAspect = 0.50;
	}

	// Leaf values

	LeafStemAngle = 360.0deg/NumLeaves; // subtended by inner sides
	LeafStemHA = LeafStemAngle/2;

	LeafOAL = OuterDia/2 – Sash – (Sash/2)/sin(LeafStemHA);

	LeafWidth = LeafAspect*LeafOAL;
	L1 = (LeafWidth/2)/tan(LeafStemHA);
	L2 = LeafOAL – L1;
	// message("Len: ",LeafOAL," L1: ",L1," L2: ",L2);

	LeafTipHA = to_deg(atan(LeafWidth/2,L2)); // subtended by outer sides
	LeafTipAngle = 2*LeafTipHA;

	// message("Width: ",LeafWidth);
	// message("Tip HA: ",LeafTipHA);

	LeafID = CenterDia + 2*Sash;
	LeafOD = LeafID + LeafOAL;

	// message("ID: ",LeafID," OD: ",LeafOD);

	// Find leaf and rim vertices

	P0 = [(Sash/2) / sin(LeafStemHA),0.0mm];

	m = tan(LeafStemHA);
	y0 = -(Sash/2) / cos(LeafStemHA);

	if (CenterDia) { // one sash width around center spot
	a = 1 + pow(m,2);
	b = 2 * m * y0;
	c = pow(y0,2) – pow(LeafID/2,2);
	xp = (-b + sqrt(pow(b,2) – 4ac))/(2*a);
	xn = (-b – sqrt(pow(b,2) – 4ac))/(2*a);
	y = xp*tan(LeafStemHA) – (Sash/2) / cos(LeafStemHA);
	P1 = [xp,y];
	if (FALSE) {
	message("a: ",a);
	message("b: ",b);
	message("c: ",c);
	message("p: ",xp," n: ",xn," y: ",y);
	}
	}
	else { // force sharp point without center spot
	P1 = P0;
	}

	P2 = P0 + [L1,LeafWidth/2];
	P3 = P0 + [LeafOAL,0mm];

	P4 = P3 + [Sash/sin(LeafTipHA),0.0mm];
	P5r = P4.x * sin(LeafTipHA) / sin(180deg – LeafStemHA – LeafTipHA);
	P5 = rotate_xy([P5r,0.0mm],LeafStemHA);
	P6 = rotate_xy(P4,LeafStemAngle);

	t2 = pow(tan(-LeafTipHA),2);
	a = 1 + t2;
	b = -2 * t2 * P4.x;
	c = t2 * pow(P4.x,2) – pow(P3.x,2);

	xp = (-b + sqrt(pow(b,2) – 4ac))/(2*a);
	xn = (-b – sqrt(pow(b,2) – 4ac))/(2*a);
	y = (xp – P4.x)*tan(-LeafTipHA);
	// message("p: ",xp," n: ",xn," y: ",y);

	P4a = [xp,y];
	P6a = rotate_xy(P4a,LeafStemAngle – 2*atan(P4a.y,P4a.x));

	if (FALSE) {
	message("P0: ",P0);
	message("P1: ",P1);
	message("P2: ",P2);
	message("P3: ",P3);
	message("P4: ",P4);
	message("P4a: ",P4a);
	message("P5: ",P5);
	message("P6: ",P6);
	message("P6a: ",P6a);
	}

	// Construct paths

	LeafPoints = {P1,P2,P3,[P2.x,-P2.y],[P1.x,-P1.y]};

	if (P0 != P1) {
	StemArc = varc_ccw(P1 – [P1.x,-P1.y],LeafID/2);
	StemArc += [P1.x,-P1.y];
	LeafPoints += StemArc;
	}

	RimChord = length(P4a – P6a);
	RimThick = OuterDia/2 – Sash – length(P5);

	RimPoints = {P4a,P5,P6a};
	RimArc = varc_cw(P4a – P6a,P4a.x);
	RimArc += P6a;
	RimPoints += RimArc;

	//— Lay out the frame

	linecolor(0xff0000);

	layer("Frame");

	if (CenterDia) {
	goto([CenterDia/2,0mm]);
	circle_cw([0mm,0mm]);
	}

	repeat(NumLeaves;i) {
	a = (i-1)*LeafStemAngle;
	tracepath(rotate_xy(LeafPoints,a));
	}

	repeat(NumLeaves;i) {
	a = (i-1)*LeafStemAngle;
	tracepath(rotate_xy(RimPoints,a));
	}

	linecolor(0xff0000);

	goto([OuterDia/2,0]);
	circle_cw([0mm,0mm]);

view raw Marquetry Layers.gcmc hosted with ❤ by GitHub

The New Hotness

Layered Paper Coaster: GCMC Test