WORK IN PROGRESS: s2 geometry functions - needed for the new regional scoreboards

external/s2geometry.js

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+/// S2 Geometry functions
+// the regional scoreboard is based on a level 6 S2 Cell
+// - https://docs.google.com/presentation/d/1Hl4KapfAENAOf4gv-pSngKwvS_jwNVHRPZTTDzXXn6Q/view?pli=1#slide=id.i22
+// at the time of writing there's no actual API for the intel map to retrieve scoreboard data,
+// but it's still useful to plot the score cells on the intel map
+
+
+// the S2 geometry is based on projecting the earth sphere onto a cube, with some scaling of face coordinates to
+// keep things close to approximate equal area for adjacent cells
+// to convert a lat,lng into a cell id:
+// - convert lat,lng to x,y,z
+// - convert x,y,z into face,u,v
+// - u,v scaled to s,t (i,j?) with quadratic formula
+// - s,t (i,j?) converted to a position along a Hubbert space-filling curve
+// - combine face,position to get the cell id
+
+
+
+(function() {
+
+window.S2 = {};
+
+
+S2.LatLngToXYZ = function(latLng) {
+  var d2r = L.LatLng.DEG_TO_RAD;
+
+  var phi = latLng.lat*d2r;
+  var theta = latLng.lng*d2r;
+
+  var cosphi = Math.cos(phi);
+
+  return [Math.cos(theta)*cosphi, Math.sin(theta)*cosphi, Math.sin(phi)];
+};
+
+var largestAbsComponent = function(xyz) {
+  var temp = [Math.abs(xyz[0]), Math.abs(xyz[1]), Math.abs(xyz[2])];
+
+  if (temp[0] > temp[1]) {
+    if (temp[0] > temp[2]) {
+      return 0;
+    } else {
+      return 1;
+    }
+  } else {
+    if (temp[1] > temp[2]) {
+      return 1;
+    } else {
+      return 2;
+    }
+  }
+
+};
+
+var faceXYZToUV = function(face,xyz) {
+  var u,v;
+
+  switch (face) {
+    case 0: u =  xyz[1]/xyz[0]; v =  xyz[2]/xyz[0]; break;
+    case 1: u = -xyz[0]/xyz[1]; v =  xyz[2]/xyz[1]; break;
+    case 2: u = -xyz[0]/xyz[2]; v = -xyz[1]/xyz[2]; break;
+    case 3: u =  xyz[2]/xyz[0]; v =  xyz[1]/xyz[0]; break;
+    case 4: u =  xyz[2]/xyz[1]; v = -xyz[0]/xyz[1]; break;
+    case 5: u = -xyz[1]/xyz[2]; v = -xyz[0]/xyz[2]; break;
+    default: throw {error: 'Invalid face'}; break;
+  }
+
+  return [u,v];
+}
+
+var singleSTtoUV = function(st) {
+
+  if (st >= 0.5) {
+    return (1/3.0) * (4*st*st - 1);
+  } else {
+    return (1/3.0) * (1 - (4*(1-st)*(1-st)));
+  }
+}
+
+var singleUVtoST = function(uv) {
+  if (uv >= 0) {
+    return 0.5 * Math.sqrt (1 + 3*uv);
+  } else {
+    return 1 - 0.5 * Math.sqrt (1 - 3*uv);
+  }
+}
+
+
+S2.XYZToFaceUV = function(xyz) {
+  var face = largestAbsComponent(xyz);
+
+  if (xyz[face] < 0) {
+    face += 3;
+  }
+
+  uv = faceXYZToUV (face,xyz);
+
+  return [face, uv];
+};
+
+S2.UVToST = function(uv) {
+  return [singleUVToST(uv[0]), singleUVToST(uv[1])];
+};
+
+
+var singleSTtoIJ = function(st) {
+  var ij = Math.floor(st * kMaxSize);
+  return Math.max(0, Math.min(kMaxSize-1, ij));
+};
+
+
+})();