polylabel.js

import Queue from 'tinyqueue';

export default function polylabel(polygon, precision = 1.0, debug = false) {
    // find the bounding box of the outer ring
    let minX = Infinity;
    let minY = Infinity;
    let maxX = -Infinity;
    let maxY = -Infinity;

    for (const [x, y] of polygon[0]) {
        if (x < minX) minX = x;
        if (y < minY) minY = y;
        if (x > maxX) maxX = x;
        if (y > maxY) maxY = y;
    }

    const width = maxX - minX;
    const height = maxY - minY;
    const cellSize = Math.max(precision, Math.min(width, height));

    if (cellSize === precision) {
        const result = [minX, minY];
        result.distance = 0;
        return result;
    }

    // a priority queue of cells in order of their "potential" (max distance to polygon)
    const cellQueue = new Queue([], (a, b) => b.max - a.max);

    // take centroid as the first best guess
    let bestCell = getCentroidCell(polygon);

    // second guess: bounding box centroid
    const bboxCell = new Cell(minX + width / 2, minY + height / 2, 0, polygon);
    if (bboxCell.d > bestCell.d) bestCell = bboxCell;

    let numProbes = 2;

    function potentiallyQueue(x, y, h) {
        const cell = new Cell(x, y, h, polygon);
        numProbes++;
        if (cell.max > bestCell.d + precision) cellQueue.push(cell);

        // update the best cell if we found a better one
        if (cell.d > bestCell.d) {
            bestCell = cell;
            if (debug) console.log(`found best ${Math.round(1e4 * cell.d) / 1e4} after ${numProbes} probes`);
        }
    }

    // cover polygon with initial cells
    let h = cellSize / 2;
    for (let x = minX; x < maxX; x += cellSize) {
        for (let y = minY; y < maxY; y += cellSize) {
            potentiallyQueue(x + h, y + h, h);
        }
    }

    while (cellQueue.length) {
        // pick the most promising cell from the queue
        const {max, x, y, h: ch} = cellQueue.pop();

        // do not drill down further if there's no chance of a better solution
        if (max - bestCell.d <= precision) break;

        // split the cell into four cells
        h = ch / 2;
        potentiallyQueue(x - h, y - h, h);
        potentiallyQueue(x + h, y - h, h);
        potentiallyQueue(x - h, y + h, h);
        potentiallyQueue(x + h, y + h, h);
    }

    if (debug) {
        console.log(`num probes: ${numProbes}\nbest distance: ${bestCell.d}`);
    }

    const result = [bestCell.x, bestCell.y];
    result.distance = bestCell.d;
    return result;
}

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) {
    let inside = false;
    let minDistSq = Infinity;

    for (const ring of polygon) {
        for (let i = 0, len = ring.length, j = len - 1; i < len; j = i++) {
            const a = ring[i];
            const 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) {
    let area = 0;
    let x = 0;
    let y = 0;
    const points = polygon[0];

    for (let i = 0, len = points.length, j = len - 1; i < len; j = i++) {
        const a = points[i];
        const b = points[j];
        const f = a[0] * b[1] - b[0] * a[1];
        x += (a[0] + b[0]) * f;
        y += (a[1] + b[1]) * f;
        area += f * 3;
    }
    const centroid = new Cell(x / area, y / area, 0, polygon);
    if (area === 0 || centroid.d < 0) return new Cell(points[0][0], points[0][1], 0, polygon);
    return centroid;
}

// get squared distance from a point to a segment
function getSegDistSq(px, py, a, b) {
    let x = a[0];
    let y = a[1];
    let dx = b[0] - x;
    let dy = b[1] - y;

    if (dx !== 0 || dy !== 0) {
        const 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;
}