Published
Edited
Jul 7, 2020
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md`# Copy of PolyLabel
From https://github.com/mapbox/polylabel
Added code to deal with disconnected regions, which are lists of polygons. This is needed for some datasets such as the US County map data at https://unpkg.com/us-atlas@3/counties-albers-10m.json.
Uses TinyQueue from https://github.com/mourner/tinyqueue
`
class TinyQueue {
constructor(data = [], compare = defaultCompare) {
this.data = data;
this.length = this.data.length;
this.compare = compare;
if (this.length > 0) {
for (let i = (this.length >> 1) - 1; i >= 0; i--) this._down(i);
}
}
push(item) {
this.data.push(item);
this._up(this.length++);
}
pop() {
if (this.length === 0) return undefined;
const top = this.data[0];
const bottom = this.data.pop();
if (--this.length > 0) {
this.data[0] = bottom;
this._down(0);
}
return top;
}
peek() {
return this.data[0];
}
_up(pos) {
const {data, compare} = this;
const item = data[pos];
while (pos > 0) {
const parent = (pos - 1) >> 1;
const current = data[parent];
if (compare(item, current) >= 0) break;
data[pos] = current;
pos = parent;
}
data[pos] = item;
}
_down(pos) {
const {data, compare} = this;
const halfLength = this.length >> 1;
const item = data[pos];
while (pos < halfLength) {
let bestChild = (pos << 1) + 1; // initially it is the left child
const right = bestChild + 1;
if (right < this.length && compare(data[right], data[bestChild]) < 0) {
bestChild = right;
}
if (compare(data[bestChild], item) >= 0) break;
data[pos] = data[bestChild];
pos = bestChild;
}
data[pos] = item;
}
}
function defaultCompare(a, b) {
return a < b ? -1 : a > b ? 1 : 0;
}
function polylabel(polygon, precision, debug) {
precision = precision || 1.0;
// is this a single polygon or a list of them? -- call recursively on lists
if (isNaN(polygon[0][0][0])) {
var bestpoint = polylabel(polygon[0], precision, debug);
for (p = 1; p < polygon.length; p++) {
const thispoint = polylabel(polygon[p], precision, debug);
if (thispoint.distance > bestpoint.distance) {
bestpoint = thispoint;
}
}
return bestpoint;
}
// find the bounding box of the outer ring
var minX, minY, maxX, maxY;
for (var i = 0; i < polygon[0].length; i++) {
var p = polygon[0][i];
if (!i || p[0] < minX) minX = p[0];
if (!i || p[1] < minY) minY = p[1];
if (!i || p[0] > maxX) maxX = p[0];
if (!i || p[1] > maxY) maxY = p[1];
}
var width = maxX - minX;
var height = maxY - minY;
var cellSize = Math.min(width, height);
var h = cellSize / 2;
if (cellSize === 0) {
var degeneratePoleOfInaccessibility = [minX, minY];
degeneratePoleOfInaccessibility.distance = 0;
return degeneratePoleOfInaccessibility;
}
// a priority queue of cells in order of their "potential" (max distance to polygon)
var cellQueue = new TinyQueue(undefined, compareMax);
// cover polygon with initial cells
for (var x = minX; x < maxX; x += cellSize) {
for (var y = minY; y < maxY; y += cellSize) {
cellQueue.push(new Cell(x + h, y + h, h, polygon));
}
}
// take centroid as the first best guess
var bestCell = getCentroidCell(polygon);
// special case for rectangular polygons
var bboxCell = new Cell(minX + width / 2, minY + height / 2, 0, polygon);
if (bboxCell.d > bestCell.d) bestCell = bboxCell;
var numProbes = cellQueue.length;
while (cellQueue.length) {
// pick the most promising cell from the queue
var cell = cellQueue.pop();
// update the best cell if we found a better one
if (cell.d > bestCell.d) {
bestCell = cell;
if (debug) console.log('found best %d after %d probes', Math.round(1e4 * cell.d) / 1e4, numProbes);
}
// do not drill down further if there's no chance of a better solution
if (cell.max - bestCell.d <= precision) continue;
// split the cell into four cells
h = cell.h / 2;
cellQueue.push(new Cell(cell.x - h, cell.y - h, h, polygon));
cellQueue.push(new Cell(cell.x + h, cell.y - h, h, polygon));
cellQueue.push(new Cell(cell.x - h, cell.y + h, h, polygon));
cellQueue.push(new Cell(cell.x + h, cell.y + h, h, polygon));
numProbes += 4;
}
if (debug) {
console.log('num probes: ' + numProbes);
console.log('best distance: ' + bestCell.d);
console.log('best point: [' + bestCell.x + ', ' + bestCell.y + ']');
console.log(polygon);
}
var poleOfInaccessibility = [bestCell.x, bestCell.y];
poleOfInaccessibility.distance = bestCell.d;
return poleOfInaccessibility;
}
function compareMax(a, b) {
return b.max - a.max;
}
function Cell(x, y, h, polygon) {
this.x = x; // cell center x
this.y = y; // cell center y
this.h = h; // half the cell size
this.d = pointToPolygonDist(x, y, polygon); // distance from cell center to polygon
this.max = this.d + this.h * Math.SQRT2; // max distance to polygon within a cell
}
// signed distance from point to polygon outline (negative if point is outside)
function pointToPolygonDist(x, y, polygon) {
var inside = false;
var minDistSq = Infinity;
for (var k = 0; k < polygon.length; k++) {
var ring = polygon[k];
for (var i = 0, len = ring.length, j = len - 1; i < len; j = i++) {
var a = ring[i];
var b = ring[j];
if ((a[1] > y !== b[1] > y) &&
(x < (b[0] - a[0]) * (y - a[1]) / (b[1] - a[1]) + a[0])) inside = !inside;
minDistSq = Math.min(minDistSq, getSegDistSq(x, y, a, b));
}
}
return minDistSq === 0 ? 0 : (inside ? 1 : -1) * Math.sqrt(minDistSq);
}
// get polygon centroid
function getCentroidCell(polygon) {
var area = 0;
var x = 0;
var y = 0;
var points = polygon[0];
for (var i = 0, len = points.length, j = len - 1; i < len; j = i++) {
var a = points[i];
var b = points[j];
var f = a[0] * b[1] - b[0] * a[1];
x += (a[0] + b[0]) * f;
y += (a[1] + b[1]) * f;
area += f * 3;
}
if (area === 0) return new Cell(points[0][0], points[0][1], 0, polygon);
return new Cell(x / area, y / area, 0, polygon);
}
// get squared distance from a point to a segment
function getSegDistSq(px, py, a, b) {
var x = a[0];
var y = a[1];
var dx = b[0] - x;
var dy = b[1] - y;
if (dx !== 0 || dy !== 0) {
var t = ((px - x) * dx + (py - y) * dy) / (dx * dx + dy * dy);
if (t > 1) {
x = b[0];
y = b[1];
} else if (t > 0) {
x += dx * t;
y += dy * t;
}
}
dx = px - x;
dy = py - y;
return dx * dx + dy * dy;
}
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