def test_point_belongs_to_line_negative():
l1 = line_segment_from_coordinates(5, 0, 10, 3)
p1 = Point(20, 6)
assert not point_belongs_to_line(l1, p1)
l3 = line_segment_from_coordinates(0, 0, 0, 10)
p3 = Point(1, 10)
assert not point_belongs_to_line(l3, p3)
def test_line_segment_equal():
p1 = Point(0, 1)
p2 = Point(10, 20)
l1 = LineSegment(p1, p2)
l2 = LineSegment(p1, p2)
l3 = LineSegment(p2, p1)
assert l1 == l2
assert l1 == l3
def test_vector_angle():
v1 = Vector(Point(0, 0), Point(0, 10))
v2 = Vector(Point(0, 0), Point(20, 0))
assert v1.angle(v2) == 90
v2 = Vector(Point(0, 0), Point(0, -10))
assert v1.angle(v2) == 180
v2 = Vector(Point(0, 0), Point(-10, 0))
assert v1.angle(v2) == 90 # even it should be 270
v2 = Vector(Point(0, 0), Point(0, 10))
assert v1.angle(v2) == 0
def test_point_belongs_to_line_positive():
l1 = line_segment_from_coordinates(5, 0, 15, 6)
p1 = Point(10, 3)
assert point_belongs_to_line(l1, p1)
l2 = line_segment_from_coordinates(0, 0, 0, 10)
p2 = Point(0, 5)
assert point_belongs_to_line(l2, p2)
# Point outside line segment but on the same line
l3 = line_segment_from_coordinates(5, 0, 10, 3)
p3 = Point(15, 6)
assert point_belongs_to_line(l3, p3)
l4 = line_segment_from_coordinates(0, 0, 0, 10)
p4 = Point(0, 12)
assert point_belongs_to_line(l4, p4)
def add_point_to_polygon(self, event):
point = Point(event.x, event.y)
self.plot_point(point, radius=2)
if len(self.polygon_points):
self.answer_label['text'] = ''
prev_point = self.polygon_points[-1]
self.plot_line(point, prev_point)
self.polygon_points.append(point)
def point_belongs_to_a_polygon(z_point: Point, polygon: List[Point]):
# just a sanity check for the easiest case
for polygon_point in polygon:
if polygon_point == z_point:
return True # test point the same as a polygon point
# check intersection of each polygon edge and point-infinity line
distant_coordinate = int(sys.maxsize**.5 / 1000)
point_ray = LineSegment(z_point, Point(distant_coordinate, z_point.y))
# identify intersection point for each edge
intersected_points = []
for idx in range(len(polygon)):
next_idx = (idx + 1) % len(polygon)
edge = LineSegment(polygon[idx], polygon[next_idx])
intersection_point = lines_segment_intersection_point(point_ray, edge)
if intersection_point:
if Point(*intersection_point) == z_point:
return True
intersected_points.append(intersection_point)
return len(intersected_points) % 2
def test_point_belongs_to_a_polygon_false():
"""
_________
| /\\ |
| / \\ |
|/ \\|
"""
polygon = [
Point(0, 0),
Point(0, 10),
Point(10, 10),
Point(10, 0),
Point(5, 9),
]
# point lies on "inside" concave part of polygon
p1 = Point(5, 5)
assert not point_belongs_to_a_polygon(p1, polygon)
p2 = Point(5, 0)
assert not point_belongs_to_a_polygon(p2, polygon)
p3 = Point(12, 0)
assert not point_belongs_to_a_polygon(p3, polygon)
def test_PointsPolygonChecker_false():
"""
_________
| |
| |
| |
| |
---------
"""
points_polygon_checker = PointsPolygonChecker([
Point(0, 0),
Point(10, 0),
Point(10, 10),
Point(0, 10),
])
# point lies on "inside" concave part of polygon
assert not points_polygon_checker(Point(11, 11))
assert not points_polygon_checker(Point(5, 43))
assert not points_polygon_checker(Point(12, 0))
def test_point_belongs_to_a_polygon_true():
"""
_________
| |
| |
| |
| |
---------
"""
polygon = [Point(0, 0), Point(0, 10), Point(10, 10), Point(10, 0)]
# point exist inside tha polygon
p1 = Point(5, 5)
assert point_belongs_to_a_polygon(p1, polygon)
# point belongs to a polygon edge
p2 = Point(0, 5)
assert point_belongs_to_a_polygon(p2, polygon)
# point is the same as on of polygon edges
p3 = Point(10, 10)
assert point_belongs_to_a_polygon(p3, polygon)
def test_PointsPolygonChecker_true():
"""
_________
| |
| |
| |
| |
---------
"""
points_polygon_checker = PointsPolygonChecker([
Point(0, 0),
Point(10, 0),
Point(10, 10),
Point(0, 10),
])
# point exist inside tha polygon
assert points_polygon_checker(Point(5, 5))
# point belongs to a polygon edge
assert points_polygon_checker(Point(0, 5))
# point is the same as on of polygon edges
assert points_polygon_checker(Point(10, 10))
def get_triangle_centroid(p1: Point, p2: Point, p3: Point):
centroid_x = (p1.x + p2.x + p3.x) / 3
centroid_y = (p1.y + p2.y + p3.y) / 3
return Point(centroid_x, centroid_y)
def test_point__neg__():
assert -Point(10, 20) == Point(-10, -20)
def test_points_and_line_segments_turns_are_the_same():
p1 = Point(5, 10)
p2 = Point(5, 20)
p3 = Point(15, 15)
assert points_turn_value(p1, p2, p3) == line_segments_turn_value(
LineSegment(p1, p2), LineSegment(p1, p3))
def test_turn_left():
assert 1 == turn(Point(5, 10), Point(5, 20), Point(0, 15))
def test_vectors_properties():
Vector(Point(10, 0), Point(0, 0)).len == 10
Vector(Point(0, 10), Point(0, 0)).len == 10
Vector(Point(0, 0), Point(10, 0)).len == 10
Vector(Point(0, 0), Point(0, 10)).len == 10
Vector(Point(0, 0), Point(3, 4)).len == 5
Vector(Point(1, 2), Point(4, 6)).len == 5
def test_points_equal():
assert Point(10, 20) == Point(10, 20)
assert Point(10, 20) == Point(10.0, 20.0)
assert Point(2.13, 14.17) == Point(2.13, 14.17)
def test_line_segment_impossible_to_create():
p1 = Point(0, 1)
with pytest.raises(ValueError):
LineSegment(p1, p1)
def test_line_segment_not_equal():
l1 = LineSegment(Point(1, 2), Point(3, 4))
l2 = LineSegment(Point(5, 6), Point(7, 8))
assert l1 != l2
def test_point__add__():
assert Point(12, 15) == (Point(2, 10) + Point(10, 5))
def test_polar_angle():
ans1 = polar_angle(Point(0, 0), Point(-1, -1))
ans2 = polar_angle(Point(1, 1), Point(0, 0))
assert ans1 == ans2 == pytest.approx(-2.356194490192345)
def test_line_segment_from_coordinates():
p1_x, p1_y, p2_x, p2_y = list(range(1, 5))
line_1 = line_segment_from_coordinates(p1_x, p1_y, p2_x, p2_y)
line_2 = LineSegment(Point(x=p1_x, y=p1_y), Point(x=p2_x, y=p2_y))
assert line_1 == line_2
def plot_point_event(self, event):
self.plot_point(event, color='black', radius=3)
self.ploted_points.append(Point(event.x, event.y))
def test_points_not_equal():
assert Point(0, 1) != Point(0, 2)
assert Point(1, 0) != Point(2, 0)
def plot_z_point(self, event):
if self.z_point:
self.plot_point(self.z_point, color='white', radius=3)
point = Point(event.x, event.y)
self.z_point = point
self.plot_point(point, color="green", radius=3)
def test_turn_right():
assert -1 == turn(Point(5, 10), Point(5, 20), Point(15, 15))
def test_turn_colinear():
assert 0 == turn(Point(5, 10), Point(5, 20), Point(5, 30))
def test_point__sub__():
assert Point(12, 15) - Point(2, 10) == Point(10, 5)