d3-jsnext/src/geom/voronoi/index.js

d3, but futuristic

import { ε, ε2 } from '../../math/trigonometry';
import { abs } from '../../math/abs';
import { d3_geom_clipLine } from '../clip-line';

var d3_geom_voronoiEdges,
    d3_geom_voronoiCells,
    d3_geom_voronoiBeaches,
    d3_geom_voronoiBeachPool = [],
    d3_geom_voronoiFirstCircle,
    d3_geom_voronoiCircles,
    d3_geom_voronoiCirclePool = [];

function d3_geom_voronoiBeach() {
  d3_geom_voronoiRedBlackNode(this);
  this.edge =
  this.site =
  this.circle = null;
}

function d3_geom_voronoiCreateBeach(site) {
  var beach = d3_geom_voronoiBeachPool.pop() || new d3_geom_voronoiBeach;
  beach.site = site;
  return beach;
}

function d3_geom_voronoiDetachBeach(beach) {
  d3_geom_voronoiDetachCircle(beach);
  d3_geom_voronoiBeaches.remove(beach);
  d3_geom_voronoiBeachPool.push(beach);
  d3_geom_voronoiRedBlackNode(beach);
}

function d3_geom_voronoiRemoveBeach(beach) {
  var circle = beach.circle,
      x = circle.x,
      y = circle.cy,
      vertex = {x: x, y: y},
      previous = beach.P,
      next = beach.N,
      disappearing = [beach];

  d3_geom_voronoiDetachBeach(beach);

  var lArc = previous;
  while (lArc.circle
      && abs(x - lArc.circle.x) < ε
      && abs(y - lArc.circle.cy) < ε) {
    previous = lArc.P;
    disappearing.unshift(lArc);
    d3_geom_voronoiDetachBeach(lArc);
    lArc = previous;
  }

  disappearing.unshift(lArc);
  d3_geom_voronoiDetachCircle(lArc);

  var rArc = next;
  while (rArc.circle
      && abs(x - rArc.circle.x) < ε
      && abs(y - rArc.circle.cy) < ε) {
    next = rArc.N;
    disappearing.push(rArc);
    d3_geom_voronoiDetachBeach(rArc);
    rArc = next;
  }

  disappearing.push(rArc);
  d3_geom_voronoiDetachCircle(rArc);

  var nArcs = disappearing.length,
      iArc;
  for (iArc = 1; iArc < nArcs; ++iArc) {
    rArc = disappearing[iArc];
    lArc = disappearing[iArc - 1];
    d3_geom_voronoiSetEdgeEnd(rArc.edge, lArc.site, rArc.site, vertex);
  }

  lArc = disappearing[0];
  rArc = disappearing[nArcs - 1];
  rArc.edge = d3_geom_voronoiCreateEdge(lArc.site, rArc.site, null, vertex);

  d3_geom_voronoiAttachCircle(lArc);
  d3_geom_voronoiAttachCircle(rArc);
}

function d3_geom_voronoiAddBeach(site) {
  var x = site.x,
      directrix = site.y,
      lArc,
      rArc,
      dxl,
      dxr,
      node = d3_geom_voronoiBeaches._;

  while (node) {
    dxl = d3_geom_voronoiLeftBreakPoint(node, directrix) - x;
    if (dxl > ε) node = node.L; else {
      dxr = x - d3_geom_voronoiRightBreakPoint(node, directrix);
      if (dxr > ε) {
        if (!node.R) {
          lArc = node;
          break;
        }
        node = node.R;
      } else {
        if (dxl > -ε) {
          lArc = node.P;
          rArc = node;
        } else if (dxr > -ε) {
          lArc = node;
          rArc = node.N;
        } else {
          lArc = rArc = node;
        }
        break;
      }
    }
  }

  var newArc = d3_geom_voronoiCreateBeach(site);
  d3_geom_voronoiBeaches.insert(lArc, newArc);

  if (!lArc && !rArc) return;

  if (lArc === rArc) {
    d3_geom_voronoiDetachCircle(lArc);
    rArc = d3_geom_voronoiCreateBeach(lArc.site);
    d3_geom_voronoiBeaches.insert(newArc, rArc);
    newArc.edge = rArc.edge = d3_geom_voronoiCreateEdge(lArc.site, newArc.site);
    d3_geom_voronoiAttachCircle(lArc);
    d3_geom_voronoiAttachCircle(rArc);
    return;
  }

  if (!rArc) { // && lArc
    newArc.edge = d3_geom_voronoiCreateEdge(lArc.site, newArc.site);
    return;
  }

  // else lArc !== rArc
  d3_geom_voronoiDetachCircle(lArc);
  d3_geom_voronoiDetachCircle(rArc);

  var lSite = lArc.site,
      ax = lSite.x,
      ay = lSite.y,
      bx = site.x - ax,
      by = site.y - ay,
      rSite = rArc.site,
      cx = rSite.x - ax,
      cy = rSite.y - ay,
      d = 2 * (bx * cy - by * cx),
      hb = bx * bx + by * by,
      hc = cx * cx + cy * cy,
      vertex = {x: (cy * hb - by * hc) / d + ax, y: (bx * hc - cx * hb) / d + ay};

  d3_geom_voronoiSetEdgeEnd(rArc.edge, lSite, rSite, vertex);
  newArc.edge = d3_geom_voronoiCreateEdge(lSite, site, null, vertex);
  rArc.edge = d3_geom_voronoiCreateEdge(site, rSite, null, vertex);
  d3_geom_voronoiAttachCircle(lArc);
  d3_geom_voronoiAttachCircle(rArc);
}

function d3_geom_voronoiLeftBreakPoint(arc, directrix) {
  var site = arc.site,
      rfocx = site.x,
      rfocy = site.y,
      pby2 = rfocy - directrix;

  if (!pby2) return rfocx;

  var lArc = arc.P;
  if (!lArc) return -Infinity;

  site = lArc.site;
  var lfocx = site.x,
      lfocy = site.y,
      plby2 = lfocy - directrix;

  if (!plby2) return lfocx;

  var hl = lfocx - rfocx,
      aby2 = 1 / pby2 - 1 / plby2,
      b = hl / plby2;

  if (aby2) return (-b + Math.sqrt(b * b - 2 * aby2 * (hl * hl / (-2 * plby2) - lfocy + plby2 / 2 + rfocy - pby2 / 2))) / aby2 + rfocx;

  return (rfocx + lfocx) / 2;
}

function d3_geom_voronoiRightBreakPoint(arc, directrix) {
  var rArc = arc.N;
  if (rArc) return d3_geom_voronoiLeftBreakPoint(rArc, directrix);
  var site = arc.site;
  return site.y === directrix ? site.x : Infinity;
}

function d3_geom_voronoiCell(site) {
  this.site = site;
  this.edges = [];
}

d3_geom_voronoiCell.prototype.prepare = function() {
  var halfEdges = this.edges,
      iHalfEdge = halfEdges.length,
      edge;

  while (iHalfEdge--) {
    edge = halfEdges[iHalfEdge].edge;
    if (!edge.b || !edge.a) halfEdges.splice(iHalfEdge, 1);
  }

  halfEdges.sort(d3_geom_voronoiHalfEdgeOrder);
  return halfEdges.length;
};

function d3_geom_voronoiCloseCells(extent) {
  var x0 = extent[0][0],
      x1 = extent[1][0],
      y0 = extent[0][1],
      y1 = extent[1][1],
      x2,
      y2,
      x3,
      y3,
      cells = d3_geom_voronoiCells,
      iCell = cells.length,
      cell,
      iHalfEdge,
      halfEdges,
      nHalfEdges,
      start,
      end;

  while (iCell--) {
    cell = cells[iCell];
    if (!cell || !cell.prepare()) continue;
    halfEdges = cell.edges;
    nHalfEdges = halfEdges.length;
    iHalfEdge = 0;
    while (iHalfEdge < nHalfEdges) {
      end = halfEdges[iHalfEdge].end(), x3 = end.x, y3 = end.y;
      start = halfEdges[++iHalfEdge % nHalfEdges].start(), x2 = start.x, y2 = start.y;
      if (abs(x3 - x2) > ε || abs(y3 - y2) > ε) {
        halfEdges.splice(iHalfEdge, 0, new d3_geom_voronoiHalfEdge(d3_geom_voronoiCreateBorderEdge(cell.site, end,
            abs(x3 - x0) < ε && y1 - y3 > ε ? {x: x0, y: abs(x2 - x0) < ε ? y2 : y1}
            : abs(y3 - y1) < ε && x1 - x3 > ε ? {x: abs(y2 - y1) < ε ? x2 : x1, y: y1}
            : abs(x3 - x1) < ε && y3 - y0 > ε ? {x: x1, y: abs(x2 - x1) < ε ? y2 : y0}
            : abs(y3 - y0) < ε && x3 - x0 > ε ? {x: abs(y2 - y0) < ε ? x2 : x0, y: y0}
            : null), cell.site, null));
        ++nHalfEdges;
      }
    }
  }
}

function d3_geom_voronoiHalfEdgeOrder(a, b) {
  return b.angle - a.angle;
}

function d3_geom_voronoiCircle() {
  d3_geom_voronoiRedBlackNode(this);
  this.x =
  this.y =
  this.arc =
  this.site =
  this.cy = null;
}

function d3_geom_voronoiAttachCircle(arc) {
  var lArc = arc.P,
      rArc = arc.N;

  if (!lArc || !rArc) return;

  var lSite = lArc.site,
      cSite = arc.site,
      rSite = rArc.site;

  if (lSite === rSite) return;

  var bx = cSite.x,
      by = cSite.y,
      ax = lSite.x - bx,
      ay = lSite.y - by,
      cx = rSite.x - bx,
      cy = rSite.y - by;

  var d = 2 * (ax * cy - ay * cx);
  if (d >= -ε2) return;

  var ha = ax * ax + ay * ay,
      hc = cx * cx + cy * cy,
      x = (cy * ha - ay * hc) / d,
      y = (ax * hc - cx * ha) / d,
      cy = y + by;

  var circle = d3_geom_voronoiCirclePool.pop() || new d3_geom_voronoiCircle;
  circle.arc = arc;
  circle.site = cSite;
  circle.x = x + bx;
  circle.y = cy + Math.sqrt(x * x + y * y); // y bottom
  circle.cy = cy;

  arc.circle = circle;

  var before = null,
      node = d3_geom_voronoiCircles._;

  while (node) {
    if (circle.y < node.y || (circle.y === node.y && circle.x <= node.x)) {
      if (node.L) node = node.L;
      else { before = node.P; break; }
    } else {
      if (node.R) node = node.R;
      else { before = node; break; }
    }
  }

  d3_geom_voronoiCircles.insert(before, circle);
  if (!before) d3_geom_voronoiFirstCircle = circle;
}

function d3_geom_voronoiDetachCircle(arc) {
  var circle = arc.circle;
  if (circle) {
    if (!circle.P) d3_geom_voronoiFirstCircle = circle.N;
    d3_geom_voronoiCircles.remove(circle);
    d3_geom_voronoiCirclePool.push(circle);
    d3_geom_voronoiRedBlackNode(circle);
    arc.circle = null;
  }
}

function d3_geom_voronoiClipEdges(extent) {
  var edges = d3_geom_voronoiEdges,
      clip = d3_geom_clipLine(extent[0][0], extent[0][1], extent[1][0], extent[1][1]),
      i = edges.length,
      e;
  while (i--) {
    e = edges[i];
    if (!d3_geom_voronoiConnectEdge(e, extent)
        || !clip(e)
        || (abs(e.a.x - e.b.x) < ε && abs(e.a.y - e.b.y) < ε)) {
      e.a = e.b = null;
      edges.splice(i, 1);
    }
  }
}

function d3_geom_voronoiConnectEdge(edge, extent) {
  var vb = edge.b;
  if (vb) return true;

  var va = edge.a,
      x0 = extent[0][0],
      x1 = extent[1][0],
      y0 = extent[0][1],
      y1 = extent[1][1],
      lSite = edge.l,
      rSite = edge.r,
      lx = lSite.x,
      ly = lSite.y,
      rx = rSite.x,
      ry = rSite.y,
      fx = (lx + rx) / 2,
      fy = (ly + ry) / 2,
      fm,
      fb;

  if (ry === ly) {
    if (fx < x0 || fx >= x1) return;
    if (lx > rx) {
      if (!va) va = {x: fx, y: y0};
      else if (va.y >= y1) return;
      vb = {x: fx, y: y1};
    } else {
      if (!va) va = {x: fx, y: y1};
      else if (va.y < y0) return;
      vb = {x: fx, y: y0};
    }
  } else {
    fm = (lx - rx) / (ry - ly);
    fb = fy - fm * fx;
    if (fm < -1 || fm > 1) {
      if (lx > rx) {
        if (!va) va = {x: (y0 - fb) / fm, y: y0};
        else if (va.y >= y1) return;
        vb = {x: (y1 - fb) / fm, y: y1};
      } else {
        if (!va) va = {x: (y1 - fb) / fm, y: y1};
        else if (va.y < y0) return;
        vb = {x: (y0 - fb) / fm, y: y0};
      }
    } else {
      if (ly < ry) {
        if (!va) va = {x: x0, y: fm * x0 + fb};
        else if (va.x >= x1) return;
        vb = {x: x1, y: fm * x1 + fb};
      } else {
        if (!va) va = {x: x1, y: fm * x1 + fb};
        else if (va.x < x0) return;
        vb = {x: x0, y: fm * x0 + fb};
      }
    }
  }

  edge.a = va;
  edge.b = vb;
  return true;
}

function d3_geom_voronoiEdge(lSite, rSite) {
  this.l = lSite;
  this.r = rSite;
  this.a = this.b = null; // for border edges
}

function d3_geom_voronoiCreateEdge(lSite, rSite, va, vb) {
  var edge = new d3_geom_voronoiEdge(lSite, rSite);
  d3_geom_voronoiEdges.push(edge);
  if (va) d3_geom_voronoiSetEdgeEnd(edge, lSite, rSite, va);
  if (vb) d3_geom_voronoiSetEdgeEnd(edge, rSite, lSite, vb);
  d3_geom_voronoiCells[lSite.i].edges.push(new d3_geom_voronoiHalfEdge(edge, lSite, rSite));
  d3_geom_voronoiCells[rSite.i].edges.push(new d3_geom_voronoiHalfEdge(edge, rSite, lSite));
  return edge;
}

function d3_geom_voronoiCreateBorderEdge(lSite, va, vb) {
  var edge = new d3_geom_voronoiEdge(lSite, null);
  edge.a = va;
  edge.b = vb;
  d3_geom_voronoiEdges.push(edge);
  return edge;
}

function d3_geom_voronoiSetEdgeEnd(edge, lSite, rSite, vertex) {
  if (!edge.a && !edge.b) {
    edge.a = vertex;
    edge.l = lSite;
    edge.r = rSite;
  } else if (edge.l === rSite) {
    edge.b = vertex;
  } else {
    edge.a = vertex;
  }
}

function d3_geom_voronoiHalfEdge(edge, lSite, rSite) {
  var va = edge.a,
      vb = edge.b;
  this.edge = edge;
  this.site = lSite;
  this.angle = rSite ? Math.atan2(rSite.y - lSite.y, rSite.x - lSite.x)
      : edge.l === lSite ? Math.atan2(vb.x - va.x, va.y - vb.y)
      : Math.atan2(va.x - vb.x, vb.y - va.y);
};

d3_geom_voronoiHalfEdge.prototype = {
  start: function() { return this.edge.l === this.site ? this.edge.a : this.edge.b; },
  end: function() { return this.edge.l === this.site ? this.edge.b : this.edge.a; }
};

function d3_geom_voronoiRedBlackTree() {
  this._ = null; // root node
}

function d3_geom_voronoiRedBlackNode(node) {
  node.U = // parent node
  node.C = // color - true for red, false for black
  node.L = // left node
  node.R = // right node
  node.P = // previous node
  node.N = null; // next node
}

d3_geom_voronoiRedBlackTree.prototype = {

  insert: function(after, node) {
    var parent, grandpa, uncle;

    if (after) {
      node.P = after;
      node.N = after.N;
      if (after.N) after.N.P = node;
      after.N = node;
      if (after.R) {
        after = after.R;
        while (after.L) after = after.L;
        after.L = node;
      } else {
        after.R = node;
      }
      parent = after;
    } else if (this._) {
      after = d3_geom_voronoiRedBlackFirst(this._);
      node.P = null;
      node.N = after;
      after.P = after.L = node;
      parent = after;
    } else {
      node.P = node.N = null;
      this._ = node;
      parent = null;
    }
    node.L = node.R = null;
    node.U = parent;
    node.C = true;

    after = node;
    while (parent && parent.C) {
      grandpa = parent.U;
      if (parent === grandpa.L) {
        uncle = grandpa.R;
        if (uncle && uncle.C) {
          parent.C = uncle.C = false;
          grandpa.C = true;
          after = grandpa;
        } else {
          if (after === parent.R) {
            d3_geom_voronoiRedBlackRotateLeft(this, parent);
            after = parent;
            parent = after.U;
          }
          parent.C = false;
          grandpa.C = true;
          d3_geom_voronoiRedBlackRotateRight(this, grandpa);
        }
      } else {
        uncle = grandpa.L;
        if (uncle && uncle.C) {
          parent.C = uncle.C = false;
          grandpa.C = true;
          after = grandpa;
        } else {
          if (after === parent.L) {
            d3_geom_voronoiRedBlackRotateRight(this, parent);
            after = parent;
            parent = after.U;
          }
          parent.C = false;
          grandpa.C = true;
          d3_geom_voronoiRedBlackRotateLeft(this, grandpa);
        }
      }
      parent = after.U;
    }
    this._.C = false;
  },

  remove: function(node) {
    if (node.N) node.N.P = node.P;
    if (node.P) node.P.N = node.N;
    node.N = node.P = null;

    var parent = node.U,
        sibling,
        left = node.L,
        right = node.R,
        next,
        red;

    if (!left) next = right;
    else if (!right) next = left;
    else next = d3_geom_voronoiRedBlackFirst(right);

    if (parent) {
      if (parent.L === node) parent.L = next;
      else parent.R = next;
    } else {
      this._ = next;
    }

    if (left && right) {
      red = next.C;
      next.C = node.C;
      next.L = left;
      left.U = next;
      if (next !== right) {
        parent = next.U;
        next.U = node.U;
        node = next.R;
        parent.L = node;
        next.R = right;
        right.U = next;
      } else {
        next.U = parent;
        parent = next;
        node = next.R;
      }
    } else {
      red = node.C;
      node = next;
    }

    if (node) node.U = parent;
    if (red) return;
    if (node && node.C) { node.C = false; return; }

    do {
      if (node === this._) break;
      if (node === parent.L) {
        sibling = parent.R;
        if (sibling.C) {
          sibling.C = false;
          parent.C = true;
          d3_geom_voronoiRedBlackRotateLeft(this, parent);
          sibling = parent.R;
        }
        if ((sibling.L && sibling.L.C)
            || (sibling.R && sibling.R.C)) {
          if (!sibling.R || !sibling.R.C) {
            sibling.L.C = false;
            sibling.C = true;
            d3_geom_voronoiRedBlackRotateRight(this, sibling);
            sibling = parent.R;
          }
          sibling.C = parent.C;
          parent.C = sibling.R.C = false;
          d3_geom_voronoiRedBlackRotateLeft(this, parent);
          node = this._;
          break;
        }
      } else {
        sibling = parent.L;
        if (sibling.C) {
          sibling.C = false;
          parent.C = true;
          d3_geom_voronoiRedBlackRotateRight(this, parent);
          sibling = parent.L;
        }
        if ((sibling.L && sibling.L.C)
          || (sibling.R && sibling.R.C)) {
          if (!sibling.L || !sibling.L.C) {
            sibling.R.C = false;
            sibling.C = true;
            d3_geom_voronoiRedBlackRotateLeft(this, sibling);
            sibling = parent.L;
          }
          sibling.C = parent.C;
          parent.C = sibling.L.C = false;
          d3_geom_voronoiRedBlackRotateRight(this, parent);
          node = this._;
          break;
        }
      }
      sibling.C = true;
      node = parent;
      parent = parent.U;
    } while (!node.C);

    if (node) node.C = false;
  }

};

function d3_geom_voronoiRedBlackRotateLeft(tree, node) {
  var p = node,
      q = node.R,
      parent = p.U;

  if (parent) {
    if (parent.L === p) parent.L = q;
    else parent.R = q;
  } else {
    tree._ = q;
  }

  q.U = parent;
  p.U = q;
  p.R = q.L;
  if (p.R) p.R.U = p;
  q.L = p;
}

function d3_geom_voronoiRedBlackRotateRight(tree, node) {
  var p = node,
      q = node.L,
      parent = p.U;

  if (parent) {
    if (parent.L === p) parent.L = q;
    else parent.R = q;
  } else {
    tree._ = q;
  }

  q.U = parent;
  p.U = q;
  p.L = q.R;
  if (p.L) p.L.U = p;
  q.R = p;
}

function d3_geom_voronoiRedBlackFirst(node) {
  while (node.L) node = node.L;
  return node;
}


function d3_geom_voronoi(sites, bbox) {
  var site = sites.sort(d3_geom_voronoiVertexOrder).pop(),
      x0,
      y0,
      circle;

  d3_geom_voronoiEdges = [];
  d3_geom_voronoiCells = new Array(sites.length);
  d3_geom_voronoiBeaches = new d3_geom_voronoiRedBlackTree;
  d3_geom_voronoiCircles = new d3_geom_voronoiRedBlackTree;

  while (true) {
    circle = d3_geom_voronoiFirstCircle;
    if (site && (!circle || site.y < circle.y || (site.y === circle.y && site.x < circle.x))) {
      if (site.x !== x0 || site.y !== y0) {
        d3_geom_voronoiCells[site.i] = new d3_geom_voronoiCell(site);
        d3_geom_voronoiAddBeach(site);
        x0 = site.x, y0 = site.y;
      }
      site = sites.pop();
    } else if (circle) {
      d3_geom_voronoiRemoveBeach(circle.arc);
    } else {
      break;
    }
  }

  if (bbox) d3_geom_voronoiClipEdges(bbox), d3_geom_voronoiCloseCells(bbox);

  var diagram = {cells: d3_geom_voronoiCells, edges: d3_geom_voronoiEdges};

  d3_geom_voronoiBeaches =
  d3_geom_voronoiCircles =
  d3_geom_voronoiEdges =
  d3_geom_voronoiCells = null;

  return diagram;
};

function d3_geom_voronoiVertexOrder(a, b) {
  return b.y - a.y || b.x - a.x;
}

export {
  d3_geom_voronoiVertexOrder,
  d3_geom_voronoi,
  d3_geom_voronoiRedBlackFirst,
  d3_geom_voronoiRedBlackRotateRight,
  d3_geom_voronoiRedBlackRotateLeft,
  d3_geom_voronoiRedBlackNode,
  d3_geom_voronoiRedBlackTree,
  d3_geom_voronoiHalfEdge,
  d3_geom_voronoiSetEdgeEnd,
  d3_geom_voronoiCreateBorderEdge,
  d3_geom_voronoiCreateEdge,
  d3_geom_voronoiEdge,
  d3_geom_voronoiConnectEdge,
  d3_geom_voronoiClipEdges,
  d3_geom_voronoiDetachCircle,
  d3_geom_voronoiAttachCircle,
  d3_geom_voronoiCircle,
  d3_geom_voronoiHalfEdgeOrder,
  d3_geom_voronoiCloseCells,
  d3_geom_voronoiCell,
  d3_geom_voronoiRightBreakPoint,
  d3_geom_voronoiLeftBreakPoint,
  d3_geom_voronoiAddBeach,
  d3_geom_voronoiRemoveBeach,
  d3_geom_voronoiDetachBeach,
  d3_geom_voronoiCreateBeach,
  d3_geom_voronoiBeach,
  d3_geom_voronoiEdges,
  d3_geom_voronoiCells,
  d3_geom_voronoiBeaches,
  d3_geom_voronoiBeachPool,
  d3_geom_voronoiFirstCircle,
  d3_geom_voronoiCircles,
  d3_geom_voronoiCirclePool
};