engineN/public/theme/plugins/d3-geo/src/centroid.js

import {asin, atan2, cos, degrees, epsilon, epsilon2, radians, sin, sqrt} from "./math";
import noop from "./noop";
import stream from "./stream";

var W0, W1,
    X0, Y0, Z0,
    X1, Y1, Z1,
    X2, Y2, Z2,
    lambda00, phi00, // first point
    x0, y0, z0; // previous point

var centroidStream = {
  sphere: noop,
  point: centroidPoint,
  lineStart: centroidLineStart,
  lineEnd: centroidLineEnd,
  polygonStart: function() {
    centroidStream.lineStart = centroidRingStart;
    centroidStream.lineEnd = centroidRingEnd;
  },
  polygonEnd: function() {
    centroidStream.lineStart = centroidLineStart;
    centroidStream.lineEnd = centroidLineEnd;
  }
};

// Arithmetic mean of Cartesian vectors.
function centroidPoint(lambda, phi) {
  lambda *= radians, phi *= radians;
  var cosPhi = cos(phi);
  centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi));
}

function centroidPointCartesian(x, y, z) {
  ++W0;
  X0 += (x - X0) / W0;
  Y0 += (y - Y0) / W0;
  Z0 += (z - Z0) / W0;
}

function centroidLineStart() {
  centroidStream.point = centroidLinePointFirst;
}

function centroidLinePointFirst(lambda, phi) {
  lambda *= radians, phi *= radians;
  var cosPhi = cos(phi);
  x0 = cosPhi * cos(lambda);
  y0 = cosPhi * sin(lambda);
  z0 = sin(phi);
  centroidStream.point = centroidLinePoint;
  centroidPointCartesian(x0, y0, z0);
}

function centroidLinePoint(lambda, phi) {
  lambda *= radians, phi *= radians;
  var cosPhi = cos(phi),
      x = cosPhi * cos(lambda),
      y = cosPhi * sin(lambda),
      z = sin(phi),
      w = atan2(sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z);
  W1 += w;
  X1 += w * (x0 + (x0 = x));
  Y1 += w * (y0 + (y0 = y));
  Z1 += w * (z0 + (z0 = z));
  centroidPointCartesian(x0, y0, z0);
}

function centroidLineEnd() {
  centroidStream.point = centroidPoint;
}

// See J. E. Brock, The Inertia Tensor for a Spherical Triangle,
// J. Applied Mechanics 42, 239 (1975).
function centroidRingStart() {
  centroidStream.point = centroidRingPointFirst;
}

function centroidRingEnd() {
  centroidRingPoint(lambda00, phi00);
  centroidStream.point = centroidPoint;
}

function centroidRingPointFirst(lambda, phi) {
  lambda00 = lambda, phi00 = phi;
  lambda *= radians, phi *= radians;
  centroidStream.point = centroidRingPoint;
  var cosPhi = cos(phi);
  x0 = cosPhi * cos(lambda);
  y0 = cosPhi * sin(lambda);
  z0 = sin(phi);
  centroidPointCartesian(x0, y0, z0);
}

function centroidRingPoint(lambda, phi) {
  lambda *= radians, phi *= radians;
  var cosPhi = cos(phi),
      x = cosPhi * cos(lambda),
      y = cosPhi * sin(lambda),
      z = sin(phi),
      cx = y0 * z - z0 * y,
      cy = z0 * x - x0 * z,
      cz = x0 * y - y0 * x,
      m = sqrt(cx * cx + cy * cy + cz * cz),
      w = asin(m), // line weight = angle
      v = m && -w / m; // area weight multiplier
  X2 += v * cx;
  Y2 += v * cy;
  Z2 += v * cz;
  W1 += w;
  X1 += w * (x0 + (x0 = x));
  Y1 += w * (y0 + (y0 = y));
  Z1 += w * (z0 + (z0 = z));
  centroidPointCartesian(x0, y0, z0);
}

export default function(object) {
  W0 = W1 =
  X0 = Y0 = Z0 =
  X1 = Y1 = Z1 =
  X2 = Y2 = Z2 = 0;
  stream(object, centroidStream);

  var x = X2,
      y = Y2,
      z = Z2,
      m = x * x + y * y + z * z;

  // If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid.
  if (m < epsilon2) {
    x = X1, y = Y1, z = Z1;
    // If the feature has zero length, fall back to arithmetic mean of point vectors.
    if (W1 < epsilon) x = X0, y = Y0, z = Z0;
    m = x * x + y * y + z * z;
    // If the feature still has an undefined ccentroid, then return.
    if (m < epsilon2) return [NaN, NaN];
  }

  return [atan2(y, x) * degrees, asin(z / sqrt(m)) * degrees];
}