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$fa = $preview ? 10 : 10; // 1;
$fs = $preview ? 0.2 : 0.2; // 0.01;
colors = [
"#df0000",
"#fb8721",
"#f1e100",
"#158f25",
"#2c3ee5",
"#7706af",
"#333333",
"#88502b",
"#5dccfb",
"#f0a67b",
"#ffffff"
];
wideR = 65;
braidScale = 5;
braidR = 12;
strands = len(colors);
strandGap = 3;
wideRes = $preview ? 90 : 360;
strandRes = $preview ? 20 : 180;
extraHeight=50;
braidCircumference = 2 * PI * braidR;
strandR = (braidCircumference / strands - strandGap) / 2;
outermostCircumference = 2 * PI * (wideR + braidR);
strandH = outermostCircumference * wideRes / 360 + 0.1;
function rodriguesRotation(vector, axis, angle) =
vector * cos(angle) + cross(axis, vector) * sin(angle) + axis * (axis * vector) * (1 - cos(angle));
/*
these cross sections were always parallel to the Z axis,
but that’s not really correct
actual d/dwideT of center of braid is (-wideR sin wideT, wideR cos wideT, 0)
magnitude of that is wideR
absolute d/dwideT of center of strand is
(
-wideR sin wideT - braidR (braidScale cos wideT sin braidT + sin wideT cos braidT),
wideR cos wideT + braidR (-braidScale sin wideT sin braidT + cos wideT cos braidT),
braidR braidScale cos braidT
)
the Maxima CAS says that the magnitude of that is
sqrt(wideR² + 2wideRbraidR cos braidT + braidR²cos²braidT + braidR²braidScale²)
but actually OpenSCAD has a norm() function to get magnitudes anyway oops
strand plane basis is strand plane normal x braid center normal,
since we know those two vectors are never parallel with braidScale ≠ 0
*/
function point(wideT, strandI, strandT) =
let (
braidO = [wideR * cos(wideT), wideR * sin(wideT), 0],
braidPlaneNormal = [-wideR * sin(wideT), wideR * cos(wideT), 0],
braidPlaneNormalUnit = braidPlaneNormal / wideR,
braidT = wideT * braidScale - strandI * 360 / strands,
braidPlaneRel = [braidR * cos(braidT), braidR * sin(braidT)],
strandO = [braidO.x + braidPlaneRel.x * cos(wideT), braidO.y + braidPlaneRel.x * sin(wideT), braidPlaneRel.y],
strandPlaneNormal = [braidPlaneNormal.x - braidR * (braidScale * cos(wideT) * sin(braidT) + sin(wideT) * cos(braidT)), braidPlaneNormal.y + braidR * (-braidScale * sin(wideT) * sin(braidT) + cos(wideT) * cos(braidT)), braidR * braidScale * cos(braidT)],
strandPlaneNormalUnit = strandPlaneNormal / norm(strandPlaneNormal),
strandPlaneBasis = cross(strandPlaneNormalUnit, braidPlaneNormalUnit),
strandRelDir = rodriguesRotation(strandPlaneBasis, strandPlaneNormalUnit, strandT),
strandRel = strandRelDir * strandR / norm(strandRelDir)
) strandO + strandRel;
pointCount = (wideRes + 1) * (strandRes + 1);
module theStrand(strandI) {
color(colors[strandI])
polyhedron(
[ for (wideT = [0 : 360/wideRes : 360.01])
each [ for (strandT = [0 : 360/strandRes : 360.01])
point(wideT, strandI, strandT)
]
],
[ for (wideTI = [0 : (strandRes + 1) : pointCount - 1])
each [ for (strandTI = [wideTI : wideTI + strandRes + 1])
each [
[(strandTI + 1) % pointCount, strandTI % pointCount, (strandTI + strandRes + 1) % pointCount],
[(strandTI + strandRes + 1) % pointCount, strandTI % pointCount, (strandTI + strandRes) % pointCount],
]
]
]
);
}
module prideBraid() {
for (strandI = [0 : strands - 1]) {
theStrand(strandI);
}
}
function pointForSlot(wideT, strandI, strandT) =
let (
braidO = [wideR * cos(wideT), wideR * sin(wideT), 0],
braidPlaneNormal = [-wideR * sin(wideT), wideR * cos(wideT), 0],
braidPlaneNormalUnit = braidPlaneNormal / wideR,
braidT = wideT * braidScale - strandI * 360 / strands,
braidPlaneRel = [braidR * cos(braidT), braidR * sin(braidT)],
strandO = [braidO.x + braidPlaneRel.x * cos(wideT), braidO.y + braidPlaneRel.x * sin(wideT), braidPlaneRel.y],
strandPlaneNormal = [braidPlaneNormal.x - braidR * (braidScale * cos(wideT) * sin(braidT) + sin(wideT) * cos(braidT)), braidPlaneNormal.y + braidR * (-braidScale * sin(wideT) * sin(braidT) + cos(wideT) * cos(braidT)), braidR * braidScale * cos(braidT)],
strandPlaneNormalUnit = strandPlaneNormal / norm(strandPlaneNormal),
strandPlaneBasis = cross(strandPlaneNormalUnit, braidPlaneNormalUnit),
strandRelDir = rodriguesRotation(strandPlaneBasis, strandPlaneNormalUnit, strandT),
strandRel = strandRelDir * (strandR + 0.75) / norm(strandRelDir)
) strandO + strandRel;
module theStrandForSlot(strandI) {
polyhedron(
[ for (wideT = [0 : 360/wideRes : 360.01])
each [ for (strandT = [0 : 360/strandRes : 360.01])
pointForSlot(wideT, strandI, strandT)
]
],
[ for (wideTI = [0 : (strandRes + 1) : pointCount - 1])
each [ for (strandTI = [wideTI : wideTI + strandRes + 1])
each [
[(strandTI + 1) % pointCount, strandTI % pointCount, (strandTI + strandRes + 1) % pointCount],
[(strandTI + strandRes + 1) % pointCount, strandTI % pointCount, (strandTI + strandRes) % pointCount],
]
]
]
);
}
module prideBraidForSlot() {
for (strandI = [0 : strands - 1]) {
theStrandForSlot(strandI);
}
}
module prideBraidTorus() {
rotate_extrude()
translate([wideR, 0, 0])
circle(r=braidR+0.25);
}
module slotForDifference() {
maxR=wideR+braidR+strandR;
union() {
translate([0, 0, (braidR+strandR+2.5)/2])
prideBraidTorus();
translate([0, 0, (braidR+strandR+2.5)/2])
prideBraidForSlot();
translate([0, 0, braidR+strandR/2])
rotate_extrude()
translate([wideR, 0, 0])
circle(r=braidR+strandR+3);
}
}
module peg() {
rotate([0, 0, 45])
cube([2, 2, 10], center=true);
}
sliceX = 1;
sliceY = 1;
slices = 3;
//color("#000000")
intersection() {
r = (wideR + braidR + strandR + 3) * 2;
difference() {
slotCenterR=r*0.75;
translate([0, 0, -10-extraHeight*0.5])
cylinder(h=(braidR+strandR+3)*2+extraHeight, r=r, center=true);
translate([slotCenterR,0,0])
slotForDifference();
translate([slotCenterR*cos(120),slotCenterR*sin(120),0])
slotForDifference();
translate([slotCenterR*cos(-120),slotCenterR*sin(-120),0])
slotForDifference();
}
difference() {
translate([-r+2*r*sliceX/slices, -r+2*r*sliceY/slices, -500000])
cube([2*r/slices, 2*r/slices, 1000000]);
// pegs parallel to the Y axis
for (pegX = [0 : slices - 1]) {
for (pegY = [1 : slices - 1]) {
for (pegZ = [0 : 90 : 360]) {
translate([-r+2*r*(pegX+0.5)/slices, -r+2*r*pegY/slices, -10-extraHeight*0.5])
translate([0.75 * r/slices * cos(pegZ+45), 0, 0.75 * (braidR+strandR+3+extraHeight/2) * sin(pegZ+45) * 0.8 - 6])
rotate([90, 0, 0])
peg();
}}}
// pegs parallel to the X axis
for (pegX = [1 : slices - 1]) {
for (pegY = [0 : slices - 1]) {
for (pegZ = [0 : 90 : 360]) {
translate([-r+2*r*pegX/slices, -r+2*r*(pegY+0.5)/slices, -10-extraHeight*0.5])
translate([0, 0.75 * r/slices * cos(pegZ+45), 0.75 * (braidR+strandR+3+extraHeight/2) * sin(pegZ+45) * 0.8 - 6])
rotate([0, 90, 0])
peg();
}}}
}
}
rotate([0, 0, 30])
translate([0, 7, 6.9]) {
color("#057748")
translate([0, 4, -0.01])
scale(34)
union() {
translate([wideR*0.4/34, 0, 0])
import("my-hand.stl");
translate([-wideR*0.4/34, 0, 0])
scale([-1, 1, 1])
import("my-hand.stl");
}
color("#057748")
translate([0, -40, 3.4/2-0.01])
rotate([180, 0, -45])
scale([25, 25, 1])
linear_extrude(height = 3.4, center = true) {
polygon([
[0, 0.5],
[0.5, 0.5],
[0.5, -0.5],
[0.4, -0.5],
[0.4, 0.4],
[0, 0.4]
]);
}
}
// !peg();
|
