Add aperiodic monotiles to landing page

app/assets/config/manifest.js

@@ -2,4 +2,6 @@
 //= link_directory ../javascripts .js
 //= link_directory ../stylesheets .css
 //= link commontator/manifest.js
-//= link thredded_katex.css
+//= link thredded_katex.css
+//= link monotile/geometry.js
+//= link monotile/hat.js

app/assets/javascripts/monotile/geometry.js

@@ -0,0 +1,94 @@
+// BSD-3-Clause licensed by Craig S. Kaplan
+// adapted from: https://github.com/isohedral/hatviz
+
+// This file is mostly code that will get replaced anyways since
+// the monotiles will probably not stay on the front screen forever.
+// Having to properly use modules here and import/export the respective variables
+// would be overkill. This is mostly external code from the monotile project.
+// It works as intended and is pretty much unrelated to the rest of our code base.
+// For these reasons, we disable some ESLint rules for this file.
+/* eslint-disable no-undef, no-unused-vars */
+
+const r3 = 1.7320508075688772;
+const hr3 = 0.8660254037844386;
+const ident = [1, 0, 0, 0, 1, 0];
+
+function pt(x, y) {
+  return { x: x, y: y };
+}
+
+function hexPt(x, y) {
+  return pt(x + 0.5 * y, hr3 * y);
+}
+
+// Affine matrix inverse
+function inv(T) {
+  const det = T[0] * T[4] - T[1] * T[3];
+  return [T[4] / det, -T[1] / det, (T[1] * T[5] - T[2] * T[4]) / det,
+    -T[3] / det, T[0] / det, (T[2] * T[3] - T[0] * T[5]) / det];
+}
+
+// Affine matrix multiply
+function mul(A, B) {
+  return [A[0] * B[0] + A[1] * B[3],
+    A[0] * B[1] + A[1] * B[4],
+    A[0] * B[2] + A[1] * B[5] + A[2],
+
+    A[3] * B[0] + A[4] * B[3],
+    A[3] * B[1] + A[4] * B[4],
+    A[3] * B[2] + A[4] * B[5] + A[5]];
+}
+
+function padd(p, q) {
+  return { x: p.x + q.x, y: p.y + q.y };
+}
+
+function psub(p, q) {
+  return { x: p.x - q.x, y: p.y - q.y };
+}
+
+// Rotation matrix
+function trot(ang) {
+  const c = cos(ang);
+  const s = sin(ang);
+  return [c, -s, 0, s, c, 0];
+}
+
+// Translation matrix
+function ttrans(tx, ty) {
+  return [1, 0, tx, 0, 1, ty];
+}
+
+function rotAbout(p, ang) {
+  return mul(ttrans(p.x, p.y),
+    mul(trot(ang), ttrans(-p.x, -p.y)));
+}
+
+// Matrix * point
+function transPt(M, P) {
+  return pt(M[0] * P.x + M[1] * P.y + M[2], M[3] * P.x + M[4] * P.y + M[5]);
+}
+
+// Match unit interval to line segment p->q
+function matchSeg(p, q) {
+  return [q.x - p.x, p.y - q.y, p.x, q.y - p.y, q.x - p.x, p.y];
+}
+
+// Match line segment p1->q1 to line segment p2->q2
+function matchTwo(p1, q1, p2, q2) {
+  return mul(matchSeg(p2, q2), inv(matchSeg(p1, q1)));
+}
+
+// Intersect two lines defined by segments p1->q1 and p2->q2
+function intersect(p1, q1, p2, q2) {
+  const d = (q2.y - p2.y) * (q1.x - p1.x) - (q2.x - p2.x) * (q1.y - p1.y);
+  const uA = ((q2.x - p2.x) * (p1.y - p2.y) - (q2.y - p2.y) * (p1.x - p2.x)) / d;
+  return pt(p1.x + uA * (q1.x - p1.x), p1.y + uA * (q1.y - p1.y));
+}
+
+const hat_outline = [
+  hexPt(0, 0), hexPt(-1, -1), hexPt(0, -2), hexPt(2, -2),
+  hexPt(2, -1), hexPt(4, -2), hexPt(5, -1), hexPt(4, 0),
+  hexPt(3, 0), hexPt(2, 2), hexPt(0, 3), hexPt(0, 2),
+  hexPt(-1, 2),
+];