// Constructs a new quadtree for the specified array of points. A quadtree is a
// two-dimensional recursive spatial subdivision. This implementation uses
// square partitions, dividing each square into four equally-sized squares. Each
// point exists in a unique node; if multiple points are in the same position,
// some points may be stored on internal nodes rather than leaf nodes. Quadtrees
// can be used to accelerate various spatial operations, such as the Barnes-Hut
// approximation for computing n-body forces, or collision detection.
d3.geom.quadtree = function(points, x1, y1, x2, y2) {
  var p,
      i = -1,
      n = points.length;

  // Type conversion for deprecated API.
  if (n && isNaN(points[0].x)) points = points.map(d3_geom_quadtreePoint);

  // Allow bounds to be specified explicitly.
  if (arguments.length < 5) {
    if (arguments.length === 3) {
      y2 = x2 = y1;
      y1 = x1;
    } else {
      x1 = y1 = Infinity;
      x2 = y2 = -Infinity;

      // Compute bounds.
      while (++i < n) {
        p = points[i];
        if (p.x < x1) x1 = p.x;
        if (p.y < y1) y1 = p.y;
        if (p.x > x2) x2 = p.x;
        if (p.y > y2) y2 = p.y;
      }

      // Squarify the bounds.
      var dx = x2 - x1,
          dy = y2 - y1;
      if (dx > dy) y2 = y1 + dx;
      else x2 = x1 + dy;
    }
  }

  // Recursively inserts the specified point p at the node n or one of its
  // descendants. The bounds are defined by [x1, x2] and [y1, y2].
  function insert(n, p, x1, y1, x2, y2) {
    if (isNaN(p.x) || isNaN(p.y)) return; // ignore invalid points
    if (n.leaf) {
      var v = n.point;
      if (v) {
        // If the point at this leaf node is at the same position as the new
        // point we are adding, we leave the point associated with the
        // internal node while adding the new point to a child node. This
        // avoids infinite recursion.
        if ((Math.abs(v.x - p.x) + Math.abs(v.y - p.y)) < .01) {
          insertChild(n, p, x1, y1, x2, y2);
        } else {
          n.point = null;
          insertChild(n, v, x1, y1, x2, y2);
          insertChild(n, p, x1, y1, x2, y2);
        }
      } else {
        n.point = p;
      }
    } else {
      insertChild(n, p, x1, y1, x2, y2);
    }
  }

  // Recursively inserts the specified point p into a descendant of node n. The
  // bounds are defined by [x1, x2] and [y1, y2].
  function insertChild(n, p, x1, y1, x2, y2) {
    // Compute the split point, and the quadrant in which to insert p.
    var sx = (x1 + x2) * .5,
        sy = (y1 + y2) * .5,
        right = p.x >= sx,
        bottom = p.y >= sy,
        i = (bottom << 1) + right;

    // Recursively insert into the child node.
    n.leaf = false;
    n = n.nodes[i] || (n.nodes[i] = d3_geom_quadtreeNode());

    // Update the bounds as we recurse.
    if (right) x1 = sx; else x2 = sx;
    if (bottom) y1 = sy; else y2 = sy;
    insert(n, p, x1, y1, x2, y2);
  }

  // Create the root node.
  var root = d3_geom_quadtreeNode();

  root.add = function(p) {
    insert(root, p, x1, y1, x2, y2);
  };

  root.visit = function(f) {
    d3_geom_quadtreeVisit(f, root, x1, y1, x2, y2);
  };

  // Insert all points.
  points.forEach(root.add);
  return root;
};

function d3_geom_quadtreeNode() {
  return {
    leaf: true,
    nodes: [],
    point: null
  };
}

function d3_geom_quadtreeVisit(f, node, x1, y1, x2, y2) {
  if (!f(node, x1, y1, x2, y2)) {
    var sx = (x1 + x2) * .5,
        sy = (y1 + y2) * .5,
        children = node.nodes;
    if (children[0]) d3_geom_quadtreeVisit(f, children[0], x1, y1, sx, sy);
    if (children[1]) d3_geom_quadtreeVisit(f, children[1], sx, y1, x2, sy);
    if (children[2]) d3_geom_quadtreeVisit(f, children[2], x1, sy, sx, y2);
    if (children[3]) d3_geom_quadtreeVisit(f, children[3], sx, sy, x2, y2);
  }
}

function d3_geom_quadtreePoint(p) {
  return {
    x: p[0],
    y: p[1]
  };
}