def conductTrial(label, items):
samples = 128
n = len(items)
rt = RTree(m=2, M=4)
for r in items:
rt.add(r)
box = rt.root.region
width = box.x_max - box.x_min
height = box.y_max - box.y_min
# can compute density for any tree, samples at 128 random spots
ct = 0
for _ in range(samples):
x = box.x_min + random.random() * width
y = box.y_min + random.random() * height
for triple in rt.range(Region(x, y, x, y)):
assert triple[2] == False
ct += 1
print("Density", n, "{:.2f}%".format(100 * ct / (n * samples)), "intersect random point in ", str(box))
trials(n, items, BUILD, "Build")
trials(n, items, SEARCH, "Search")
trials(n, items, DELETE, "Delete")
def conductTrial(label, items):
samples = 128
n = len(items)
rt = RTree(m=2, M=4)
for r in items:
rt.add(r)
box = rt.root.region
width = box.x_max - box.x_min
height = box.y_max - box.y_min
# can compute density for any tree, samples at 128 random spots
ct = 0
for _ in range(samples):
x = box.x_min + random.random() * width
y = box.y_min + random.random() * height
for triple in rt.range(Region(x, y, x, y)):
assert (triple[2] == False)
ct += 1
print("Density", n, "{:.2f}%".format(100 * ct / (n * samples)),
"intersect random point in ", str(box))
trials(n, items, BUILD, "Build")
trials(n, items, SEARCH, "Search")
trials(n, items, DELETE, "Delete")
def __init__(self):
"""App for creating R tree dynamically and executing range queries"""
self.tree = RTree(m=2, M=4)
self.ready = False
# for range query
self.selectedRegion = None
self.newRegionStart = None
self.newRegion = None
# for identifiers
self.counter = 0
self.master = tkinter.Tk()
self.master.title('R Tree Range Query Application')
self.w = tkinter.Frame(self.master, width=512, height=512)
self.canvas = tkinter.Canvas(self.w, width=512, height=512)
self.paint()
self.canvas.bind("<Button-1>", self.startAdd)
self.canvas.bind("<B1-Motion>",
self.extendAdd) # only when right mouse dragged
self.canvas.bind("<ButtonRelease-1>", self.endAdd)
self.canvas.bind("<Button-3>", self.range) # when right mouse clicked
self.canvas.bind("<ButtonRelease-3>", self.clear)
self.canvas.bind("<B3-Motion>",
self.range) # only when right mouse dragged
self.w.pack()
def __init__(self):
"""App for creating R tree dynamically and executing range queries"""
self.tree = RTree(m=2, M=4)
self.ready = False
# for range query
self.selectedRegion = None
self.newRegionStart = None
self.newRegion = None
# for identifiers
self.counter = 0
self.master = tkinter.Tk()
self.master.title('R Tree Range Query Application')
self.w = tkinter.Frame(self.master, width=512, height=512)
self.canvas = tkinter.Canvas(self.w, width=512, height=512)
self.paint()
self.canvas.bind("<Button-1>", self.startAdd)
self.canvas.bind("<B1-Motion>", self.extendAdd) # only when right mouse dragged
self.canvas.bind("<ButtonRelease-1>", self.endAdd)
self.canvas.bind("<Button-3>", self.range) # when right mouse clicked
self.canvas.bind("<ButtonRelease-3>", self.clear)
self.canvas.bind("<B3-Motion>", self.range) # only when right mouse dragged
self.w.pack()
def test_multipleM(self):
# check multiple m,M values
for m,M in zip([3, 4, 5, 6], [7, 8, 10, 13]):
self.tree = RTree(m,M)
regions = []
for ctr in range(500):
r = Region(2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250))
regions.append((r, ctr))
self.tree.add(r,ctr)
# make sure all can be individually found
for ctr in range(len(regions)):
match = [m for m in self.tree.search(regions[ctr][0])][0]
self.assertEquals(match, regions[ctr][0])
# make sure that all are contained within the
self.ensure_maxBounding(self.tree.root)
def performanceR():
"""Demonstrate RTree stores all rectangles."""
n = 1024
while n <= 131072:
rt = RTree()
added = []
for _ in range(n):
new = randomRectangle()
if rt.search(new) is None:
rt.add(new)
added.append(new)
random.shuffle(added)
for r in added:
if rt.search(r) is None:
print ("Cannot find:" + r)
assert False
print ("pass " + str(n))
n *= 2
def performanceR():
"""Demonstrate RTree stores all rectangles."""
n = 1024
while n <= 131072:
rt = RTree()
added = []
for _ in range(n):
new = randomRectangle()
if rt.search(new) is None:
rt.add(new)
added.append(new)
random.shuffle(added)
for r in added:
if rt.search(r) is None:
print("Cannot find:" + r)
assert False
print("pass " + str(n))
n *= 2
class RTreeApp:
def __init__(self):
"""App for creating R tree dynamically and executing range queries"""
self.tree = RTree(m=2, M=4)
self.ready = False
# for range query
self.selectedRegion = None
self.newRegionStart = None
self.newRegion = None
# for identifiers
self.counter = 0
self.master = tkinter.Tk()
self.master.title('R Tree Range Query Application')
self.w = tkinter.Frame(self.master, width=512, height=512)
self.canvas = tkinter.Canvas(self.w, width=512, height=512)
self.paint()
self.canvas.bind("<Button-1>", self.startAdd)
self.canvas.bind("<B1-Motion>", self.extendAdd) # only when right mouse dragged
self.canvas.bind("<ButtonRelease-1>", self.endAdd)
self.canvas.bind("<Button-3>", self.range) # when right mouse clicked
self.canvas.bind("<ButtonRelease-3>", self.clear)
self.canvas.bind("<B3-Motion>", self.range) # only when right mouse dragged
self.w.pack()
def startAdd(self, event):
"""End of range search."""
x = event.x
y = self.toCartesian(event.y)
self.newRegionStart = (x,y)
def extendAdd(self, event):
"""End of range search."""
if self.newRegionStart:
x = event.x
y = self.toCartesian(event.y)
self.newRegion = Region (x,y,x,y).unionPoint(self.newRegionStart)
self.paint()
def endAdd(self, event):
"""End of range search."""
if self.newRegionStart:
self.newRegionStart = None
self.counter += 1
if self.newRegion:
self.tree.add(self.newRegion, str(self.counter))
self.newRegion = None
self.paint()
def toCartesian(self, y):
"""Convert tkinter point into Cartesian."""
return self.w.winfo_height() - y
def toTk(self,y):
"""Convert Cartesian into tkinter point."""
if y == maxValue: return 0
tk_y = self.w.winfo_height()
if y != minValue:
tk_y -= y
return tk_y
def clear(self, event):
"""End of range search."""
self.selectedRegion = None
self.paint()
def range(self, event):
"""Initiate a range search using a selected rectangular region."""
p = (event.x, self.toCartesian(event.y))
if self.selectedRegion is None:
self.selectedStart = Region(p[X],p[Y], p[X],p[Y])
self.selectedRegion = self.selectedStart.unionPoint(p)
self.paint()
# return (node,0,True) where status is True if draining entire tree rooted at node. If False,
# then (rect,id,False). Draw these
# as shaded red rectangle to identify whole sub-tree is selected.
for triple in self.tree.range(self.selectedRegion):
if triple[2]:
r = triple[0].region
self.canvas.create_rectangle(r.x_min, self.toTk(r.y_min), r.x_max, self.toTk(r.y_max),
fill='Red', stipple='gray12')
else:
r = triple[0]
self.canvas.create_rectangle(r.x_min, self.toTk(r.y_min), r.x_max, self.toTk(r.y_max),
fill='Red')
def click(self, event):
"""Add point to KDtree."""
p = (event.x, self.toCartesian(event.y))
self.tree.add(p)
self.paint()
def visit (self, n):
""" Visit node to paint properly."""
if n == None: return
if n.level == 0:
for idx in range(n.count):
r = n.children[idx].region
self.canvas.create_rectangle(r.x_min, self.toTk(r.y_min), r.x_max, self.toTk(r.y_max),
fill='Gray')
for idx in range(n.count):
self.visit(n.children[idx])
# Do after all children so we can see interior nodes, too.
r = n.region
self.canvas.create_rectangle(r.x_min, self.toTk(r.y_min), r.x_max, self.toTk(r.y_max),
outline='Black', dash=(2, 4))
color = 'Gray'
if n.level == 0:
color='Black'
self.canvas.create_text(r.x_max - 16*len(n.id), self.toTk(r.y_max) + 16, anchor = tkinter.W,
font = "Times 16 bold", fill=color, text=n.id)
def prepare(self, event):
"""prepare to add points."""
if self.label:
self.label.destroy()
self.label = None
self.canvas.pack()
def paint(self):
"""Paint R tree by visiting all nodes, or show introductory message."""
if self.ready:
self.canvas.delete(tkinter.ALL)
self.visit(self.tree.root)
if self.newRegion:
self.canvas.create_rectangle(self.newRegion.x_min, self.toTk(self.newRegion.y_min),
self.newRegion.x_max, self.toTk(self.newRegion.y_max),
outline='Black', dash=(2, 4))
if self.selectedRegion:
self.canvas.create_rectangle(self.selectedRegion.x_min, self.toTk(self.selectedRegion.y_min),
self.selectedRegion.x_max, self.toTk(self.selectedRegion.y_max),
outline='Red', dash=(2, 4))
else:
self.label = tkinter.Label(self.w, width=100, height = 40, text="Click To Add Points")
self.label.bind("<Button-1>", self.prepare)
self.label.pack()
self.ready = True
class TestRMethods(unittest.TestCase):
def setUp(self):
self.tree = RTree()
def tearDown(self):
self.tree = None
def test_basic(self):
r = Region(10,20,50,60)
self.tree.add(r, 99)
for node,_,status in self.tree.range(r):
self.assertTrue(status)
for rect, ident in node.leafOrder():
self.assertEquals(99, ident)
self.assertEquals(r, rect)
# Expanded region for node with multiple insertions.
def test_expand(self):
r = Region(10,20,50,60)
r2 = Region(30,60,70,80)
self.tree.add(r, 99)
self.tree.add(r2, 101)
self.assertEquals(Region(10,20,70,80), self.tree.root.region)
# Add five regions and watch split.
def test_split(self):
r1 = Region(10,20,50,60)
r2 = Region(30,60,70,80)
r3 = Region(-30,60,70,80)
r4 = Region(40,70,60,100)
self.tree.add(r1, 99)
self.tree.add(r2, 101)
self.tree.add(r3, 103)
self.tree.add(r4, 105)
self.assertEquals(Region(-30,20,70,100), self.tree.root.region)
r5 = Region(10,60,0,90)
self.tree.add(r5, 107)
self.assertEquals(Region(-30,20,70,100), self.tree.root.region)
# finds all rectangles.
r_ids = []
for triple in self.tree.range(Region(-100, -100, 200, 200)):
if triple[2]:
for d in triple[0].leafOrder():
r_ids.append(d[1])
else:
r_ids.append(triple[1])
r_ids.sort()
self.assertEquals ([99,101,103,105,107], r_ids)
def expand(self, region):
"""When Full Sub-trees returned as nodes traverse to expand nodes."""
result = [p for p in self.tree.range(region)]
expanded = []
for triple in result:
if triple[2]:
for d in triple[0].leafOrder():
expanded.append(d[0])
else:
expanded.append(triple[0])
return expanded
def test_iterator(self):
# rectangles have all even numbered coordinates
for _ in range(500):
self.tree.add(Region(2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250)))
count = 0
for _ in self.tree:
count = count + 1
self.assertEquals(500, count)
def test_adding(self):
# rectangles have all even numbered coordinates. Doesn't really matter since
# range returns regions that intersect target, rather than being wholly contained
for _ in range(500):
self.tree.add(Region(2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250)))
# make sure not to overlap!
q_ne = self.expand(Region(125, 125, 501, 501))
q_nw = self.expand(Region(1, 125, 125, 501))
q_sw = self.expand(Region(1, 1, 125, 125))
q_se = self.expand(Region(125, 1, 511, 125))
q_all = self.expand(Region(1,1, 501, 501))
# quick check to see if any were missing
combined = []
for r in q_ne + q_nw + q_sw + q_se:
if r not in combined:
combined.append(r)
for q in q_all:
if q not in combined:
print (q, " missing ")
# check duplicates
for i in range(len(combined)):
for j in range(len(combined)):
if j <= i:
pass
else:
if combined[i] == combined[j]:
print ("Duplicate:", combined[i])
self.assertEquals(len(q_all), len(combined))
def ensure_maxBounding(self, node):
"""Ensures R-Node guarantees max bounding rectangle for all interior nodes covers descendants."""
for i in range(node.count):
n = node.children[i]
self.assertTrue(node.region.containsRegion(n.region))
self.ensure_maxBounding(n)
def test_verticalSlices(self):
# check case of vertical rectangles all in a row. This forces regular extensions.
# Make sure bounding rectangles are computed properly.
for x in range(1,50):
self.tree.add(Region(x*6,10, x*6+3,100))
# sliding window always grabs eight of them since there is one rect every 6 pixels and query width is 47
for x in range(1, 40):
s = Region(x*6, 2, x*6+47, 100)
match = self.expand(s)
self.assertEquals(8, len(match))
self.ensure_maxBounding(self.tree.root)
def test_tiling(self):
# create evenly placed rectangles (s=16_ and validate queries
for x in range(1,8):
for y in range(1,8):
self.tree.add(Region(x*64,y*64, x*64+32,y*64+32))
for x in range(1,5):
for y in range(1,5):
s = Region(x*64, y*64, x*64+255, y*64+127) # includes 2x4 selection or 8
match = self.expand(s)
self.assertEquals(8, len(match))
def test_multipleM(self):
# check multiple m,M values
for m,M in zip([3, 4, 5, 6], [7, 8, 10, 13]):
self.tree = RTree(m,M)
regions = []
for ctr in range(500):
r = Region(2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250))
regions.append((r, ctr))
self.tree.add(r,ctr)
# make sure all can be individually found
for ctr in range(len(regions)):
match = [m for m in self.tree.search(regions[ctr][0])][0]
self.assertEquals(match, regions[ctr][0])
# make sure that all are contained within the
self.ensure_maxBounding(self.tree.root)
# test deletions
def test_deleteOnlyOne(self):
r = Region(10,20,50,60)
self.tree.add(r, 99)
self.assertTrue(self.tree.search(r))
self.assertEquals(Region(10,20,50,60), self.tree.root.region)
# not in tree.
self.assertFalse(self.tree.remove(Region(2,4,22,50)))
self.assertTrue(self.tree.remove(r))
# Not present.
self.assertTrue(self.tree.search(r) is None)
# test deletions
def test_delete(self):
r = Region(10,20,50,60)
r2 = Region(30,60,70,80)
self.tree.add(r, 99)
self.tree.add(r2, 101)
self.assertTrue(self.tree.search(r))
self.assertTrue(self.tree.search(r2))
self.assertEquals(Region(10,20,70,80), self.tree.root.region)
# not in tree.
self.assertFalse(self.tree.remove(Region(2,4,22,50)))
self.assertTrue(self.tree.remove(r2))
# one is in, other is out
self.assertTrue(self.tree.search(r))
self.assertTrue(self.tree.search(r2) is None)
def test_deleteFive(self):
r1 = Region(38,148 , 300,288)
r2 = Region(164,384 , 432,428)
r3 = Region(316,342 , 456,392)
r4 = Region(12,242 , 172,484)
r5 = Region(324,200 , 494,276)
for r in [r1,r2,r3,r4,r5]:
self.tree.add(r)
for r in [r1,r2,r3,r4,r5]:
self.assertTrue(self.tree.search(r))
self.tree.remove(r)
self.assertFalse(self.tree.search(r))
self.assertTrue (self.tree.root == None)
def test_deleteThirteen(self):
r1 = Region(410,168 , 482,348)
r2 = Region(136,236 , 250,266)
r3 = Region(290,26 , 496,470) ## FAILS when deleting 10
r4 = Region(398,24 , 444,100)
r5 = Region(160,388 , 462,480)
r6 = Region(50,124 , 120,486)
r7 = Region(22,258 , 144,322)
r8 = Region(28,148 , 392,236)
r9 = Region(78,190 , 174,370) # problem on this one
r10 = Region(38,142 , 232,184)
r11 = Region(52,346 , 52,424)
r12 = Region(70,120 , 248,400)
r13 = Region(274,368 , 444,370)
for r in [r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13]:
self.tree.add(r)
for r in [r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13]:
self.assertTrue(self.tree.search(r))
self.tree.remove(r)
self.assertFalse(self.tree.search(r))
self.assertTrue (self.tree.root == None)
def test_multipleDeletions(self):
# rectangles have all even numbered coordinates
added = []
for _ in range(4096):
r = Region(2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250), 2*random.randint(2,250))
self.tree.add(r)
added.append(r)
print (self.tree.root.level)
random.shuffle(added)
for r in added:
self.assertTrue(self.tree.search(r))
self.tree.remove(r)
self.assertFalse(self.tree.search(r))
# once done, R-Tree is empty once again
ct = 0
for _ in self.tree:
ct += 1
self.assertEquals (0, ct)
def setUp(self):
self.tree = RTree()
class RTreeApp:
def __init__(self):
"""App for creating R tree dynamically and executing range queries"""
self.tree = RTree(m=2, M=4)
self.ready = False
# for range query
self.selectedRegion = None
self.newRegionStart = None
self.newRegion = None
# for identifiers
self.counter = 0
self.master = tkinter.Tk()
self.master.title('R Tree Range Query Application')
self.w = tkinter.Frame(self.master, width=512, height=512)
self.canvas = tkinter.Canvas(self.w, width=512, height=512)
self.paint()
self.canvas.bind("<Button-1>", self.startAdd)
self.canvas.bind("<B1-Motion>",
self.extendAdd) # only when right mouse dragged
self.canvas.bind("<ButtonRelease-1>", self.endAdd)
self.canvas.bind("<Button-3>", self.range) # when right mouse clicked
self.canvas.bind("<ButtonRelease-3>", self.clear)
self.canvas.bind("<B3-Motion>",
self.range) # only when right mouse dragged
self.w.pack()
def startAdd(self, event):
"""End of range search."""
x = event.x
y = self.toCartesian(event.y)
self.newRegionStart = (x, y)
def extendAdd(self, event):
"""End of range search."""
if self.newRegionStart:
x = event.x
y = self.toCartesian(event.y)
self.newRegion = Region(x, y, x, y).unionPoint(self.newRegionStart)
self.paint()
def endAdd(self, event):
"""End of range search."""
if self.newRegionStart:
self.newRegionStart = None
self.counter += 1
if self.newRegion:
self.tree.add(self.newRegion, str(self.counter))
self.newRegion = None
self.paint()
def toCartesian(self, y):
"""Convert tkinter point into Cartesian."""
return self.w.winfo_height() - y
def toTk(self, y):
"""Convert Cartesian into tkinter point."""
if y == maxValue: return 0
tk_y = self.w.winfo_height()
if y != minValue:
tk_y -= y
return tk_y
def clear(self, event):
"""End of range search."""
self.selectedRegion = None
self.paint()
def range(self, event):
"""Initiate a range search using a selected rectangular region."""
p = (event.x, self.toCartesian(event.y))
if self.selectedRegion is None:
self.selectedStart = Region(p[X], p[Y], p[X], p[Y])
self.selectedRegion = self.selectedStart.unionPoint(p)
self.paint()
# return (node,0,True) where status is True if draining entire tree rooted at node. If False,
# then (rect,id,False). Draw these
# as shaded red rectangle to identify whole sub-tree is selected.
for triple in self.tree.range(self.selectedRegion):
if triple[2]:
r = triple[0].region
self.canvas.create_rectangle(r.x_min,
self.toTk(r.y_min),
r.x_max,
self.toTk(r.y_max),
fill='Red',
stipple='gray12')
else:
r = triple[0]
self.canvas.create_rectangle(r.x_min,
self.toTk(r.y_min),
r.x_max,
self.toTk(r.y_max),
fill='Red')
def click(self, event):
"""Add point to KDtree."""
p = (event.x, self.toCartesian(event.y))
self.tree.add(p)
self.paint()
def visit(self, n):
""" Visit node to paint properly."""
if n == None: return
if n.level == 0:
for idx in range(n.count):
r = n.children[idx].region
self.canvas.create_rectangle(r.x_min,
self.toTk(r.y_min),
r.x_max,
self.toTk(r.y_max),
fill='Gray')
for idx in range(n.count):
self.visit(n.children[idx])
# Do after all children so we can see interior nodes, too.
r = n.region
self.canvas.create_rectangle(r.x_min,
self.toTk(r.y_min),
r.x_max,
self.toTk(r.y_max),
outline='Black',
dash=(2, 4))
color = 'Gray'
if n.level == 0:
color = 'Black'
self.canvas.create_text(r.x_max - 16 * len(n.id),
self.toTk(r.y_max) + 16,
anchor=tkinter.W,
font="Times 16 bold",
fill=color,
text=n.id)
def prepare(self, event):
"""prepare to add points."""
if self.label:
self.label.destroy()
self.label = None
self.canvas.pack()
def paint(self):
"""Paint R tree by visiting all nodes, or show introductory message."""
if self.ready:
self.canvas.delete(tkinter.ALL)
self.visit(self.tree.root)
if self.newRegion:
self.canvas.create_rectangle(self.newRegion.x_min,
self.toTk(self.newRegion.y_min),
self.newRegion.x_max,
self.toTk(self.newRegion.y_max),
outline='Black',
dash=(2, 4))
if self.selectedRegion:
self.canvas.create_rectangle(
self.selectedRegion.x_min,
self.toTk(self.selectedRegion.y_min),
self.selectedRegion.x_max,
self.toTk(self.selectedRegion.y_max),
outline='Red',
dash=(2, 4))
else:
self.label = tkinter.Label(self.w,
width=100,
height=40,
text="Click To Add Points")
self.label.bind("<Button-1>", self.prepare)
self.label.pack()
self.ready = True
