1 files changed, 91 insertions, 0 deletions
diff --git a/pride-braid.scad b/pride-braid.scad
new file mode 100644
index 0000000..b25f3e4
--- /dev/null
+++ b/pride-braid.scad
@@ -0,0 +1,91 @@
+$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 ? 180 : 360;
+strandRes = $preview ? 36 : 180;
+
+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],
+                    ]
+                ]
+            ]
+        );
+}
+
+for (strandI = [0 : strands - 1]) {
+    theStrand(strandI);
+}