def test_threeByThree(self):
points = [(x,y) for x in range(2,9,3) for y in range(2,9,3)]
v = Voronoi(width=10, height=10)
self.perturb(points)
v.process(points)
for e in v.edges:
print (e)
def test_threeVertical(self):
points = [(10,x) for x in range(2,9,3) ]
v = Voronoi(width=20, height=20)
v.process(points)
for e in v.points:
print (e, e.polygon)
def test_threeVertical(self):
points = [(10, x) for x in range(2, 9, 3)]
v = Voronoi(width=20, height=20)
v.process(points)
for e in v.points:
print(e, e.polygon)
def test_threeByThree(self):
points = [(x, y) for x in range(2, 9, 3) for y in range(2, 9, 3)]
v = Voronoi(width=10, height=10)
self.perturb(points)
v.process(points)
for e in v.edges:
print(e)
def test_another(self):
p1 = (11, 26)
p2 = (28, 15)
p3 = (22, 41)
v = Voronoi(width=50, height=50)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_slightlyOff(self):
p1 = (6, 6)
p2 = (6, 8)
p3 = (6.1, 4)
v = Voronoi(width=10, height=10)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_slightlyOff(self):
p1 = (6, 6)
p2 = (6, 8)
p3 = (6.1, 4)
v = Voronoi(width=10, height=10)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_fortune(self):
p1 = (2, 6)
p2 = (7, 5)
p3 = (4, 2)
v = Voronoi(width=10, height=10)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_another(self):
p1 = (11, 26)
p2 = (28, 15)
p3 = (22, 41)
v = Voronoi(width=50, height=50)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_fortune(self):
p1 = (2,6)
p2 = (7,5)
p3 = (4,2)
v = Voronoi(width=10, height=10)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_multipleFirstSweepLine(self):
p1 = (150, 200)
p2 = (250, 200)
p3 = (200, 150)
v = Voronoi(width=300, height=300)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_missing(self):
p1 = (110.0, 229.0)
p2 = (187.0, 231.0)
p3 = (150.0, 107.0)
v = Voronoi(width=400, height=400)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_missing(self):
p1 = (110.0, 229.0)
p2 = (187.0, 231.0)
p3 = (150.0, 107.0)
v = Voronoi(width=400, height=400)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_badCase(self):
p1 = (14, 20)
p2 = (19, 15)
p3 = (5, 12)
v = Voronoi(width=40, height=40)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_multipleFirstSweepLine(self):
p1 = (150,200)
p2 = (250,200)
p3 = (200,150)
v = Voronoi(width=300, height=300)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_badCase(self):
p1 = (14, 20)
p2 = (19, 15)
p3 = (5, 12)
v = Voronoi(width=40, height=40)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_crossover(self):
p1 = (138, 243)
p2 = (180, 184)
p3 = (113, 115)
p4 = (245, 112)
v = Voronoi(width=400, height=400)
v.process([p1, p2, p3, p4])
for e in v.edges:
print(e)
def test_crossover(self):
p1 = (138, 243)
p2 = (180, 184)
p3 = (113, 115)
p4 = (245, 112)
v = Voronoi(width=400, height=400)
v.process([p1,p2,p3,p4])
for e in v.edges:
print (e)
def test_twoInitialVerticalBisection(self):
p1 = (3,3)
p2 = (8,3)
e1 = [Point((5.5,10)),Point((5.5,0))]
edges = [e1]
v = Voronoi(10, 10)
v.process([p1,p2])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_whenPointAtCircumcircle(self):
p1 = (2,5)
p2 = (6,5)
p3 = (4,3)
# This is challenging and not yet solved.
v = Voronoi(10,10)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_whenPointAtCircumcircle(self):
p1 = (2, 5)
p2 = (6, 5)
p3 = (4, 3)
# This is challenging and not yet solved.
v = Voronoi(10, 10)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_twoInitialVerticalBisection(self):
p1 = (3, 3)
p2 = (8, 3)
e1 = [Point((5.5, 10)), Point((5.5, 0))]
edges = [e1]
v = Voronoi(10, 10)
v.process([p1, p2])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_twoInitial(self):
p1 = (8,4)
p2 = (10,0)
e1 = [Point((0,-2.5)),Point((20,7.5))]
edges = [e1]
v = Voronoi(20,20)
v.process([p1,p2])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_twoInitial(self):
p1 = (8, 4)
p2 = (10, 0)
e1 = [Point((0, -2.5)), Point((20, 7.5))]
edges = [e1]
v = Voronoi(20, 20)
v.process([p1, p2])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeHorizontal(self):
points = [(x,5) for x in range(2,9,3) ]
e1 = [Point((3.5,10)),Point((3.5,0))]
e2 = [Point((6.5,10)),Point((6.5,0))]
edges = [e1,e2]
v = Voronoi(width=10, height=10)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeHorizontal(self):
points = [(x, 5) for x in range(2, 9, 3)]
e1 = [Point((3.5, 10)), Point((3.5, 0))]
e2 = [Point((6.5, 10)), Point((6.5, 0))]
edges = [e1, e2]
v = Voronoi(width=10, height=10)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeIsoceles(self):
points = [(5, 2), (11, 2), (8, 4)]
e1 = [Point((8.0, 0.75)), Point((0, 12.75))]
e2 = [Point((15, 11.25)), Point((8.0, 0.75))]
e3 = [Point((8.0, 0.75)), Point((8.0, 0.0))]
edges = [e1, e2, e3]
v = Voronoi(width=15, height=15)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeIsoceles(self):
points = [(5,2), (11,2), (8,4) ]
e1 = [Point((8.0,0.75)),Point((0,12.75))]
e2 = [Point((15,11.25)),Point((8.0,0.75))]
e3 = [Point((8.0,0.75)),Point((8.0,0.0))]
edges = [e1,e2,e3]
v = Voronoi(width=15, height=15)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeIsocelesTilted(self):
points = [(5, 2), (5, 8), (9, 5)]
e1 = [Point((9.625, 10)), Point((5.875, 5.0))]
e2 = [Point((5.875, 5.0)), Point((0, 5.0))]
e3 = [Point((5.875, 5.0)), Point((9.625, 0))]
edges = [e1, e2, e3]
v = Voronoi(width=10, height=10)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeIsocelesTilted(self):
points = [(5,2), (5,8), (9,5) ]
e1 = [Point((9.625,10)),Point((5.875,5.0))]
e2 = [Point((5.875,5.0)),Point((0,5.0))]
e3 = [Point((5.875,5.0)),Point((9.625,0))]
edges = [e1,e2,e3]
v = Voronoi(width=10, height=10)
v.process(points)
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_edgeExplanation(self):
#p1 = (83, 181)
#p2 = (108, 181)
#p3 = (380, 308)
p1 = (4, 6)
p2 = (2, 4)
p3 = (6, 4)
p4 = (3, 1)
p5 = (5, 1)
v = Voronoi(width=8, height=8)
v.process([p1, p2, p3, p4, p5])
for e in v.edges:
print(e)
def test_edgeExplanation(self):
#p1 = (83, 181)
#p2 = (108, 181)
#p3 = (380, 308)
p1 = (4,6)
p2 = (2,4)
p3 = (6,4)
p4 = (3,1)
p5 = (5,1)
v = Voronoi(width=8, height=8)
v.process([p1,p2,p3,p4,p5])
for e in v.edges:
print (e)
def test_threeSameY(self):
p1 = (50, 200)
p2 = (100, 200)
p3 = (150, 200)
e1 = [Point((75, 300)), Point((75, 0))]
e2 = [Point((125, 300)), Point((125, 0))]
edges = [e1, e2]
v = Voronoi(300, 300)
v.process([p1, p2, p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeSameY(self):
p1 = (50,200)
p2 = (100,200)
p3 = (150,200)
e1 = [Point((75,300)),Point((75,0))]
e2 = [Point((125,300)),Point((125,0))]
edges = [e1,e2]
v = Voronoi(300,300)
v.process([p1,p2,p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeL(self):
p1 = (2, 5)
p2 = (2, 2)
p3 = (5, 2)
e1 = [Point((0, 3.5)), Point((3.5, 3.5))]
e2 = [Point((3.5, 3.5)), Point((3.5, 0))]
e3 = [Point((3.5, 3.5)), Point((10, 10.0))]
edges = [e1, e2, e3]
v = Voronoi(10, 10)
v.process([p1, p2, p3])
self.assertEquals(3, len(v.edges))
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_collinearOtherParallel(self):
p1 = (2,7)
p2 = (4,5)
p3 = (6,3)
p4 = (8,1)
e1 = [Point((0,3)),Point((17,20))]
e2 = [Point((0,-1)),Point((20,19))]
e3 = [Point((0,-5)),Point((20,15))]
edges = [e1,e2,e3]
v = Voronoi(width=20, height=20)
v.process([p1,p2,p3,p4])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_collinearOtherParallel(self):
p1 = (2, 7)
p2 = (4, 5)
p3 = (6, 3)
p4 = (8, 1)
e1 = [Point((0, 3)), Point((17, 20))]
e2 = [Point((0, -1)), Point((20, 19))]
e3 = [Point((0, -5)), Point((20, 15))]
edges = [e1, e2, e3]
v = Voronoi(width=20, height=20)
v.process([p1, p2, p3, p4])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeL(self):
p1 = (2,5)
p2 = (2,2)
p3 = (5,2)
e1 = [Point((0,3.5)), Point((3.5,3.5))]
e2 = [Point((3.5,3.5)), Point((3.5,0))]
e3 = [Point((3.5,3.5)), Point((10,10.0))]
edges = [e1,e2,e3]
v = Voronoi(10,10)
v.process([p1,p2,p3])
self.assertEquals (3, len(v.edges))
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeOneParallelOneIntersect(self):
p1 = (3,3)
p2 = (5,3)
p3 = (8,2)
# outside bounding box area
e1 = [Point((4,10)),Point((4,-5.0))]
e2 = [Point((4,-5.0)),Point((9,10))]
e3 = [Point((4,-5.0)),Point((0,-25))] ## This one is completely outside and can't be fixed.
edges = [e1,e2,e3]
v = Voronoi(10, 10)
v.process([p1,p2,p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_firstCircleEvent(self):
p1 = (6,3)
p2 = (8,4)
p3 = (5,1)
e1 = [Point((0,4.75)),Point((8.5,0.5))]
e2 = [Point((0,17.5)),Point((8.5,0.5))]
e3 = [Point((8.5,0.5)),Point((9,0))]
e4 = [Point((6,5.5)), Point((8.5,0.5))]
e5 = [Point((5, 2.25)), Point((8.5, 0.5))]
edges = [e1,e2,e3,e4,e5]
v = Voronoi(width=10, height=10)
v.process([p1,p2,p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeOneParallelOneIntersect(self):
p1 = (3, 3)
p2 = (5, 3)
p3 = (8, 2)
# outside bounding box area
e1 = [Point((4, 10)), Point((4, -5.0))]
e2 = [Point((4, -5.0)), Point((9, 10))]
e3 = [Point((4, -5.0)), Point(
(0, -25))] ## This one is completely outside and can't be fixed.
edges = [e1, e2, e3]
v = Voronoi(10, 10)
v.process([p1, p2, p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_firstCircleEvent(self):
p1 = (6, 3)
p2 = (8, 4)
p3 = (5, 1)
e1 = [Point((0, 4.75)), Point((8.5, 0.5))]
e2 = [Point((0, 17.5)), Point((8.5, 0.5))]
e3 = [Point((8.5, 0.5)), Point((9, 0))]
e4 = [Point((6, 5.5)), Point((8.5, 0.5))]
e5 = [Point((5, 2.25)), Point((8.5, 0.5))]
edges = [e1, e2, e3, e4, e5]
v = Voronoi(width=10, height=10)
v.process([p1, p2, p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def process(self, collection):
"""Now that Voronoi diagram is computed, act on it."""
self.voronoi = Voronoi(400, 400)
self.voronoi.process(collection)
self.canvas.delete(tkinter.ALL)
for fp in collection:
self.canvas.create_rectangle(fp[X] - RectangleSize,
self.toTk(fp[Y]) - RectangleSize,
fp[X] + RectangleSize,
self.toTk(fp[Y]) + RectangleSize,
fill='Red')
for edge in self.voronoi.edges:
start = edge.start
end = edge.end
self.canvas.create_line(start.x, self.toTk(start.y), end.x,
self.toTk(end.y))
def test_threeBasic(self):
p1 = (6, 7)
p2 = (2, 3)
p3 = (8, 1)
e1 = [Point((0, 9.0)), Point((5.5, 3.5))]
e2 = [Point((5.5, 3.5)), Point((0, -13.0))]
e3 = [Point((5.5, 3.5)), Point((10, 5.0))]
edges = [e1, e2, e3]
v = Voronoi(10, 10)
v.process([p1, p2, p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
for p in v.points:
print(p.polygon)
def test_perfectCircle(self):
#p1 = (83, 181)
#p2 = (108, 181)
#p3 = (380, 308)
p1 = (4,6)
p2 = (2,4)
p3 = (6,4)
e1 = [Point((0,8)),Point((4,4))]
e2 = [Point((4,4)),Point((4,0))]
e3 = [Point((4,4)),Point((8,8))]
edges = [e1,e2,e3]
v = Voronoi(8,8)
v.process([p1,p2,p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_threeBasic(self):
p1 = (6,7)
p2 = (2,3)
p3 = (8,1)
e1 = [Point((0,9.0)), Point((5.5,3.5))]
e2 = [Point((5.5,3.5)), Point((0,-13.0))]
e3 = [Point((5.5,3.5)), Point((10,5.0))]
edges = [e1,e2,e3]
v = Voronoi(10,10)
v.process([p1,p2,p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
for p in v.points:
print (p.polygon)
def test_perfectCircle(self):
#p1 = (83, 181)
#p2 = (108, 181)
#p3 = (380, 308)
p1 = (4, 6)
p2 = (2, 4)
p3 = (6, 4)
e1 = [Point((0, 8)), Point((4, 4))]
e2 = [Point((4, 4)), Point((4, 0))]
e3 = [Point((4, 4)), Point((8, 8))]
edges = [e1, e2, e3]
v = Voronoi(8, 8)
v.process([p1, p2, p3])
for e in v.edges:
self.valid([e.start, e.end], edges)
def test_good_bad(self):
p1 = (205, 238)
p2 = (156, 157)
p3 = (255, 133)
v = Voronoi(width=400, height=400)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
print("----")
p1 = (205, 238)
p2 = (156, 157)
p3 = (254, 133) ## small change causes one more circle event
v = Voronoi(width=400, height=400)
v.process([p1, p2, p3])
for e in v.edges:
print(e)
def test_good_bad(self):
p1 = (205,238)
p2 = (156,157 )
p3 = (255,133)
v = Voronoi(width=400, height=400)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
print ("----")
p1 = (205,238)
p2 = (156,157 )
p3 = (254,133) ## small change causes one more circle event
v = Voronoi(width=400, height=400)
v.process([p1,p2,p3])
for e in v.edges:
print (e)
def test_singlePoint(self):
p1 = (8,4)
v = Voronoi(20,20)
v.process([p1])
self.assertEquals(0, len(v.edges))
class VoronoiApp:
def __init__(self):
"""App for creating KD tree dynamically and executing nearest neighbor queries."""
# Points that we have added.
self.points = []
self.voronoi = None
# set to true when you want to view a set of points that
# were set not by user control.
self.static = False
self.master = tkinter.Tk()
self.master.title('Voronoi Diagram Application')
self.w = tkinter.Frame(self.master, width=410, height=410)
self.canvas = tkinter.Canvas(self.w, width=400, height=400)
self.paint()
self.canvas.bind("<Button-1>", self.click)
self.canvas.bind("<Motion>", self.moved)
self.w.pack()
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 moved(self, event):
"""React to mouse move events."""
if self.static:
self.process(self.points)
return
# during movement, add points to track mouse
p = (event.x, self.toCartesian(event.y))
# Avoid duplicates for cleaner implementation
if p not in self.points:
fullPoints = self.points + [p]
self.process(fullPoints)
def click(self, event):
"""Add point to Voronoi collection."""
if self.static:
self.process(self.points)
return
p = (event.x, self.toCartesian(event.y))
# Avoid duplicates for cleaner implementation
if p not in self.points:
self.points.append(p)
self.process(self.points)
def process(self, collection):
"""Now that Voronoi diagram is computed, act on it."""
self.voronoi = Voronoi(400, 400)
self.voronoi.process(collection)
self.canvas.delete(tkinter.ALL)
for fp in collection:
self.canvas.create_rectangle(fp[X] - RectangleSize,
self.toTk(fp[Y]) - RectangleSize,
fp[X] + RectangleSize,
self.toTk(fp[Y]) + RectangleSize,
fill='Red')
for edge in self.voronoi.edges:
start = edge.start
end = edge.end
self.canvas.create_line(start.x, self.toTk(start.y), end.x,
self.toTk(end.y))
def prepare(self, event):
"""prepare to add points."""
if self.label:
self.label.destroy()
self.label = None
self.canvas.pack()
def paint(self):
"""Paint KDTree by visiting all nodes, or show introductory message."""
if self.voronoi:
self.canvas.delete(tkinter.ALL)
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()
def test_singlePoint(self):
p1 = (8, 4)
v = Voronoi(20, 20)
v.process([p1])
self.assertEquals(0, len(v.edges))