def test_nonIntersectEndPoints(self):
p = Point(0, 0)
e = Edge(p, Point(2, 3))
f = Edge(p, Point(-2, 3))
self.assertIsNone(e.intersect(f))
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 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 computeRandom(x, y, u, v):
"""
Compute random convex polygon within given (x,y), (u,v) bounding area.
Start from relatively small number of points so polygon has some
interesting shapes
"""
points = [Point(random.randint(x,u),random.randint(y,v)) for i in range(10)]
return computeHull(points)
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 aim (p, q):
"""Return true if p is "aiming towards" q's half-plane edge."""
# First check if p.tail is in the half-plane of q
inside = inhalfplane(p.tail(), q)
# compute cross product of q x p to determine orientation
# en.wikipedia.org/wiki/Cross_product#Computational_geometry
# normalize p and q
pnorm = Point(p.tail().x() - p.head().x(),
p.tail().y() - p.head().y())
qnorm = Point(q.tail().x() - q.head().x(),
q.tail().y() - q.head().y())
cross = qnorm.x()*pnorm.y() - qnorm.y()*pnorm.x()
if inside:
# in half-plane, so now check orientation
return cross < 0
else:
# not in half-plane.
return cross >= 0
def intersect(self, e):
"""Return intersection between two edges (aside from end-points)."""
if self.head() == e.head() or self.head() == e.tail():
return None
if self.tail() == e.head() or self.tail() == e.tail():
return None
# compute intersection of two line segments using x,y coords
pt = intersect(self.head().x(),
self.head().y(),
self.tail().x(),
self.tail().y(),
e.head().x(),
e.head().y(),
e.tail().x(),
e.tail().y())
if pt is None:
return None
return Point (pt[0], pt[1])
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 add(self, event):
"""Add point to polygon and redraw."""
self.points.append(Point(event.x, self.toCartesian(event.y)))
self.visit()
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 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_canIntersectEndPointWithRealIntersection(self):
e = Edge(Point(0, 0), Point(2, 2))
f = Edge(Point(-2, 2), Point(2, -2))
self.assertTrue(e.intersect(f))
def add(self, x, y):
"""Extend polygon with additional (x,y) point."""
self.points.append(Point(x, y))
n = len(self.points)
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_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))
