def test_mapoverlay4(self):
M1 = PlanarMap(Triangle(3, 0, 6, 6, 0, 6))
#M1 = PlanarMap(Triangle(3., 0., 6., 6., 0., 6.))
M2 = PlanarMap(Triangle(3, 8, 0, 2, 6, 2))
M3 = M1.map_overlay(M2)
self.assertEqual(M3.v(), 12)
self.assertEqual(M3.e(), 18)
self.assertEqual(M3.f(), 8)
def test_make3(self):
t1 = Triangle(0, 0, 6, 0, 2, 4)
t2 = Triangle(6, 0, 0, 12, 2, 4)
t3 = Triangle(0, 12, 0, 0, 2, 4)
result = self.t1.make3()
self.assertTrue(t1 in result)
self.assertTrue(t2 in result)
self.assertTrue(t3 in result)
def test_make4(self):
t1 = Triangle(0, 0, 3, 0, 0, 6)
t2 = Triangle(6, 0, 3, 6, 3, 0)
t3 = Triangle(0, 12, 0, 6, 3, 6)
t4 = Triangle(3, 0, 3, 6, 0, 6)
result = self.t1.make4()
self.assertTrue(t1 in result)
self.assertTrue(t2 in result)
self.assertTrue(t3 in result)
self.assertTrue(t4 in result)
def run(self):
for (p1, p2, p3) in itertools.combinations(self.point_list, 3):
# Counterclockwise orientation of points.
if orientation(p1, p2, p3) < 0:
p2, p3 = p3, p2
elif orientation(p1, p2, p3) == 0: # collinear points
continue
triangle = Triangle(p1, p2, p3)
if all(not triangle.in_circumcircle(p4) for p4 in self.point_list
if p4 != p1 and p4 != p2 and p4 != p3):
self.tc.insert(triangle)
def legalize(self, point, segment):
#print ( "legalize {} {}".format(point, segment) )
# Trzeba znalezc trojkaty sasiadujace z krawedzia.
tlist = self.tc.search(segment.center())
if len(tlist) == 1: # przypadek (i) de Berga
# Nie przekrecamy krawedzi duzego trojkata, jest legalna.
#print ( "big triangle segment" )
assert segment.pt1 in self.big_nodes and segment.pt2 in self.big_nodes
return
#print ( "tlist {}".format(tlist) )
assert len(tlist) == 2
t1 = tlist.pop()
t2 = tlist.pop()
if point in t2: # chcemy point in t1
t1, t2 = t2, t1
pt3 = t2.third_node(segment.pt1, segment.pt2)
illegal = t1.in_circumcircle(pt3)
if pt3 in self.big_nodes:
#print ( "{} in big_nodes".format(pt3) )
# Trzeba sprawdzic, czy koniec krawedzi nie jest z big triangle.
if segment.pt1 in self.big_nodes: # przypadek (iv) de Berga
# Dokladnie dwa indeksy sa ujemne, jeden z krawedzi.
illegal = False if segment.pt1 < pt3 else True
#print ( "illegal 2 {}".format(illegal) )
elif segment.pt2 in self.big_nodes: # przypadek (iv) de Berga
# Dokladnie dwa indeksy sa ujemne, jeden z krawedzi.
illegal = False if segment.pt2 < pt3 else True
#print ( "illegal 2 {}".format(illegal) )
else: # przypadek (iii) de Berga
# Dokladnie jeden indeks ujemny (pt3), ale nie przy krawedzi.
illegal = False # krawedz jest legalna
#print ( "illegal 1 {}".format(illegal) )
else: # jeden koniec krawedzi moze byc z big triangle
if segment.pt1 in self.big_nodes or segment.pt2 in self.big_nodes:
# Przypadek (iii) de Berga, jeden indeks ujemny z krawedzi.
illegal = True
#print ( "illegal 1 {}".format(illegal) )
else: # cztery indeksy sa dodatnie, przypadek (ii) de Berga,
pass # procedujemy normalnie
if illegal:
if orientation(point, segment.pt1, pt3) * orientation(
point, segment.pt2, pt3) > 0:
# Czworokat wklesly! Nie przekrecamy!
#print ( "concave quadrilateral!" )
illegal = False
if illegal: # jezeli krawedz nielegalna
# Przekrecamy krawedz (edge flipping).
#print ( "segment flip" )
self.tc.remove(t1)
self.tc.remove(t2)
self.tc.insert(Triangle(segment.pt1, point, pt3))
self.tc.insert(Triangle(segment.pt2, point, pt3))
self.legalize(point, Segment(segment.pt1, pt3))
self.legalize(point, Segment(segment.pt2, pt3))
def test_mapoverlay5(self):
M1 = PlanarMap(Triangle(0, 0, 3, 1, 0, 2))
M2 = PlanarMap(Rectangle(1, 0, 2, 2))
M3 = M1.map_overlay(M2)
self.assertEqual(M3.v(), 11)
self.assertEqual(M3.e(), 15)
self.assertEqual(M3.f(), 6)
def insert_big_triangle(self):
big = max(max(abs(point.x), abs(point.y)) for point in self.point_list)
m = 4 # najlepiej typu int
# m = 3 sugeruje de Berg, ale moze byc na styk, jezeli beda punkty
# Point(big, -big) lub Point(-big, big).
p1 = Point(m * big, 0)
p2 = Point(0, m * big)
p3 = Point(-m * big, -m * big)
# Counterclockwise orientation of points.
self.big_nodes = set([p1, p2, p3])
self.tc.insert(Triangle(p1, p2, p3))
def test_triangulation(self):
p1 = Point(-1, -1)
p2 = Point(1, -1)
p3 = Point(2, 1)
p4 = Point(-1, 1)
point_list = [p1, p2, p3, p4]
algorithm = BowyerWatson(point_list)
algorithm.run()
self.assertEqual(len(algorithm.tc), 2)
self.assertTrue(Triangle(p1, p2, p4) in algorithm.tc)
self.assertTrue(Triangle(p2, p3, p4) in algorithm.tc)
#print ( "tc {}".format(algorithm.tc) )
G = algorithm.tc.to_graph()
#G.show()
self.assertEqual(G.v(), 4)
self.assertEqual(G.e(), 5)
self.assertTrue(G.has_edge(Edge(p1, p2)))
self.assertTrue(G.has_edge(Edge(p1, p4)))
self.assertTrue(G.has_edge(Edge(p2, p4)))
self.assertTrue(G.has_edge(Edge(p2, p3)))
self.assertTrue(G.has_edge(Edge(p3, p4)))
def add_to_triangulation(self, point):
#print ( "add_to_triangulation {}".format(point) )
bad_triangles = list()
for triangle in self.tc.itertriangles():
if triangle.in_circumcircle(point):
bad_triangles.append(triangle)
sdict = dict()
for triangle in bad_triangles:
# Sprawdzanie krawedzi.
for segment in triangle.itersegments():
sdict[segment] = sdict.get(segment, 0) + 1
for triangle in bad_triangles:
self.tc.remove(triangle)
for segment in sdict:
if sdict[segment] == 1:
self.tc.insert(Triangle(point, segment.pt1, segment.pt2))
def add_to_triangulation(self, point):
#print ( "add_to_triangulation {}".format(point) )
# Szukamy trojkata do ktorego wpada punkt.
# Punkt moze byc na krawedzi, na granicy dwoch trojkatow.
tlist = self.tc.search(point)
# tlist moze zawierac jeden lub dwa trojkaty (wspolna krawedz).
#print ( "tlist {}".format(tlist) )
if len(tlist) == 1: # punkt we wnetrzu trojkata
# UWAGA Punkt moze trafic na krawedz big triangle,
# a wtedy bedzie degeneracja.
# Chyba ze zrobimy jeszcze wiekszy big triangle.
t1 = tlist.pop()
self.tc.remove(t1)
self.tc.insert(Triangle(t1.pt1, t1.pt2, point))
self.tc.insert(Triangle(t1.pt2, t1.pt3, point))
self.tc.insert(Triangle(t1.pt3, t1.pt1, point))
self.legalize(point, Segment(t1.pt1, t1.pt2))
self.legalize(point, Segment(t1.pt2, t1.pt3))
self.legalize(point, Segment(t1.pt3, t1.pt1))
elif len(tlist) == 2: # punkt na krawedzi
t1 = tlist.pop()
t2 = tlist.pop()
# Trzeba znalezc wspolna krawedz.
segment = t1.common_segment(t2)
assert point in segment
# Konce wspolnej krawedzi.
q1 = segment.pt1
q2 = segment.pt2
q3 = t1.third_node(q1, q2)
q4 = t2.third_node(q1, q2)
self.tc.remove(t1)
self.tc.remove(t2)
self.tc.insert(Triangle(q1, q3, point))
self.tc.insert(Triangle(q2, q3, point))
self.tc.insert(Triangle(q1, q4, point))
self.tc.insert(Triangle(q2, q4, point))
self.legalize(point, Segment(q1, q3))
self.legalize(point, Segment(q2, q3))
self.legalize(point, Segment(q1, q4))
self.legalize(point, Segment(q2, q4))
else:
raise ValueError("more than 2 points in tlist")
def setUp(self):
self.t1 = Triangle(0, 0, 2, 0, 0, 2)
self.t2 = Triangle(2, 0, 2, 2, 0, 2)
self.tc = TriangleCollection()
class TestTriangle(unittest.TestCase):
def setUp(self):
self.t1 = Triangle(0, 0, 6, 0, 0, 12)
self.t2 = Triangle(3, 0, 9, 0, 6, 6)
self.t3 = Triangle(Point(0, 0), Point(2, 0), Point(1, 2))
self.t4 = Triangle(Fraction(1, 2), Fraction(2, 3), Fraction(3, 4),
Fraction(4, 5), Fraction(5, 6), Fraction(6, 7))
def test_init(self):
self.assertRaises(ValueError, Triangle, 0, 0, 1, 1, 3, 3)
self.assertRaises(ValueError, Triangle, 0, 0, 1, 1, 3)
self.assertRaises(ValueError, Triangle, 0, 0, 1, 1)
self.assertRaises(ValueError, Triangle, Point(1, 1), Point(2, 2), 3)
self.assertEqual(self.t1.pt1, Point(0, 0))
self.assertEqual(self.t1.pt2, Point(6, 0))
self.assertEqual(self.t1.pt3, Point(0, 12))
self.assertEqual(self.t3.pt1, Point(0, 0))
self.assertEqual(self.t3.pt2, Point(2, 0))
self.assertEqual(self.t3.pt3, Point(1, 2))
def test_print(self):
self.assertEqual(repr(self.t1), "Triangle(0, 0, 6, 0, 0, 12)")
self.assertEqual(repr(self.t2), "Triangle(3, 0, 9, 0, 6, 6)")
self.assertEqual(repr(self.t3), "Triangle(0, 0, 2, 0, 1, 2)")
self.assertEqual(
repr(self.t4),
"Triangle(Fraction(1, 2), Fraction(2, 3), Fraction(3, 4), Fraction(4, 5), Fraction(5, 6), Fraction(6, 7))"
)
def test_cmp(self):
self.assertEqual(Triangle(), Triangle(0, 0, 1, 0, 0, 1))
self.assertTrue(self.t1 == Triangle(0, 0, 6, 0, 0, 12))
self.assertFalse(self.t1 == self.t2)
self.assertTrue(self.t1 != self.t2)
self.assertFalse(self.t1 != Triangle(0, 0, 6, 0, 0, 12))
def test_copy(self):
t3 = self.t1.copy()
self.assertEqual(t3, self.t1)
self.assertNotEqual(id(t3), id(self.t1))
def test_center(self):
self.assertEqual(self.t1.center(), Point(2, 4))
self.assertEqual(self.t2.center(), Point(6, 2))
def test_area(self):
self.assertEqual(self.t1.area(), 36)
self.assertEqual(self.t2.area(), 18)
def test_move(self):
self.assertEqual(self.t1.move(1, 2), Triangle(1, 2, 7, 2, 1, 14))
self.assertEqual(self.t1.move(Point(1, 2)),
Triangle(1, 2, 7, 2, 1, 14))
self.assertRaises(ValueError, Triangle.move, self.t1, 1)
def test_make3(self):
t1 = Triangle(0, 0, 6, 0, 2, 4)
t2 = Triangle(6, 0, 0, 12, 2, 4)
t3 = Triangle(0, 12, 0, 0, 2, 4)
result = self.t1.make3()
self.assertTrue(t1 in result)
self.assertTrue(t2 in result)
self.assertTrue(t3 in result)
def test_make4(self):
t1 = Triangle(0, 0, 3, 0, 0, 6)
t2 = Triangle(6, 0, 3, 6, 3, 0)
t3 = Triangle(0, 12, 0, 6, 3, 6)
t4 = Triangle(3, 0, 3, 6, 0, 6)
result = self.t1.make4()
self.assertTrue(t1 in result)
self.assertTrue(t2 in result)
self.assertTrue(t3 in result)
self.assertTrue(t4 in result)
def test_hash(self):
aset = set()
aset.add(self.t1)
aset.add(self.t1) # ignored
self.assertEqual(len(aset), 1)
aset.add(self.t2)
self.assertEqual(len(aset), 2)
def test_contains(self):
self.assertTrue(Point(2, 2) in self.t1)
self.assertTrue(Point(4, 4) in self.t1)
self.assertTrue(Point(3, 0) in self.t1)
self.assertTrue(Point(0, 8) in self.t1)
self.assertFalse(Point(6, 6) in self.t1)
self.assertFalse(Point(7, 0) in self.t1)
self.assertFalse(Point(0, 13) in self.t1)
self.assertRaises(ValueError, Triangle.__contains__, self.t1, 1)
# segment in tringle
self.assertTrue(Segment(1, 1, 2, 2) in self.t1)
self.assertFalse(Segment(1, 1, 6, 6) in self.t1)
def test_orientation(self):
self.assertEqual(self.t1.orientation(), 1)
self.assertEqual(Triangle(0, 0, 1, 1, 1, 0).orientation(), -1)
def test_gnu(self):
s1 = 'set label "" at 0.0,0.0 point pt 7 ps 0.5\n'
s2 = 'set label "" at 6.0,0.0 point pt 7 ps 0.5\n'
s3 = 'set label "" at 0.0,12.0 point pt 7 ps 0.5\n'
s4 = 'set arrow from 0.0,0.0 to 6.0,0.0 nohead\n'
s5 = 'set arrow from 0.0,0.0 to 0.0,12.0 nohead\n'
s6 = 'set arrow from 6.0,0.0 to 0.0,12.0 nohead\n'
self.assertEqual(self.t1.gnu(True), s1 + s2 + s3 + s4 + s5 + s6)
def test_third_node(self):
p1 = Point(0, 0)
p2 = Point(6, 0)
p3 = Point(0, 12)
self.assertEqual(self.t1.third_node(p1, p2), p3)
self.assertEqual(self.t1.third_node(p1, p3), p2)
self.assertEqual(self.t1.third_node(p3, p2), p1)
self.assertRaises(KeyError, Triangle.third_node, self.t1, p1,
Point(1, 1))
def test_in_circumcircle(self):
# Srodek okregu opisanego na t1 jest w Point(3, 6).
self.assertTrue(self.t1.in_circumcircle(Point(1, 1)))
self.assertTrue(self.t1.in_circumcircle(Point(6, 11)))
self.assertFalse(self.t1.in_circumcircle(Point(7, 0)))
def test_circumcenter(self):
self.assertEqual(self.t1.circumcenter(), Point(3, 6))
self.assertEqual(self.t2.circumcenter(), Point(6, Fraction(9, 4)))
self.assertEqual(self.t3.circumcenter(), Point(1, Fraction(3, 4)))
def test_iterpoints(self):
L = list(self.t1.iterpoints())
self.assertEqual(L[0], self.t1.pt1)
self.assertEqual(L[1], self.t1.pt2)
self.assertEqual(L[2], self.t1.pt3)
def test_itersegments(self):
L = list(self.t1.itersegments())
self.assertTrue(Segment(0, 0, 6, 0) in L)
self.assertTrue(Segment(0, 0, 0, 12) in L)
self.assertTrue(Segment(0, 12, 6, 0) in L)
def test_itersegments_oriented(self):
L = list(self.t1.itersegments_oriented())
self.assertTrue(Segment(6, 0, 0, 0) in L)
self.assertTrue(Segment(0, 0, 0, 12) in L)
self.assertTrue(Segment(0, 12, 6, 0) in L)
def tearDown(self):
pass
def test_move(self):
self.assertEqual(self.t1.move(1, 2), Triangle(1, 2, 7, 2, 1, 14))
self.assertEqual(self.t1.move(Point(1, 2)),
Triangle(1, 2, 7, 2, 1, 14))
self.assertRaises(ValueError, Triangle.move, self.t1, 1)
import random
import Gnuplot # Python 2 only
from planegeometry.structures.points import Point
from planegeometry.structures.segments import Segment
from planegeometry.structures.rectangles import Rectangle
from planegeometry.structures.triangles import Triangle
from planegeometry.structures.circles import Circle
gnu = Gnuplot.Gnuplot(persist=1)
visible = True
rectangle = Rectangle(0.1, 0.3, 0.9, 0.7)
gnu(rectangle.gnu(visible))
triangle = Triangle(0.2, 0.2, 0.8, 0.4, 0.6, 0.8)
gnu(triangle.gnu(visible))
circle = Circle(0.4, 0.6, 0.2)
gnu(circle.gnu(visible))
# Wyswietlenie grafu.
gnu('set terminal pdf enhanced')
gnu('set output "random_figures.pdf"')
gnu('set grid')
gnu('unset key')
gnu('set size square')
#gnu('unset border')
#gnu('unset tics')
gnu('set xlabel "x"')
gnu('set ylabel "y"')
def test_cmp(self):
self.assertEqual(Triangle(), Triangle(0, 0, 1, 0, 0, 1))
self.assertTrue(self.t1 == Triangle(0, 0, 6, 0, 0, 12))
self.assertFalse(self.t1 == self.t2)
self.assertTrue(self.t1 != self.t2)
self.assertFalse(self.t1 != Triangle(0, 0, 6, 0, 0, 12))
def test_orientation(self):
self.assertEqual(self.t1.orientation(), 1)
self.assertEqual(Triangle(0, 0, 1, 1, 1, 0).orientation(), -1)
def setUp(self):
self.t1 = Triangle(0, 0, 6, 0, 0, 12)
self.t2 = Triangle(3, 0, 9, 0, 6, 6)
self.t3 = Triangle(Point(0, 0), Point(2, 0), Point(1, 2))
self.t4 = Triangle(Fraction(1, 2), Fraction(2, 3), Fraction(3, 4),
Fraction(4, 5), Fraction(5, 6), Fraction(6, 7))
from planegeometry.structures.circles import Circle
plt.axis([0, 1, 0, 1])
ax = plt.gca()
rectangle1 = Rectangle(0.1, 0.3, 0.9, 0.7)
# rectangle1 = plt.Rectangle((0.1, 0.3), 0.8, 0.4, fill=False, color='b')
rectangle2 = plt.Rectangle((0.6, 0.1), 0.2, 0.1, fill=False, color='m')
for segment in rectangle1.itersegments():
x = [segment.pt1.x, segment.pt2.x]
y = [segment.pt1.y, segment.pt2.y]
#plt.plot(x, y, 'bo-')
plt.plot(x, y, 'b.-')
triangle1 = Triangle(0.2, 0.2, 0.8, 0.4, 0.6, 0.8)
for segment in triangle1.itersegments():
x = [segment.pt1.x, segment.pt2.x]
y = [segment.pt1.y, segment.pt2.y]
#plt.plot(x, y, 'ro-')
plt.plot(x, y, 'r.-')
#circle1 = Circle(0.4, 0.6, 0.2)
circle1 = plt.Circle((0.4, 0.6), 0.2, color='g', fill=False)
ax.add_patch(circle1)
ax.add_patch(rectangle2)
plt.title("Random figures")
plt.xlabel("x")
def test_init_triangle(self):
M1 = PlanarMap(Triangle(0, 0, 1, 0, 1, 1))
self.assertEqual(M1.v(), 3)
self.assertEqual(M1.e(), 3)
self.assertEqual(M1.f(), 2)