def test_make_simple() -> None:
"""
Tests if Polygon class method make_simple works correctly.
"""
polygon_1 = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
simple = Polygon([
Point(4, 1),
Point(5, 3),
Point(5, 6),
Point(3, 4),
Point(2, 3),
Point(4, 8),
Point(2, 5),
Point(1, 1)
])
polygon_1.make_simple()
assert simple == polygon_1
def test_make_convex() -> None:
"""
Tests if Polygon class method make_convex works correctly.
"""
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
convex = Polygon([
Point(1, 1),
Point(4, 1),
Point(5, 3),
Point(5, 6),
Point(4, 8),
Point(2, 5)
])
polygon.make_convex_hull()
assert convex == polygon
def flip_edge(triangulation: Triangulation, edge: LineSegment) -> None:
"""
If edge is illegal, replaces it with its pair and recursivly flips
neighboring edges if they need flipping, else leaves this as they are.
Args:
triangulation: Current triangulation.
edge: Potential illegal edge.
"""
pair, faces = find_pair_edge(triangulation, edge)
quad = Polygon([edge.first, pair.first, edge.second])
quad.make_simple()
quad.points.append(pair.second)
if not empty_circle(quad) and len(faces) == 2:
triangulation.remove(faces[0])
triangulation.remove(faces[1])
triangulation.add(Triangle(pair.first, pair.second, edge.first))
triangulation.add(Triangle(pair.first, pair.second, edge.second))
for triangle in faces:
for _edge in triangle.get_sides():
if not _edge.is_equal_undirected(pair) and \
not _edge.is_equal_undirected(edge):
flip_edge(triangulation, _edge)
def contains_point() -> None:
polygon = Polygon(points[0: len(points) - 1])
polygon.draw(canvas)
if polygon.does_contain(points[-1]):
messagebox.showinfo("Result", "Point is INSIDE polygon")
else:
messagebox.showinfo("Result", "Point is OUTSIDE polygon")
def is_convex() -> None:
polygon = Polygon(points)
polygon.draw(canvas)
if polygon.is_convex():
messagebox.showinfo("Result", "Polygon IS convex")
else:
messagebox.showinfo("Result", "Polygon IS NOT convex")
def test_pick_start_segment() -> None:
"""
Tests if pick_start_segment works correctly. One common and one edge case.
"""
hex_1 = Polygon([
Point(0, 0),
Point(1, -1),
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(0, 1)
])
hex_2 = Polygon([
Point(0, 0),
Point(1, 0),
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(0, 1)
])
assert pick_start_segment(hex_1) == LineSegment(Point(0, 0), Point(1, -1))
assert pick_start_segment(hex_2) == LineSegment(Point(2, 0), Point(2, 1))
def triangulate(polygon: Polygon, parent: Node) -> Node:
"""
Performs recursive triangulation of a polygon. Incomplete triangulations
are put in tree that has parent as root. Complete triangulations are leaf
nodes of that tree.
Args:
polygon: Polygon that will be triangulated.
parent: Root of tree that will contain triangulations
Returns: Leaf nodes if polygon is actually triangle.
"""
if len(polygon.points) == 3:
child = Node(extend_triangulation(parent, polygon.points[:3]))
parent.add_child(child)
return child
segment = pick_start_segment(polygon)
polygon.points = rearrange_points(segment, polygon)
for point in polygon.points[2:]:
first_triangle = Triangle(segment.first, segment.second, point)
remainders = polygon_remainders(first_triangle, polygon)
sub_root = triangulate(Polygon([segment.first, segment.second, point]),
parent)
triangulate(remainders[0], sub_root)
if remainders[1]:
second_remainder_root = Node([])
triangulate(remainders[1], second_remainder_root)
merge_triangulations(sub_root, second_remainder_root)
def test_empty_circle() -> None:
""" Tests if empty_circle method works correctly. """
a, b, c, d = [Point(4, 3), Point(-1, 2), Point(1, 1), Point(2, 1)]
poly = Polygon([a, b, c])
poly.make_simple()
poly.points.append(d)
assert empty_circle(poly)
def all_triangulations(polygon: Polygon) -> List[List[Triangle]]:
"""
Wrapper function for recursive "triangulate" function.
Args:
polygon: Polygon that will be triangulated.
Returns:
List of all possible triangulations of this polygon.
"""
polygon.make_simple()
tree = Tree(Node([]))
triangulate(polygon, tree.root)
return [node.data for node in tree.get_leaf_nodes()]
def test_delaunay_triangulation() -> None:
""" Tests if delaunay_triangulation method works correctly. """
a, b, c, d = [Point(4, 3), Point(-1, 2), Point(1, 1), Point(2, 1)]
polygon = Polygon([a, b, c, d])
triangulation = delaunay_triangulation(polygon)
assert triangulation.triangles == [Triangle(c, a, d), Triangle(c, a, b)]
def from_tuples(self, *args):
vertices = []
for arg in args:
vertices.append(arg)
if not self.__validate_vlist(vertices):
raise ValueError()
return Polygon(vertices)
class DecoratedPolygon:
def __init__(self, vlist):
corrected_vlist = self.__correct(vlist)
self.polygon = Polygon(corrected_vlist)
@property
def vlist(self):
return self.polygon.vlist
def area(self):
return self.polygon.area()
def set_areaAlg(self, alg):
self.polygon.set_areaAlg(alg)
def __correct(self, vlist):
new_vlist = vlist
if new_vlist[-1] != new_vlist[0]:
new_vlist.append(new_vlist[0])
return new_vlist
def test_orientation() -> None:
"""
Tests if Polygon class method orientation works correctly.
"""
polygon_1 = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
polygon_2 = Polygon([
Point(1, 1),
Point(2, 3),
Point(2, 5),
Point(5, 3),
Point(4, 8),
Point(5, 6),
Point(4, 1),
Point(3, 4)
])
assert polygon_1.orientation() == 1
assert polygon_2.orientation() == -1
def test_number_of_intersections() -> None:
"""
Tests if Polygon class method number_of_intersections works correctly.
"""
line_segment_intersect = LineSegment(first=Point(0, 0),
second=Point(10, 10))
line_segment_no_intersect = LineSegment(first=Point(0, 0),
second=Point(-10, -10))
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
assert polygon.intersection_count(line_segment_intersect) == (6, False)
assert polygon.intersection_count(line_segment_no_intersect) == (0, False)
def polygon_remainders(triangle: Triangle, polygon: Polygon) -> List[Polygon]:
"""
From a given polygon, and a triangle within it, creates smaller remainder or
two of them (depending on the position of the triangle within the polygon.)
Args:
triangle: Triangle object that lies within polygon.
polygon: Convex polygon.
Returns:
One or two smaller polygon remainders.
"""
diagonals = [
segment for segment in triangle.get_sides()
if polygon.has_diagonal(segment)
]
if len(diagonals) == 1:
remainder_points = list(polygon.points)
triangle_points = triangle.get_points()
for point in triangle_points:
if not diagonals[0].does_contain(point):
remainder_points.remove(point)
return [Polygon(remainder_points), None]
else:
if diagonals[1].does_contain(diagonals[0].first):
common_point = diagonals[0].first
else:
common_point = diagonals[0].second
common_point_index = polygon.points.index(common_point)
return [
Polygon(polygon.points[1:common_point_index + 1]),
Polygon([polygon.points[0]] + polygon.points[common_point_index:])
]
def test_is_empty() -> None:
"""
Tests if Polygon class method is_empty works correctly.
Two common and one edge case.
"""
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
no_points = []
points_out = [Point(0, 0), Point(10, 10), Point(0, 6), Point(-1, 12)]
points_in = [Point(0, 0), Point(4, 4), Point(0, 6), Point(-1, 12)]
assert polygon.is_empty(no_points)
assert polygon.is_empty(points_out)
assert not polygon.is_empty(points_in)
def test_does_intersect() -> None:
"""
Tests if Polygon class method does_intersect works correctly.
Two common and one edge case.
"""
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
line_segment_intersect = LineSegment(Point(0, 2), Point(2, 2))
line_segment_no_intersect = LineSegment(Point(0, 0), Point(-5, 2))
line_segment_match = LineSegment(polygon.points[4], polygon.points[5])
assert polygon.does_intersect(line_segment_intersect)
assert not polygon.does_intersect(line_segment_no_intersect)
assert polygon.does_intersect(line_segment_match)
def test_does_contain() -> None:
"""
Tests if Polygon class method does_contain works correctly.
Two common and one edge case.
"""
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
point_in = Point(4, 4)
point_out = Point(0, 0)
point_edge = Point(5, 3)
assert polygon.does_contain(point_in)
assert not polygon.does_contain(point_out)
assert polygon.does_contain(point_edge)
def delaunay_triangulation(polygon: Polygon) -> Triangulation:
"""
Generates Delaunay triangulation from a given set of points.
Args:
polygon: Polygon object that contains list of points in 2D plane.
Returns: Triangulation object containing list of triangles that form
Delaunay triangulation of passed polygon.
"""
polygon.make_simple()
start_point = find_start_point(polygon.points)
polygon.points = sort_other_points(polygon.points, start_point)
first, second, third = polygon.points[:3]
triangulation = Triangulation([Triangle(first, second, third)])
for point in polygon.points[3:]:
index = polygon.points.index(point)
add_triangles(triangulation, point, polygon.points[:index])
return triangulation
def test_polygon_remainders() -> None:
"""
Tests if polygon_remainders works correctly. Tests two possible cases.
"""
hexagon = Polygon([
Point(0, 0),
Point(1, 0),
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(0, 1)
])
triangle_1 = Triangle(Point(2, 0), Point(2, 1), Point(1, 2))
triangle_2 = Triangle(Point(1, 0), Point(2, 0), Point(1, 2))
remainders_1 = [
Polygon(
[Point(0, 0),
Point(1, 0),
Point(2, 0),
Point(1, 2),
Point(0, 1)]), None
]
remainders_2 = [
Polygon([Point(1, 0),
Point(2, 0),
Point(2, 1),
Point(1, 2)]),
Polygon([Point(0, 0), Point(1, 2),
Point(0, 1)])
]
assert polygon_remainders(triangle_1, hexagon) == remainders_1
assert polygon_remainders(triangle_2, hexagon) == remainders_2
def test_all_triangulations() -> None:
"""
Tests if all_triangulations works correctly.
"""
quad = Polygon([Point(0, 0), Point(1, -1), Point(2, 0), Point(2, 1)])
all_triangs = [[
Triangle(Point(1, -1), Point(2, 0), Point(2, 1)),
Triangle(Point(1, -1), Point(2, 1), Point(0, 0))
],
[
Triangle(Point(1, -1), Point(2, 0), Point(0, 0)),
Triangle(Point(2, 0), Point(2, 1), Point(0, 0))
]]
assert all_triangulations(quad) == all_triangs
def test_triangulate() -> None:
"""
Tests if rearrange_points works correctly.
"""
quad = Polygon([Point(0, 0), Point(1, -1), Point(2, 0), Point(2, 1)])
root = Node([])
triangulate(quad, root)
triangulation_1 = [
Triangle(Point(0, 0), Point(1, -1), Point(2, 0)),
Triangle(Point(0, 0), Point(2, 0), Point(2, 1))
]
triangulation_2 = [
Triangle(Point(0, 0), Point(1, -1), Point(2, 1)),
Triangle(Point(1, -1), Point(2, 0), Point(2, 1))
]
assert Tree(root).get_leaf_nodes()[0].data == triangulation_1
assert Tree(root).get_leaf_nodes()[1].data == triangulation_2
def test_rearrange_points() -> None:
"""
Tests if rearrange_points works correctly.
"""
hexagon = Polygon([
Point(0, 0),
Point(1, -1),
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(0, 1)
])
segment = LineSegment(Point(1, -1), Point(2, 0))
assert rearrange_points(segment, hexagon) == [
Point(1, -1),
Point(2, 0),
Point(2, 1),
Point(1, 2),
Point(0, 1),
Point(0, 0)
]
def test_is_convex() -> None:
"""
Tests if Polygon class method is_convex works correctly.
"""
polygon = Polygon([
Point(1, 1),
Point(5, 6),
Point(5, 3),
Point(2, 5),
Point(4, 8),
Point(2, 3),
Point(4, 1),
Point(3, 4)
])
convex = Polygon(
[Point(1, 1),
Point(3, 3),
Point(0, 5),
Point(-1, 4),
Point(-1, 2)])
assert not polygon.is_convex()
assert convex.is_convex()
def from_list(self, vlist):
if self.__validate_vlist(vlist):
return Polygon(vlist)
else:
raise ValueError()
from db.dal import save_triangulations
from structures.point import Point
from structures.polygon import Polygon
from triangulations.triangulations import all_triangulations
_5gon = Polygon([Point(4, 2), Point(1, 0), Point(2, 4),
Point(0, 2), Point(3, 0)])
_6gon = Polygon([Point(0, 3), Point(3, 0), Point(3, 6),
Point(1, 1), Point(6, 2), Point(5, 4)])
_7gon = Polygon([Point(3, 1), Point(4, 6), Point(1, 1), Point(0, 4),
Point(2, 8), Point(2, 0), Point(0, 3), ])
_8gon = Polygon([Point(0, 0), Point(4, 4), Point(2, 3), Point(5, 2),
Point(0, 1), Point(1, 0), Point(4, 1), Point(5, 3)])
_9gon = Polygon([Point(0, 0), Point(4, 4), Point(2, 1), Point(3, 9),
Point(5, 5), Point(0, 3), Point(3, 2), Point(4, 8),
Point(1, 5)])
_10gon = Polygon([Point(1, 0), Point(5, 4), Point(2, 0), Point(3, 8),
Point(5, 3), Point(0, 3), Point(4, 2), Point(4, 6),
Point(0, 5), Point(1, 7)])
_11gon = Polygon([Point(1, 1), Point(5, 4), Point(2, 0), Point(3, 8),
Point(4, 1), Point(0, 3), Point(5, 3), Point(4, 6),
Point(0, 6), Point(2, 9), Point(1, 9)])
print("{}: {}".format(len(_5gon.points), len(all_triangulations(_5gon))))
print("{}: {}".format(len(_6gon.points), len(all_triangulations(_6gon))))
vertices = self._polygon.vlist
area = 0.0
for i in range(0, len(vertices) - 3):
area += self.__calc_triang_area(vertices[i], vertices[i + 1],
vertices[i + 2])
return fabs(area)
def __calc_triang_area(self, v1, v2, v3):
l1 = (v2[0] - v1[0], v2[1] - v1[1])
l2 = (v3[0] - v1[0], v3[1] - v1[1])
cross = (0, 0, l1[0] * l2[1] - l1[1] * l2[0])
area = sqrt(cross[0]**2 + cross[1]**2 + cross[2]**2) / 2
return area
if __name__ == "__main__":
# Making us some pretty triangle
poly = Polygon([(0, 0), (0.866, 0.5), (1, 0)])
# Wanna know its area. Bridge will call specific area function
poly.set_areaAlg(OnlyTriangleAreaAlg(poly))
print(poly.area())
# Now it's some messed up non-convex polygon. Ouch
poly = Polygon([(0, 0), (1, 0), (2, 1), (3, 4), (3, 5), (2, 2), (1, 2),
(0, 0)])
# Need new algorithm for that
poly.set_areaAlg(GeneralAreaAlg(poly))
print(poly.area())
def make_simple_polygon() -> None:
polygon = Polygon(points)
polygon.make_simple()
polygon.draw(canvas)
def make_convex_hull() -> None:
polygon = Polygon(points)
polygon.make_convex_hull()
polygon.draw(canvas)
def delaunay() -> None:
polygon = Polygon(points)
triangulation = delaunay_triangulation(polygon)
for triangle in triangulation.triangles:
triangle.draw(canvas)