coolaj86/s2-geometry.js
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initial commit - basic s2cell support

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Jon Atkins 2014-01-23 17:07:50 +00:00
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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 with quadratic formula
// - s,t converted to integer i,j offsets
// - i,j converted to a position along a Hubbert space-filling curve
// - combine face,position to get the cell id
//NOTE: compared to the google S2 geometry library, we vary from their code in the following ways
// - cell IDs: they combine face and the hilbert curve position into a single 64 bit number. this gives efficient space
// and speed. javascript doesn't have appropriate data types, and speed is not cricical, so we use
// as [face,[bitpair,bitpair,...]] instead
// - i,j: they always use 30 bits, adjusting as needed. we use 0 to (1<<level)-1 instead
// (so GetSizeIJ for a cell is always 1)
(function() {
window.S2 = {};
var 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 XYZToLatLng = function(xyz) {
var r2d = L.LatLng.RAD_TO_DEG;
var lat = Math.atan2(xyz[2], Math.sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]));
var lng = Math.atan2(xyz[1], xyz[0]);
return L.latLng(lat*r2d, lng*r2d);
};
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 2;
}
} 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 XYZToFaceUV = function(xyz) {
var face = largestAbsComponent(xyz);
if (xyz[face] < 0) {
face += 3;
}
uv = faceXYZToUV (face,xyz);
return [face, uv];
};
var FaceUVToXYZ = function(face,uv) {
var u = uv[0];
var v = uv[1];
switch (face) {
case 0: return [ 1, u, v];
case 1: return [-u, 1, v];
case 2: return [-u,-v, 1];
case 3: return [-1,-v,-u];
case 4: return [ v,-1,-u];
case 5: return [ v, u,-1];
default: throw {error: 'Invalid face'};
}
};
var STToUV = function(st) {
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)));
}
}
return [singleSTtoUV(st[0]), singleSTtoUV(st[1])];
};
var UVToST = function(uv) {
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);
}
}
return [singleUVtoST(uv[0]), singleUVtoST(uv[1])];
};
var STToIJ = function(st,order) {
var maxSize = (1<<order);
var singleSTtoIJ = function(st) {
var ij = Math.floor(st * maxSize);
return Math.max(0, Math.min(maxSize-1, ij));
};
return [singleSTtoIJ(st[0]), singleSTtoIJ(st[1])];
};
var IJToST = function(ij,order,offsets) {
var maxSize = (1<<order);
return [
(ij[0]+offsets[0])/maxSize,
(ij[1]+offsets[1])/maxSize
];
}
// hilbert space-filling curve
// based on http://blog.notdot.net/2009/11/Damn-Cool-Algorithms-Spatial-indexing-with-Quadtrees-and-Hilbert-Curves
// note: rather then calculating the final integer hilbert position, we just return the list of quads
// this ensures no precision issues whth large orders (S3 cell IDs use up to 30), and is more
// convenient for pulling out the individual bits as needed later
var pointToHilbertQuadList = function(x,y,order) {
var hilbertMap = {
'a': [ [0,'d'], [1,'a'], [3,'b'], [2,'a'] ],
'b': [ [2,'b'], [1,'b'], [3,'a'], [0,'c'] ],
'c': [ [2,'c'], [3,'d'], [1,'c'], [0,'b'] ],
'd': [ [0,'a'], [3,'c'], [1,'d'], [2,'d'] ]
};
var currentSquare='a';
var positions = [];
for (var i=order-1; i>=0; i--) {
var mask = 1<<i;
var quad_x = x&mask ? 1 : 0;
var quad_y = y&mask ? 1 : 0;
var t = hilbertMap[currentSquare][quad_x*2+quad_y];
positions.push(t[0]);
currentSquare = t[1];
}
return positions;
};
// S2Cell class
S2.S2Cell = function(){};
//static method to construct
S2.S2Cell.FromLatLng = function(latLng,level) {
var xyz = LatLngToXYZ(latLng);
var faceuv = XYZToFaceUV(xyz);
var st = UVToST(faceuv[1]);
var ij = STToIJ(st,level);
return S2.S2Cell.FromFaceIJ (faceuv[0], ij, level);
return result;
};
S2.S2Cell.FromFaceIJ = function(face,ij,level) {
var cell = new S2.S2Cell();
cell.face = face;
cell.ij = ij;
cell.level = level;
return cell;
};
S2.S2Cell.prototype.toString = function() {
return 'F'+this.face+'ij['+this.ij[0]+','+this.ij[1]+']@'+this.level;
};
S2.S2Cell.prototype.getLatLng = function() {
var st = IJToST(this.ij,this.level, [0.5,0.5]);
var uv = STToUV(st);
var xyz = FaceUVToXYZ(this.face, uv);
return XYZToLatLng(xyz);
};
S2.S2Cell.prototype.getCornerLatLngs = function() {
var result = [];
var offsets = [
[ 0.0, 0.0 ],
[ 0.0, 1.0 ],
[ 1.0, 1.0 ],
[ 1.0, 0.0 ]
];
for (var i=0; i<4; i++) {
var st = IJToST(this.ij, this.level, offsets[i]);
var uv = STToUV(st);
var xyz = FaceUVToXYZ(this.face, uv);
result.push ( XYZToLatLng(xyz) );
}
return result;
};
S2.S2Cell.prototype.getFaceAndQuads = function() {
var quads = pointToHilbertQuadList(this.ij[0], this.ij[1], this.level);
return [this.face,quads];
};
S2.S2Cell.prototype.getNeighbors = function() {
var fromFaceIJWrap = function(face,ij,level) {
var maxSize = (1<<level);
if (ij[0]>=0 && ij[1]>=0 && ij[0]<maxSize && ij[1]<maxSize) {
// no wrapping out of bounds
return S2.S2Cell.FromFaceIJ(face,ij,level);
} else {
// the new i,j are out of range.
// with the assumption that they're only a little past the borders we can just take the points as
// just beyond the cube face, project to XYZ, then re-create FaceUV from the XYZ vector
var st = IJToST(ij,level,[0.5,0.5]);
var uv = STToUV(st);
var xyz = FaceUVToXYZ(face,uv);
var faceuv = XYZToFaceUV(xyz);
face = faceuv[0];
uv = faceuv[1];
st = UVToST(uv);
ij = STToIJ(st,level);
return S2.S2Cell.FromFaceIJ (face, ij, level);
}
};
var face = this.face;
var i = this.ij[0];
var j = this.ij[1];
var level = this.level;
return [
fromFaceIJWrap(face, [i-1,j], level),
fromFaceIJWrap(face, [i,j-1], level),
fromFaceIJWrap(face, [i+1,j], level),
fromFaceIJWrap(face, [i,j+1], level)
];
};
})();