From: Leo Alekseyev <leo.alekseyev+git.mbp@gmail.com>
Date: Wed, 26 Mar 2014 09:42:13 +0000 (-0700)
Subject: Initial commit
X-Git-Url: http://www.dnquark.com/git/?a=commitdiff_plain;h=refs%2Fheads%2Fmaster;p=quadtree.git%2F.git

Initial commit
---

f213a6b56e6230646563255d589cf85fdfb79bb4
diff --git a/geostore.py b/geostore.py
new file mode 100644
index 0000000..eebe731
--- /dev/null
+++ b/geostore.py
@@ -0,0 +1,94 @@
+from treemap2d import Cell
+from treemap2d import Entity
+import csv
+from datetime import datetime
+import json
+
+X0, X1 = 0, 256
+TESTDATA = "./testdata.csv"
+
+
+
+class Geostore(object):
+	def __init__(self):
+		self.root = Cell((X0, X0), (X1, X1))
+		# self.load_test_data()
+		self.cache = ResultsCache()
+	def load_test_data(self):
+		with open(TESTDATA, "rb") as csvfile:
+			reader = csv.reader(csvfile)
+			for row in reader:
+				self.root.add(Entity(*[float(x.strip()) for x in row]))
+	def add(self, x, y):
+		self.root.add(Entity(x, y))
+	def reset(self, ul=None, lr=None):
+		ul = ul or (X0, X0)
+		lr = lr or (X1, X1)
+		self.root = Cell(ul, lr)
+	def all_cells(self):
+		cells = self.root.all_cells()
+		res = []
+		for c in cells:
+			print c
+			cellrec = {}
+			for attr in ["x0", "x1", "y0", "y1", "xp", "yp", "level", "num_entities", "size"]:
+				cellrec[attr] = c.__getattribute__(attr)
+			res.append(cellrec)
+		return json.dumps(res)
+	def get_results(self, x, y, R, count=-1, offset=0):
+		output = {"request_x": x, "request_y": y, "request_R": R, "count": count, "offset": offset}
+		if (x, y, R) in self.cache:
+			res = self.cache[(x, y, R)]
+			output["cache_hit"] = True
+		else:
+			output["cache_hit"] = False
+			res = self.root.find(x, y, R, metadata=True)
+			self.cache[(x, y, R)] = res
+		for key in ["num_entities_estimate", "num_cells", "num_entities", "entities"]:
+			output[key] = res[key]
+		if count == -1:
+			output["entities"] = res["entities"]
+		else:
+			output["entities"] = res["entities"][offset:(offset+count)]
+		return json.dumps(output)
+	def _entity_gen(self, entities):
+		for e in entities:
+			yield e
+	def get_entity_iter(self):
+		return self._entity_gen(self.root.all_entities())
+	def get_entity_iter1(self):
+		entities = self.root.all_entities()
+		def gen():
+			for e in entities: yield e
+		return gen
+
+class ResultsCache(object):
+    """Simple LRU cache for storing results sets
+    
+    Instantiated with kwargs:
+      max_size - max number of items before expulsion
+      expunge_size - number of least-recently accessed items
+        to purge when exceeding max_size.
+
+    Class wraps a dictionary implementing a minimal interface."""
+    def __init__(self, max_size=20, expunge_size=10):
+        self.d = {}
+        self.CACHE_MAX_SIZE = max_size
+        self.CACHE_EXPUNGE_SIZE = expunge_size
+        if expunge_size >= max_size or max_size <= 2:
+            raise ValueError("Bad cache size parameters")
+    def __setitem__(self, key, value):
+        self.d[key] = [value, datetime.now()]
+        if len(self.d) > self.CACHE_MAX_SIZE:
+            for ts, key in sorted([(v[1], k) for k,v in self.d.items()])[:self.CACHE_EXPUNGE_SIZE]:
+                del self.d[key]
+    def __getitem__(self, key):
+        self.d[key][1] = datetime.now()
+        return self.d[key][0]
+    def __contains__(self, key):
+        return key in self.d
+    def __len__(self):
+        return len(self.d)
+    def __delitem__(self, key):
+        del self.d[key]
+	
diff --git a/hello.py b/hello.py
new file mode 100644
index 0000000..1f7bab4
--- /dev/null
+++ b/hello.py
@@ -0,0 +1,120 @@
+from flask import Flask
+from flask import request
+from flask import jsonify
+from flask import render_template
+from flask import make_response
+from geostore import Geostore
+app = Flask(__name__)
+
+store = Geostore()
+
+@app.route("/")
+def root():
+	return render_template('index.html')
+
+@app.route("/clickdrag2")
+def clickdrag2():
+	return render_template('clickdrag2.html')
+
+@app.route("/clickdrag3")
+def clickdrag3():
+	return render_template('clickdrag3.html')
+
+@app.route('/add', methods=['POST'])
+def add():
+	if not ('x' in request.form and 'y' in request.form):
+		raise InvalidPoint("No x ad y parameter specified in request")
+	x = float(request.form.get('x'))
+	y = float(request.form.get('y'))
+	store.add(x, y)
+	resp = make_response('{"add_point": "ok"}')
+	resp.headers['Content-Type'] = "application/json"
+	return resp
+
+@app.route('/reset', methods=['POST'])
+def reset():
+	if all(x in request.form for x in ['x0', 'y0', 'x1', 'y1']):
+		ul = ( float(request.form.get('x0')), float(request.form.get('y0')) )
+		lr = ( float(request.form.get('x1')), float(request.form.get('y1')) )
+		store.reset(ul, lr)
+	else:
+		store.reset()
+	resp = make_response('{"reset_store": "ok"}')
+	resp.headers['Content-Type'] = "application/json"
+	return resp
+	
+@app.route("/all_cells")
+def all_cells():
+	return store.all_cells()
+
+@app.route("/search")
+def search():
+	x, y, R = parse_args()
+	count = request.args.get('count', -1, type=int)
+	offset = request.args.get('offset', 0, type=int)
+	return store.get_results(x, y, R, count, offset)
+
+
+def parse_args():
+	if "long" in request.args:
+		x = request.args.get('long', 0, type=float)
+	elif "x" in request.args:
+		x = request.args.get('x', 0, type=float)
+	else:
+		raise InvalidSearch("long or x parameter missing")
+	if "lat" in request.args:
+		y = request.args.get('lat', 0, type=float)
+	elif "y" in request.args:
+		y = request.args.get('y', 0, type=float)
+	else:
+		raise InvalidSearch("lat or y parameter missing")
+	if "R" in request.args:
+		R = request.args.get('R', 0, type=float)
+	elif "r" in request.args:
+		R = request.args.get('r', 0, type=float)
+	else:	
+		raise InvalidSearch("R parameter missing")
+	return (x, y, R)
+
+
+class InvalidSearch(Exception):
+	status_code = 400
+	def __init__(self, message, status_code=None, payload=None):
+		Exception.__init__(self)
+		self.message = message
+		if status_code is not None:
+			self.status_code = status_code
+		self.payload = payload
+	def to_dict(self):
+		rv = dict(self.payload or ())
+		rv['message'] = self.message
+		return rv
+
+class InvalidPoint(Exception):
+	status_code = 400
+	def __init__(self, message, status_code=None, payload=None):
+		Exception.__init__(self)
+		self.message = message
+		if status_code is not None:
+			self.status_code = status_code
+		self.payload = payload
+	def to_dict(self):
+		rv = dict(self.payload or ())
+		rv['message'] = self.message
+		return rv
+
+@app.errorhandler(InvalidSearch)
+def handle_invalid_search(error):
+	response = jsonify(error.to_dict())
+	response.status_code = error.status_code
+	return response
+
+@app.errorhandler(InvalidPoint)
+def handle_invalid_point(error):
+	response = jsonify(error.to_dict())
+	response.status_code = error.status_code
+	return response
+
+
+if __name__ == "__main__":
+	app.run(debug=True)
diff --git a/static/application.css b/static/application.css
new file mode 100644
index 0000000..e296755
--- /dev/null
+++ b/static/application.css
@@ -0,0 +1,37 @@
+svg {
+  vertical-align: middle;
+  background: #F0F0E0;
+  box-shadow: inset 0 0 3px 0px #CECECE;
+}
+
+svg circle {
+  stroke-width: 2px;
+  stroke: #79A32B;
+  fill: transparent;
+  cursor: pointer;
+}
+
+svg circle:active {
+  stroke: #45D3C7;
+}
+
+svg circle.selected {
+  stroke: #3333FF;
+}
+
+
+.selection {
+  stroke: gray;
+  stroke-width: 1px;
+  stroke-dasharray: 4px;
+  stroke-opacity: 0.5;
+  fill: transparent;
+}
+
+.cell {
+  stroke: gray;
+  stroke-width: 1px;
+  stroke-dasharray: 4px;
+  stroke-opacity: 0.5;
+  fill: transparent;
+}
\ No newline at end of file
diff --git a/static/application.js b/static/application.js
new file mode 100644
index 0000000..ace841b
--- /dev/null
+++ b/static/application.js
@@ -0,0 +1,130 @@
+var points = [];
+var width = 300, height = 300;
+var svg;
+var origin;
+var dragging = false;
+var selectionShown = false;
+
+
+function distance(p, q) {
+	return Math.sqrt((p[0] - q[0]) * (p[0] - q[0]) + (p[1] - q[1]) * (p[1] - q[1]));
+}
+
+function renderMatchedEntities(data) {
+	console.log(data.entities);
+	svg.selectAll("circle.selected").data(data.entities).enter()
+		.append("svg:circle")
+		.attr("class", "selected")
+		.attr("stroke", "#3333FF")
+		.attr("r", 5)
+		.attr("cx", function(d) { console.log(d[1][0]); return d[1][0]; })
+		.attr("cy", function(d) { console.log(d[1][1]); return d[1][1]; });
+}		
+
+
+function getSearchData(x, y, r) {
+	$.getJSON($SCRIPT_ROOT + '/search', {x: x, y: y, R: r})
+		.done(renderMatchedEntities);
+}
+
+function renderCells(data) {
+	svg.selectAll("rect.cell").remove();
+	svg.selectAll("rect.cell").data(data).enter()
+		.append("svg:rect")
+		.attr("class", "cell")
+		.attr("x", function(d) { return d.x0; })
+		.attr("y", function(d) { return d.y0; })
+		.attr("width", function(d) { return d.size; })
+		.attr("height", function(d) { return d.size; });
+}
+	
+
+function getAllCells() {
+	$.getJSON($SCRIPT_ROOT + '/all_cells')
+		.done(renderCells);
+}
+
+
+function clickHandler() {
+	if (d3.event.defaultPrevented) {
+		console.log("click suppressed");
+		return; // click suppressed			
+	}
+	if (dragging) {
+		console.log("click prevented by my flag");
+		dragging = false;
+		return;
+	}
+	svg.selectAll("circle.selected").remove();
+	if (selectionShown) {
+		selectionShown = false;
+		return;
+	}
+	var p = d3.mouse(this);
+	points.push(p);
+	$.post($SCRIPT_ROOT + '/add', {x: p[0], y: p[1]});
+	refreshSVG(svg);
+	getAllCells();
+	
+	console.log(d3.mouse(this));
+}
+
+var drag = d3.behavior.drag()
+	.on("dragstart", function() {
+		svg.selectAll("circle.selected").remove();
+		d3.event.sourceEvent.stopPropagation(); // silence other listeners		
+		var p = d3.mouse(this);
+		origin = p;
+		svg.selectAll('.selection').remove();
+		svg.append("circle")
+			.attr({"class": "selection",
+				   "cx": p[0],
+				   "cy": p[1]});
+		console.log("dragStart");
+	})
+	.on("drag", function () {
+		var sel = svg.selectAll('.selection');
+		var p = d3.mouse(this);
+		var d = distance(p, origin);
+		dragging = true;
+		sel.attr("r", d);
+		// console.log("drag " + origin + " to " + p + ": dist " + d); 
+	})
+	.on("dragend", function () { 
+		setTimeout(function() { dragging = false; }, 100);
+		var p = d3.mouse(this);
+		var d = distance(p, origin);
+		if (d > 2) {
+			getSearchData(origin[0], origin[1], d);
+			selectionShown = true;
+		}
+		console.log("dragEnd; d=" + d); });
+
+function placeSVG() {
+	svg = d3.select("#svg-container").append("svg");
+	// .append("rect")
+	svg.attr("class", "rect-main")
+		.attr("width", width)
+		.attr("height", height)
+		.call(drag)
+		.on("click", clickHandler)
+	;
+}
+
+
+function refreshSVG() {
+	console.log(points);
+	svg.selectAll("circle.point").data(points).enter()
+		.append("svg:circle")
+		.attr("class", "point")
+		.attr("r", 4)
+		.attr("cx", function(d) { return d[0]; })
+		.attr("cy", function(d) { return d[1]; });
+}
+
+$(document).ready(function() {
+	
+	placeSVG();	
+	$.post($SCRIPT_ROOT + '/reset', {x0: 0, x1: width, y0: 0, y1: height});
+
+});
diff --git a/static/backbone-min.js b/static/backbone-min.js
new file mode 100644
index 0000000..3b2593d
--- /dev/null
+++ b/static/backbone-min.js
@@ -0,0 +1,2 @@
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new file mode 100644
index 0000000..7ed6e52
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diff --git a/templates/index.html b/templates/index.html
new file mode 100644
index 0000000..73ad09a
--- /dev/null
+++ b/templates/index.html
@@ -0,0 +1,22 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="utf-8" />
+    <link rel="stylesheet" type="text/css" media="all" href="{{url_for('static', filename='application.css') }}"/>
+    <script type=text/javascript>
+      $SCRIPT_ROOT = {{ request.script_root|tojson|safe }};
+    </script>    
+    <script type=text/javascript src="{{url_for('static', filename='jquery.min.js') }}"></script>
+    <script type=text/javascript src="{{url_for('static', filename='underscore-min.js') }}"></script>
+    <script type=text/javascript src="{{url_for('static', filename='backbone-min.js') }}"></script>
+    <script type=text/javascript src="{{url_for('static', filename='d3.v3.min.js') }}"></script>
+    <script type=text/javascript src="{{url_for('static', filename='application.js') }}"></script>
+    <script>
+      function hello(arg) {
+        $("body").append($("<div>").text("HELLO JS " + arg));
+      }
+     </script>
+</head>
+<body>
+  <div id="svg-container"></div>
+</body>
diff --git a/test_treemap2d.py b/test_treemap2d.py
new file mode 100644
index 0000000..6d354fe
--- /dev/null
+++ b/test_treemap2d.py
@@ -0,0 +1,104 @@
+import unittest
+import math
+from treemap2d import Cell
+from treemap2d import Entity as E
+
+X0, X1 = 0, 256
+
+class TestQuadtreeCell(unittest.TestCase):
+	def test_split(self):
+		cell = Cell((X0, X0), (X1, X1))
+		cell.split()
+		child0 = cell.children[0]
+		child1 = cell.children[1]
+		child2 = cell.children[2]
+		assert len(child1.neighbors) == 3
+		child1.split()
+		child13 = child1.children[3]
+		assert len(child13.neighbors) == 6
+		assert child13.is_neighbor(cell.children[0])
+		assert child13.is_neighbor(cell.children[3])
+		assert child13.is_neighbor(cell.children[2])
+		assert child13.is_neighbor(child1.children[0])
+		assert child13.is_neighbor(child1.children[1])
+		assert child13.is_neighbor(child1.children[2])
+		child13.split()
+		child132 = child13.children[2]
+		child133 = child13.children[3]
+		assert len(child132.neighbors) == 5
+		assert child132.is_neighbor(child13.children[0])
+		assert child132.is_neighbor(child13.children[1])
+		assert child132.is_neighbor(child13.children[3])
+		assert child132.is_neighbor(child1.children[2])
+		assert child132.is_neighbor(cell.children[2])
+		cell.children[0].split()
+		child02 = cell.children[0].children[2]
+		assert len(child02.neighbors) == 7
+		assert child02.is_neighbor(child1.children[0])
+		assert child02.is_neighbor(child1.children[3])
+		assert child02.is_neighbor(cell.children[2])
+		assert child02.is_neighbor(cell.children[3])
+		cell.children[3].split()
+		cell.children[3].children[1].split()
+		child311 = cell.children[3].children[1].children[1]
+		assert len(child311.neighbors) == 6
+		assert child311.is_neighbor(child133)
+		assert child311.is_neighbor(child0.children[2])
+		assert child311.is_neighbor(child2)
+	def test_all_cells(self):
+		root = Cell((X0, X0), (X1, X1))
+		root.split() # 5 cells
+		root.children[1].split() # 9 cells
+		root.children[1].children[0].split() # 13 cells
+		allcells = root.all_cells()
+		assert len(allcells) == 13
+	def test_add(self):
+		Cell.MAXENTITIES = 2
+		root = Cell((X0, X0), (X1, X1))
+		root.add(E(10, 10))
+		root.add(E(10, 10))
+		assert root.depth == 0
+		assert root.num_entities == 2
+		root.add(E(65, 65)) # expect split
+		assert root.depth == 1
+		assert root.num_entities == 3
+		assert root.children[1].num_entities == 3
+		root.add(E(66, 66)) # expect split
+		assert root.depth == 2 and root.num_entities == 4
+		assert root.children[1].children[1].num_entities == 2
+		assert root.children[1].children[3].num_entities == 2
+		root.add(E(67, 67)) # expect split
+		assert root.depth == 3 and root.num_entities == 5
+	def test_min_entity_dist(self):
+		Cell.MAXENTITIES = 2
+		root = Cell((X0, X0), (X1, X1))
+		root.add(E(10, 10))
+		root.add(E(10, 10))
+		root.add(E(65, 65)) # expect split
+		assert root.min_entity_dist(10, 10) == 0
+		assert root.min_entity_dist(10, 11) == 1
+	def test_find(self):
+		Cell.MAXENTITIES = 2
+		root = Cell((X0, X0), (X1, X1))
+		root.add(E(10, 10))
+		root.add(E(10, 10))
+		root.add(E(65, 65)) # expect split
+		root.add(E(66, 66)) # expect split
+		root.add(E(67, 67)) # expect split
+		root.add(E(127, 127))
+		root.add(E(129, 129))
+		root.add(E(67, 127))
+		root.add(E(68, 129))
+		assert len(root.find(10, 10, 0.1)) == 2
+		x, y = root.find(10, 10, 0.1)[0][1]
+		assert x == 10 and y == 10
+		assert len(root.find(63, 63, 2 * math.sqrt(2))) == 1
+		assert len(root.find(63, 63, 3 * math.sqrt(2))) == 2
+		
+if __name__ == "__main__":
+	loader = unittest.TestLoader()
+	# suite = unittest.TestSuite()
+	# suite.addTest(TestQuadtreeCell('test_split'))
+	suites = []
+	suites.append(loader.loadTestsFromTestCase(TestQuadtreeCell))
+	unittest.TextTestRunner(verbosity=2).run(unittest.TestSuite(suites))
diff --git a/testdata.csv b/testdata.csv
new file mode 100644
index 0000000..13bbe13
--- /dev/null
+++ b/testdata.csv
@@ -0,0 +1,9 @@
+10, 10
+10, 10
+65, 65
+66, 66
+67, 67
+127, 127
+129, 129
+67, 127
+68, 129
diff --git a/treemap2d.py b/treemap2d.py
new file mode 100644
index 0000000..2eb402b
--- /dev/null
+++ b/treemap2d.py
@@ -0,0 +1,240 @@
+import math
+import heapq
+from collections import namedtuple
+
+ROOT_COORDS = [0, 1]
+
+Entity = namedtuple('Entity', ['x', 'y'])
+
+def distance(e1, e2):
+	return math.sqrt((e1.x - e2.x)**2 + (e1.y - e2.y)**2)
+
+def dist_target(e1, x, y):
+	return math.sqrt((e1.x - x)**2 + (e1.y - y)**2)
+
+class CellSearchException(Exception):
+	pass
+
+class Cell(object):
+	MAXENTITIES = 2
+	MINSIZE = 2 ** -24 # if 1 is the length of the equator, this gives 2.5 m resolution
+	# coords of a cell are its UL corner
+	# coord system: x increases L->R, y increases T->B
+	# a cell is uniquely identified by its (level, x0, y0) tuple
+	def __init__(self, xy0, xy1, parent=None, level=0):
+		self.children = []
+		self._neighbors_set = set()
+		self.x0, self.y0 = xy0[0], xy0[1]
+		self.x1, self.y1 = xy1[0], xy1[1]
+		xp, yp = (self.x1 - self.x0) / 2 + self.x0, (self.y1 - self.y0) / 2 + self.y0
+		self.xp, self.yp = xp, yp  # centroid of the cell
+		self.parent = parent
+		self.level = level
+		self.is_leaf = True
+		self.entities = []
+		# min in principle unnecessary if the cells are square
+		self.size = min(abs(self.x0 - self.x1), abs(self.y0 - self.y1))
+		self.num_entities = 0
+	def __str__(self):
+		return "Cell: x0={x0}, y0={y0}, x1={x1}, y1={y1}, L={L}, N={N}".format(x0=self.x0, y0=self.y0, x1=self.x1, y1=self.y1, L=self.level, N=self.num_entities)
+	def __repr__(self):
+		return str(self)
+	def dist(self, x, y):
+		return math.sqrt((self.xp - x)**2 + (self.yp - y)**2)
+	def min_entity_dist(self, x, y):
+		"""Minimum distance to the target point of all entities below this node.
+		This might not be very efficient if (a) minimum number of entities per node is large
+		and (b) this function is invoked on a root node. In inner loops this should be called
+		only on leaves."""
+		return min(dist_target(e, x, y) for e in self.all_entities())
+	@property	
+	def neighbors(self):
+		"""This cell's neighbors.  Here a cell's neighbors are all adjacent
+		(via an adjoining side or a corner) cells at level <= L (level < L situation
+		occurs when the neighboring cell's max depth is below L).  This implies that 
+		when a cell C1 that is a neighbor of some other cell C2 gets split, and C2.level > C1.level, 
+		C2's neighbor set will need to be updated."""
+		return self._neighbors_set
+	def add_neighbor(self, neighbor):
+		self._neighbors_set.add(neighbor)
+	@property
+	def corners(self):
+		return [(self.x0, self.y0), (self.x0, self.y1), (self.x1, self.y1), (self.x1, self.y0)]
+	def is_neighbor(self, cell):
+		if cell is self:
+			return False
+		for c in self.corners:
+			if c in cell.corners:
+				return True
+		# if corners don't touch, check for a case of a small cell adjacent to a large cell
+		if self.size <= cell.size:
+			large, small = cell, self
+		else:
+			large, small = self, cell
+		if (((large.x0 == small.x1 or large.x1 == small.x0) 
+			and (small.yp > large.y0 and small.yp < large.y1)) or 
+			((large.y0 == small.y1 or large.y1 == small.y0) 
+			and (small.xp > large.x0 and small.xp < large.x1))):
+			return True
+		return False
+	def _select_neighbors(self, candidates):
+		"""Given a list of candidate neighbors, check that they are in fact neighbors
+		and add them to the neighbor set."""
+		for c in candidates:
+			if self.is_neighbor(c):
+				self.add_neighbor(c)
+	def split(self):
+		"""Split a cell. This involves:
+		1. creating 4 child cells at level L+1, being careful to compute their neighbor set
+		2. moving this cell's entities to the appropriate child cells
+		3. updating the neighbor set of neighboring L+1 level cells"""
+		def _create_children():
+			self.children = [None] * 4
+			self.children[0] = Cell((self.xp, self.y0), (self.x1, self.yp), parent=self, level=self.level+1)
+			self.children[1] = Cell((self.x0, self.y0), (self.xp, self.yp), parent=self, level=self.level+1)
+			self.children[2] = Cell((self.x0, self.yp), (self.xp, self.y1), parent=self, level=self.level+1)
+			self.children[3] = Cell((self.xp, self.yp), (self.x1, self.y1), parent=self, level=self.level+1)
+			neighbors_or_children = []
+			for n in self.neighbors:
+				if n.is_leaf:
+					neighbors_or_children.extend([n])
+				else:
+					neighbors_or_children.extend(n.children)
+			neighbor_candidates = self.children + neighbors_or_children
+			for c in self.children:
+				c._select_neighbors(neighbor_candidates)
+		def _copy_entities():
+			for e in self.entities:
+				n = self.quadrant(e.x, e.y)
+				self.children[n].entities.append(e)
+				self.children[n].num_entities += 1
+			self.entities = []
+		def _update_neighbors():
+			for n in self.neighbors:
+				for c in n.children:
+					if self in c.neighbors:
+						c.neighbors.remove(self)
+						c._select_neighbors(self.children)
+					
+		self.is_leaf = False
+		_create_children()
+		_copy_entities()
+		_update_neighbors()
+	def _all_cells(self, accum=None):
+		accum = accum or []
+		accum.append(self)
+		for c in self.children:
+			c._all_cells(accum)
+		return accum
+	def all_cells(self):
+		"""Recursively collect all the cells in the hierarchy, 
+		this cell included. Useful for debugging"""
+		return self._all_cells()
+	@property
+	def depth(self):
+		if self.is_leaf:
+			return 0
+		else:
+			return 1 + max(c.depth for c in self.children)
+	def all_entities(self):
+		"""Recursively collects all the entities in the hierarchy below
+		this cell.  Useful for debugging."""
+		if self.is_leaf:
+			return self.entities
+		entities = []
+		for c in self.children:
+			entities.extend(c.all_entities())
+		return entities
+	def quadrant(self, x, y):
+		"""Pick a quadrant for the (x, y) point"""
+		if x > self.xp and y <= self.yp:
+			return 0
+		elif x <= self.xp and y <= self.yp:
+			return 1
+		elif x <= self.xp and y > self.yp:
+			return 2
+		else:
+			return 3
+	def add(self, entity):
+		if self.is_leaf:
+			self.entities.append(entity)
+			cell = self
+			while cell is not None:
+				cell.num_entities += 1
+				cell = cell.parent
+			if len(self.entities) > Cell.MAXENTITIES and self.size > Cell.MINSIZE:
+				self.split()
+		else:
+			n = self.quadrant(entity.x, entity.y)
+			self.children[n].add(entity)
+	def get_search_space(self, x, y, R):
+		"""Find the cell forming the center of the search space.
+		This cell is the smallest cell containing target coordinate with
+		side length > R"""
+		if self.is_leaf or self.children[0].size <= R:
+			return self
+		else:
+			n = self.quadrant(x, y)
+			return self.children[n].get_search_space(x, y, R)
+	def cell_list(self, x, y, R):
+		"""Returns a list of cells which contain at least one entity falling
+		in the 2R x 2R square centered on (x, y)."""
+		search_cell = self.get_search_space(x, y, R)
+		return search_cell._get_cell_list(x, y)
+	def find(self, x, y, R, heap=False, limit=None, metadata=False):
+		"""Returns  entities falling in a circle of radius R centered
+		on (x, y).  Optional arguments:
+		- heap: return results as a Python heap (see heapq module)
+		- limit: raise an exception if the search space contains too many entities
+		         (note that this count overestimates the number of matches by 
+		          _at least_ 2.5 to 12 times)
+		"""
+		search_cell = self.get_search_space(x, y, R)
+		sspace_total_num = search_cell._search_space_num_entities()
+		if limit is not None and sspace_total_num > limit:
+			raise CellSearchException
+		nodes = search_cell._get_cell_list(x, y)
+		entities = []
+		for n in nodes:
+			for e in n.entities:
+				d = dist_target(e, x, y)
+				if d <= R:
+					if heap:
+						heapq.heappush(entities, (d, e))
+					else:
+						entities.append( (d, e) )
+		if not heap:
+			entities.sort()
+		if metadata:
+			return {"num_entities_estimate": sspace_total_num,
+					"num_cells": len(nodes),
+					"num_entities": len(entities),
+					"is_heap": heap,
+					"entities": entities}
+		else:
+			return entities
+	def _build_leaves_queue(self, queue, x, y):
+		# possible future optimization: limit the # of 
+		# nodes in the queue
+		# Note: in the future we can choose to make this into a 
+		# priority queue based on either 
+		# (a) self.min_entity_dist(x, y) (i.e. distance from target to closest entity in cell), or
+		# (b) self.dist(x, y) (i.e. distance from target to the cell's midpoint)
+		if self.is_leaf:
+			if len(self.entities) > 0:
+				queue.append(self)
+		else:
+			for c in self.children:
+				c._build_leaves_queue(queue, x, y)
+	def _search_space_num_entities(self):
+		num_entities = self.num_entities
+		for n in self.neighbors:
+			num_entities += n.num_entities
+		return num_entities
+	def _get_cell_list(self, x, y):
+		leaves = []
+		self._build_leaves_queue(leaves, x, y)
+		for n in self.neighbors:
+			n._build_leaves_queue(leaves, x, y)
+		return leaves
+