def test_nonIntersectSimplePolygonsOnEndPoints(self):
a = Point(0, 0)
b = Point(-2, 2)
c = Point(2, 2)
d = Point(-2, -2)
e = Point(2, -2)
p = Polygon([a, b, c])
q = Polygon([a, d, e])
self.assertFalse(p.intersect(q))
def drawPolygon(self, p, fill):
"""Draw polygon onto canvas."""
if p is None:
self.intersection = Polygon()
self.canvas.create_text(self.canvas.winfo_width() / 2,
self.canvas.winfo_height() / 2,
text='no intersection',
fill=fill)
else:
# create single list of (x,y) coordinates
full = [None] * 2 * p.numEdges()
idx = 0
for pt in p:
full[idx] = pt.x()
full[idx + 1] = self.toTk(pt.y())
idx += 2
self.canvas.create_polygon(full, fill=fill)
# show points in gray
for pt in p:
self.canvas.create_oval(pt.x() - 4,
self.toCartesian(pt.y() - 4),
pt.x() + 4,
self.toCartesian(pt.y() + 4),
fill='gray')
def test_weakSimple(self):
"""See Wikipedia for entry on weakly simple polygon."""
m = Point(0, 0)
a = Point(0, 4)
b = Point(8, 4)
c = Point(8, 0)
d = Point(4, 0)
e = Point(4, 1)
f = Point(6, 1)
g = Point(6, 3)
h = Point(2, 3)
j = Point(2, 1)
k = Point(4, 1) # same as e
l = Point(4, 0) # same as d
p = Polygon([a, b, c, d, e, f, g, h, j, k, l, m])
self.assertTrue(p.simple())
def test_slide(self):
"""Example to use with slide presentation."""
square = Polygon([
Point(0, 8),
Point(0, 0),
Point(8, 0),
Point(8, 8)])
triangle = Polygon([
Point(8, 10),
Point(4, 6),
Point(12, 6)])
self.assertTrue (triangle.convex())
self.assertTrue (square.convex())
p = convexIntersect(square, triangle)
q = convexIntersect(triangle, square)
self.assertEqual(p, q)
real = Polygon([
Point(8, 6),
Point(8, 8),
Point(6, 8),
Point(4, 6)
])
self.assertTrue (samePolygon(p, real))
self.assertTrue (samePolygon(real, p))
def test_defective(self):
"""
This test case detected defect in algorithm. Resolving
it explained how to choose whether to advance p or q
before an intersection had been discovered.
"""
p = Polygon([
Point(241, 243),
Point(353, 210),
Point(393, 245),
Point(375, 398),
Point(257, 303)
])
q = Polygon([
Point(108, 189),
Point(268, 116),
Point(456, 180),
Point(434, 226),
Point(125, 486)
])
self.assertTrue(p.convex())
self.assertTrue(q.convex())
i1 = convexIntersect(p, q)
i2 = convexIntersect(q, p)
self.assertTrue(samePolygon(i1, i2))
def __init__(self, master):
"""App to construct polygon by successive left-mouse clicks."""
master.title(
"Left press to add point to polygon. Right press to start new one."
)
self.master = master
# keep track of polygons being created
self.polygons = [Polygon()]
self.canvas = Canvas(master, width=512, height=512)
self.canvas.bind("<Button-1>", self.add)
self.canvas.bind("<Button-2>", self.finalize)
self.canvas.pack()
def test_enclosing(self):
"""Detect when polygon wholly contains another polygon."""
square = Polygon(
[Point(-8, -8),
Point(8, -8),
Point(8, 8),
Point(-8, 8)])
triangle = Polygon([Point(-3, 0), Point(3, 0), Point(0, 3)])
self.assertTrue(triangle.convex())
self.assertTrue(square.convex())
p = convexIntersect(square, triangle)
q = convexIntersect(triangle, square)
self.assertEqual(p, q)
real = Polygon([Point(-3, 0), Point(3, 0), Point(0, 3)])
self.assertTrue(samePolygon(p, real))
self.assertTrue(samePolygon(real, p))
def test_noIntersection(self):
"""Detect no intersection."""
square = Polygon(
[Point(-8, -8),
Point(8, -8),
Point(8, 8),
Point(-8, 8)])
triangle = Polygon([Point(23, 0), Point(25, 0), Point(24, 1)])
self.assertTrue(triangle.convex())
self.assertTrue(square.convex())
p = convexIntersect(square, triangle)
q = convexIntersect(triangle, square)
self.assertEqual(p, q)
self.assertIsNone(p)
def test_intersectNoPointsInCommon(self):
square = Polygon(
[Point(-2, -2),
Point(2, -2),
Point(2, 2),
Point(-2, 2)])
triangle = Polygon([Point(-3, 0), Point(3, 0), Point(0, 3)])
self.assertTrue(triangle.convex())
self.assertTrue(square.convex())
p = convexIntersect(square, triangle)
q = convexIntersect(triangle, square)
self.assertTrue(samePolygon(p, q))
real = Polygon([
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(-1, 2),
Point(-2, 1),
Point(-2, 0)
])
self.assertTrue(samePolygon(p, real))
self.assertTrue(samePolygon(real, p))
def test_intersect(self):
# Note: only works if convex polygons in
# normal form, with points/edges in counter-clockwise
# fashion.
square = Polygon(
[Point(-2, -2),
Point(2, -2),
Point(2, 2),
Point(-2, 2)])
triangle = Polygon([Point(-2, -2), Point(2, -2), Point(0, 4)])
self.assertTrue(triangle.convex())
self.assertTrue(square.convex())
p = convexIntersect(square, triangle)
q = convexIntersect(triangle, square)
self.assertTrue(samePolygon(p, q))
real = Polygon(
[Point(2 / 3, 2),
Point(-2 / 3, 2),
Point(-2, -2),
Point(2, -2)])
self.assertTrue(samePolygon(p, real))
self.assertTrue(samePolygon(real, p))
def computeHull (points):
"""
Compute the convex hull for given points and return as polygon.
Returned polygon is in 'counter-clockwise' fashion, with the
interior "to the left" of each edge.
"""
# sort by x coordinate (and if ==, by y coordinate).
n = len(points)
points = sorted(points, key=lambda pt:[pt.x(), pt.y()])
if n < 3:
return Polygon(points)
# Compute upper hull by starting with rightmost two points
upper = Polygon ([points[-1], points[-2]])
for i in range(n-3, -1, -1):
upper.add (points[i].x(), points[i].y())
while upper.numPoints() >=3 and lastThreeNonLeft(upper):
upper.remove(-2)
# Compute lower hull by starting with leftmost two points
lower = Polygon ([points[0], points[1]])
for i in range(2, n):
lower.add (points[i].x(), points[i].y())
while lower.numPoints() >=3 and lastThreeNonLeft(lower):
lower.remove(-2)
# Merge into upper (skip first and last to avoid duplication) and return.
upper.remove(-1)
upper.remove(0)
for pt in upper:
lower.add(pt.x(), pt.y())
return lower
def test_simpleonvexShape(self):
p = Polygon([Point(-2, 2), Point(0, -2), Point(2, 2)])
self.assertTrue(p.convex())
def test_nonConvexShape(self):
p = Polygon([Point(-2, 2), Point(0, -2), Point(2, 2), Point(0, 0)])
self.assertFalse(p.convex())
def convexIntersect(p, q):
"""
Compute and return polygon resulting from the intersection of
two convext polygons, p and q.
"""
intersection = Polygon()
pn = p.numEdges()
qn = q.numEdges()
k = 1
inside = None # can't know inside until intersection
first = None # remember 1st intersection to know when to stop
firstp = pe = p.edges()[0] # get first edge of p and q
firstq = qe = q.edges()[0]
while k < 2*(pn + qn):
pt = pe.intersect(qe)
if pt is not None:
if first == None:
first = pt
elif pt == first:
# stop when find first intersection again
break
intersection.add(pt.x(), pt.y())
if inhalfplane(pe.tail(), qe):
inside = p
else:
inside = q
# Identify relationship between edges; either we advance
# p or we advance q, based on whether p's current edge
# is aiming at qe (or vice versa).
advancep = advanceq = False
if (aim(pe,qe) and aim(qe,pe)) or (not aim(pe,qe) and not aim(qe,pe)):
if inside is p:
advanceq = True
elif inside is q:
advancep = True
else:
# no intersection yet. Choose based on
# which one is "outside"
if inhalfplane(pe.tail(), qe):
advanceq = True
else:
advancep = True
elif aim(pe, qe):
advancep = True
elif aim(qe, pe):
advanceq = True
## if aim(pe, qe):
## if aim(qe, pe):
## if inside is p:
## advanceq = True
## elif inside is q:
## advancep = True
## else:
## advancep = True # arbitrary pick
## else:
## advancep = True
## else:
## if aim(qe, pe):
## advanceq = True
## else:
## if inside is p:
## advanceq = True
## elif inside is q:
## advancep = True
## else:
## advancep = True # arbitrary pick
if advancep:
if inside is p:
intersection.add(pe.tail().x(), pe.tail().y())
pe = pe.next()
elif advanceq:
if inside is q:
intersection.add(qe.tail().x(), qe.tail().y())
qe = qe.next()
k += 1
if intersection.numPoints() == 0:
if containedWithin(firstp.tail(), q):
return p
elif containedWithin(firstq.tail(), p):
return q
else:
return None
# Return computed intersection
return intersection
def clear(self, event):
"""Clear all polygons and start again."""
self.polygons = [Polygon()]
self.visit()
def finalize(self, event):
"""Finalize polygon and add a new one."""
self.polygons.insert(0, Polygon())
self.visit()