def getDirection(self, a):
p0 = self.AO.getPoint(a)
p1 = self.OQ.getPoint(a)
p2 = self.QB.getPoint(a)
r0 = (Segment(p0, p1)).getPoint(a)
r1 = (Segment(p1, p2)).getPoint(a)
return (Segment(r0, r1)).direction
def _legalize_segment(self, triangle, segment):
changes = []
if self._is_legal_segment(triangle, segment):
return changes
point_i = segment.start
point_j = segment.end
near_triangle = triangle.get_near_triangle_by_segment(segment)
point_k = near_triangle.last_points([point_i, point_j])[0]
self._events.append(Event(ev_type=event.DELETE_SEGMENT, data=segment))
new_triangle_a, new_triangle_b = Triangle.change_common_segment(triangle, near_triangle)
new_common_segment = new_triangle_a.get_common_segment(new_triangle_b)
self._events.append(Event(ev_type=event.ADD_SEGMENT, data=new_common_segment))
changes.append([triangle, [new_triangle_a, new_triangle_b]])
changes.append([near_triangle, [new_triangle_a, new_triangle_b]])
if point_i in new_triangle_a.points:
next_changes = self._legalize_segment(new_triangle_a, Segment(point_i, point_k))
else:
next_changes = self._legalize_segment(new_triangle_b, Segment(point_i, point_k))
changes.extend(next_changes)
if point_j in new_triangle_a.points:
next_changes = self._legalize_segment(new_triangle_a, Segment(point_j, point_k))
else:
next_changes = self._legalize_segment(new_triangle_b, Segment(point_j, point_k))
changes.extend(next_changes)
return changes
def __init__(self, p1, p2, p3):
self.points = [p1, p2, p3]
self.sides = [
Segment(p1, p2).length(),
Segment(p2, p3).length(),
Segment(p3, p1).length()
]
def test_is_intersect(self):
segments = self.get_segments()
self.assertTrue(Segment.is_intersects(segments[0], segments[1]))
self.assertFalse(Segment.is_intersects(segments[0], segments[2]))
self.assertTrue(Segment.is_intersects(segments[5], segments[3]))
self.assertFalse(Segment.is_intersects(segments[4], segments[6]))
def _init_base_triangle(self):
left_bound = self._points[0].x - 1
right_bound = self._points[0].x + 1
top_bound = self._points[0].y + 1
down_bound = self._points[0].y - 1
higher_point = self._points[0]
for point in self._points:
if point.x >= right_bound:
right_bound = point.x + 1
if point.x <= left_bound:
left_bound = point.x - 1
if point.y >= top_bound:
top_bound = point.y + 1
higher_point = point
if point.y <= down_bound:
down_bound = point.y - 1
self._higher_point = higher_point
self._events.append(Event(ev_type=event.SELECT_BASE_POINT, data=higher_point))
down_base_point = self._find_down_base_point(right_bound, down_bound)
self._down_base_point = down_base_point
self._events.append(Event(ev_type=event.SELECT_BASE_POINT, data=down_base_point))
top_base_point = self._find_top_base_point(left_bound, top_bound, down_base_point)
self._top_base_point = top_base_point
self._events.append(Event(ev_type=event.SELECT_BASE_POINT, data=top_base_point))
self._base_triangle = Triangle(down_base_point, top_base_point, higher_point)
self._events.append(Event(ev_type=event.ADD_BASE_SEGMENT, data=Segment(down_base_point, top_base_point)))
self._events.append(Event(ev_type=event.ADD_BASE_SEGMENT, data=Segment(down_base_point, higher_point)))
self._events.append(Event(ev_type=event.ADD_BASE_SEGMENT, data=Segment(higher_point, top_base_point)))
def get_segments(self):
return [
Segment(Point(5, 5), Point(1, 1)),
Segment(Point(1, 1), Point(1, 6)),
Segment(Point(0, -1), Point(7, -1)),
Segment(Point(-2, 6), Point(-2, -4)),
Segment(Point(-4, 4), Point(4, -4)),
Segment(Point(-8, -1), Point(5, 1)),
Segment(Point(1, 2), Point(6, 0)),
Segment(Point(-5, 0), Point(5, 0)),
Segment(Point(0, 5), Point(0, -5)),
Segment(Point(-5, 5), Point(-1, 1))
]
def get_intersect(c1, c2):
length = Segment(c1.center, c2.center).length()
points = []
if length == 0 and c1.radius == c2.radius:
return {"orientation": CircleOrientation.EQUAL, "points": points}
if c1.radius + c2.radius < length:
return {
"orientation": CircleOrientation.NOT_INTERSECT,
"points": points
}
if fabs(c1.radius - c2.radius) > length:
return {
"orientation": CircleOrientation.NOT_INTERSECT,
"points": points
}
b = (c2.radius**2 - c1.radius**2 + length**2) / (2 * length)
a = length - b
h = sqrt(c1.radius**2 - a**2)
p0 = Point(c1.center.x + a / length * (c2.center.x - c1.center.x),
c1.center.y + a / length * (c2.center.y - c1.center.y))
points.append(
Point(p0.x + h / length * (c2.center.y - c1.center.y),
p0.y - h / length * (c2.center.x - c1.center.x)))
points.append(
Point(p0.x - h / length * (c2.center.y - c1.center.y),
p0.y + h / length * (c2.center.x - c1.center.x)))
return {"orientation": CircleOrientation.INTERSECT, "points": points}
def get_tangents(self, point: Point):
point_position = self.substitute(point)
if point_position < 0:
return None
if point_position == 0:
return LineBuilder.from_points(self.center, point).get_orthogonal()
catheter = Segment(point, self.center).length()
hypotenuse = sqrt(self.radius**2 + catheter**2)
c = self.center.x - point.x
d = self.center.y - point.y
b = [
hypotenuse * (c * self.radius - d) / (c**2 - d**2),
hypotenuse * (-c * self.radius - d) / (c**2 - d**2)
]
a = [hypotenuse**2 - d * b[0] / c, hypotenuse**2 - d * b[1] / c]
tangent_points = [
Point(point.x - a[0], point.y - b[0]),
Point(point.x - a[1], point.y - b[1])
]
return [
LineBuilder.from_points(point, tangent_points[0]),
LineBuilder.from_points(point, tangent_points[1])
]
def _find_top_base_point(self, left_bound, top_bound, down_base_point):
points_a = copy.deepcopy(self._points + [down_base_point])
points_b = copy.deepcopy(self._points + [down_base_point])
left = -1e9
right = left_bound
res_point = None
while right - left >= 0:
middle = left + (right - left) // 2
base.BASE_POINT = Point(x=middle, y=top_bound)
points_a = sort_point(points_a, lexicographical_comparator)
points_b = sort_point(points_b, ccw_comparator)
equal_point_sets = True
for i in range(len(points_a)):
if points_a[i] != points_b[i]:
equal_point_sets = False
if points_a[i] != self._down_base_point:
if Segment(base.BASE_POINT, self._down_base_point).contains_point(points_a[i]):
equal_point_sets = False
if equal_point_sets:
left = middle + 1
res_point = base.BASE_POINT
else:
right = middle - 1
return res_point
def get_segments(self):
segments = []
points = self.points
length = len(points)
for i in range(0, length):
j = (i + 1) % length
segments.append(Segment(points[i], points[j]))
return segments
def is_simple(self):
segments = self.get_segments()
length = len(segments)
for i in range(0, length):
for j in range(i + 2, i + length - 1):
if Segment.is_intersects(segments[i], segments[j % length]):
return False
return True
def __init__(self, A: Point, B: Point, O: Point, Q: Point):
self.A = A
self.B = B
self.O = O
self.Q = Q
self.AB = Segment(self.A, self.B)
self.AO = Segment(self.A, self.O)
self.OQ = Segment(self.O, self.Q)
self.QB = Segment(self.Q, self.B)
self._length = None
def test_contain_point(self):
segment = Segment(Point(1, 1), Point(4, 4))
self.assertTrue(segment.contain_point(Point(2, 2)))
self.assertTrue(segment.contain_point(Point(1, 1)))
self.assertTrue(segment.contain_point(Point(4, 4)))
self.assertFalse(segment.contain_point(Point(0, 0)))
self.assertFalse(segment.contain_point(Point(-5, 88)))
self.assertFalse(segment.contain_point(Point(-1, 0.5)))
def get_optimal_point(points):
"""
Returns the point the sum of the distances
from which to other points is minimal
"""
min_length = inf
point = None
for i in range(0, len(points)):
length = 0
for j in range(0, len(points)):
if i == j:
continue
length += Segment(points[i], points[j]).length()
if min_length > length:
min_length = length
point = points[i]
return point
class Curve():
def __init__(self, A: Point, B: Point, O: Point, Q: Point):
self.A = A
self.B = B
self.O = O
self.Q = Q
self.AB = Segment(self.A, self.B)
self.AO = Segment(self.A, self.O)
self.OQ = Segment(self.O, self.Q)
self.QB = Segment(self.Q, self.B)
self._length = None
@property
def length(self):
if self._length is None:
pointsNumber = 10
previousPoint = None
self._length = 0
for i in range(pointsNumber):
point = self.getPoint(i / pointsNumber)
if previousPoint is not None:
self._length += (point - previousPoint).length
previousPoint = point
return self._length
def getPoint(self, a):
p0 = self.AO.getPoint(a)
p1 = self.OQ.getPoint(a)
p2 = self.QB.getPoint(a)
r0 = (Segment(p0, p1)).getPoint(a)
r1 = (Segment(p1, p2)).getPoint(a)
return (Segment(r0, r1)).getPoint(a)
def getDirection(self, a):
p0 = self.AO.getPoint(a)
p1 = self.OQ.getPoint(a)
p2 = self.QB.getPoint(a)
r0 = (Segment(p0, p1)).getPoint(a)
r1 = (Segment(p1, p2)).getPoint(a)
return (Segment(r0, r1)).direction
def getSides(self):
return [
Segment(source, target)
for source, target in zip(self.pointList, [self.pointList[-1]].
extend(self.pointList[0:-1]))
]
def getSide(self, i) -> Segment:
vertices = self.getVertices()
return Segment(vertices[i], vertices[(i + 1) % 4])
def _insert_point(self, point):
base_triangle = self._locator.point_location(point)
res_triangles, changes = base_triangle.split_by_point(point)
for key in changes:
self._locator.add_triangle_children(key, changes[key])
next_changes = []
used_triangles = []
for triangle in changes:
# inside triangle
if len(changes[triangle]) == 3:
self._events.append(Event(ev_type=event.ADD_SEGMENT, data=Segment(point, base_triangle.point_a)))
self._events.append(Event(ev_type=event.ADD_SEGMENT, data=Segment(point, base_triangle.point_b)))
self._events.append(Event(ev_type=event.ADD_SEGMENT, data=Segment(point, base_triangle.point_c)))
segment_a = Segment(base_triangle.point_a, base_triangle.point_b)
temp_changes = self._legalize_by_segment(changes[triangle], segment_a)
next_changes.extend(temp_changes)
segment_b = Segment(base_triangle.point_b, base_triangle.point_c)
temp_changes = self._legalize_by_segment(changes[triangle], segment_b)
next_changes.extend(temp_changes)
segment_c = Segment(base_triangle.point_c, base_triangle.point_a)
temp_changes = self._legalize_by_segment(changes[triangle], segment_c)
next_changes.extend(temp_changes)
# on segment
else:
triangle_a, triangle_b = changes[triangle]
common_segment = triangle_a.get_common_segment(triangle_b)
self._events.append(Event(ev_type=event.ADD_SEGMENT, data=common_segment))
point_i = triangle_a.last_points([common_segment.start, common_segment.end])[0]
point_j = triangle_b.last_points([common_segment.start, common_segment.end])[0]
base_segment = Segment(point_i, point_j)
if base_segment.contains_point(common_segment.start):
start_point = common_segment.end
else:
start_point = common_segment.start
segment_a = Segment(point_i, start_point)
next_changes = self._legalize_segment(triangle_a, segment_a)
segment_b = Segment(point_j, start_point)
temp_changes = self._legalize_segment(triangle_b, segment_b)
next_changes.extend(temp_changes)
for base_triangle, new_triangles in next_changes:
self._locator.add_triangle_children(base_triangle, new_triangles)
next_changes.clear()
used_triangles.append(triangle)
for triangle in used_triangles:
self._locator.clear_leaf(triangle)