The New Hotness

Having figured out how to intersect a line with a circle, I figured I could do it twice to put arcs on both the inside and the outside of each petal:

Chipboard coaster - double arcs — Chipboard coaster – double arcs

As before, scribbling markers on plain chipboard makes for a … subdued … coaster, so I tried chipboard with one white surface:

Chipboard coaster - plain vs white — Chipboard coaster – plain vs white

Much better.

Clamping the coaster produces a flatter result:

Chipboard coaster - clamping — Chipboard coaster – clamping

With the risk of squishing excess glue through the kerf:

Chipboard coaster - excess glue — Chipboard coaster – excess glue

That’s the same coaster as in the first picture, carefully arranged with light reflecting off the flat glue surface. In real life, the nearly transparent glue doesn’t look nearly so awful, but smoothing much less glue than seems necessary across the bottom disk suffices.

The geometry doodle with the arcs:

Chipboard coaster - double arc petal geometry doodle — Chipboard coaster – double arc petal geometry doodle

I suppose I should refactor the code with a quadratic solver returning a list of roots, but copypasta suffices for now.

The GCMC and Bash source code as a GitHub Gist:

	#!/bin/bash
	# Simple petals test piece
	# Ed Nisley KE4ZNU – 2022-07-01

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

	SVGFlags='-P 4 –pedantic –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='Simple Petals.gcmc'

	[ -z "$1" ] && petals="6" \|\| petals="$1"

	fn=Petals-$petals.svg
	echo Output: $fn

	gcmc $SVGFlags \
	-D "NumPetals=$petals" \
	–include "$LibPath" \
	"$ScriptPath"/"$Script" > "$fn"

view raw petals.sh hosted with ❤ by GitHub

	// Simple Petals Test Piece
	// Ed Nisley KE4ZNU
	// 2022-07-12 Simplest possible petals

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

	//—–
	// Library routines

	include("tracepath.inc.gcmc");
	include("tracepath_comp.inc.gcmc");
	include("varcs.inc.gcmc");
	include("engrave.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 = 100.0mm;
	}

	if (!isdefined("CenterDia")) {
	CenterDia = 25.0mm;
	}

	if (!isdefined("NumPetals")) {
	NumPetals = 6;
	}

	if (!isdefined("Sash")) {
	Sash = 5.0mm;
	}

	// Petal values

	PetalAngle = 360.0deg/NumPetals; // subtended by inner sides
	PetalHA = PetalAngle/2;

	PetalOD = OuterDia – 2*Sash;
	PetalID = CenterDia + 2*Sash;

	PetalOAL = OuterDia/2 – Sash – (Sash/2)/sin(PetalHA);
	//message("petalOAL: ",PetalOAL);

	// Find petal vertices

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

	t1 = tan(PetalHA);
	sc = (Sash/2) / cos(PetalHA);

	if (P0.x < PetalID/2) {
	a = 1 + pow(t1,2);
	b = -2 * t1 * sc;
	c = pow(sc,2) – pow(PetalID/2,2);
	xp = (-b + sqrt(pow(b,2) – 4ac))/(2*a);
	xn = (-b – sqrt(pow(b,2) – 4ac))/(2*a);
	y = xp*t1 – sc;
	if (FALSE) {
	message("a: ",a);
	message("b: ",b);
	message("c: ",c);
	message("p: ",xp," n: ",xn," y: ",y);
	}
	P1 = [xp,y];
	}
	else {
	P1 = P0;
	}

	a = 1 + pow(t1,2);
	b = -2 * t1 * sc;
	c = pow(sc,2) – pow(PetalOD/2,2);

	if (FALSE) {
	message("a: ",a);
	message("b: ",b);
	message("c: ",c);
	}

	xp = (-b + sqrt(pow(b,2) – 4ac))/(2*a);
	xn = (-b – sqrt(pow(b,2) – 4ac))/(2*a);
	y = to_mm(sqrt(pow(PetalOD/2,2) – pow(xp,2)));
	//message("p: ",xp," n: ",xn," y: ",y);

	P2 = [xp,y];

	PetalWidth = 2*P2.y;

	P3 = [PetalOD/2,0.0mm];

	if (FALSE) {
	message("P0: ",P0);
	message("P1: ",P1);
	message("P2: ",P2);
	message("P3: ",P3);
	}

	// Construct paths

	PetalPoints = {P1,P2};

	OutArc = varc_cw([P2.x,-P2.y] – P2,PetalOD/2);
	OutArc += P2;
	PetalPoints += OutArc;

	if (P0 != P1) {
	PetalPoints += {[P1.x,-P1.y]};
	InArc = varc_ccw(P1 – [P1.x,-P1.y],PetalID/2);
	InArc += [P1.x,-P1.y];
	PetalPoints += InArc;
	}
	else {
	PetalPoints += {P0};
	}

	//— Lay out the frame

	linecolor(0xff0000);

	layer("Frame");

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

	repeat(NumPetals;i) {
	a = (i-1)*PetalAngle;
	tracepath(rotate_xy(PetalPoints,a));
	}

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

	//— Lay out internal pieces for oriented cutting

	// baseplate

	layer("Base");

	relocate([OuterDia + 2*Sash,0]);
	goto([OuterDia/2,0]);
	circle_cw([0mm,0mm]);

	// central circle

	if (CenterDia) {
	layer("Center");

	relocate([OuterDia/2 + Sash,-(OuterDia – CenterDia)/2]);
	goto([CenterDia/2,0mm]);
	circle_cw([0mm,0mm]);
	}

	// petals

	layer("Petals");

	repeat(NumPetals;i) {
	org = [PetalWidth/2 – OuterDia/2,-(OuterDia + Sash)];
	relocate([(i-1)*(PetalWidth + Sash) + org.x,org.y]);
	tracepath(rotate_xy(PetalPoints,90deg));
	}

	// Debugging by printf()

	if (FALSE) {
	layer("Tool1");
	linecolor(0xff1f00);

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

	goto(P0);
	circle_cw([0mm,0mm]);

	goto([0,0]);
	move([OuterDia/2,0]);

	goto([0,0]);
	move(OuterDia/2 * [cos(PetalHA),sin(PetalHA)]);

	goto(P2);
	move_r([0,-PetalWidth/2]);

	}

view raw Simple Petals.gcmc hosted with ❤ by GitHub

The New Hotness

Coaster Generator: Simple Petals