def get_bounds(center, size):
x_scale = 1.6
upper_left = Point(center.x - size * x_scale, center.y + size)
upper_right = Point(center.x + size * x_scale, center.y + size)
lower_left = Point(center.x - size * x_scale, center.y - size)
lower_right = Point(center.x + size * x_scale, center.y - size)
bounds = [(upper_left, upper_right), (lower_left, lower_right), (upper_right, lower_right),
(upper_left, lower_left)]
return bounds
def find_intersection_of_parabolas(parabola1, parabola2, sweep_line):
if parabola1.x == parabola2.x:
py = (parabola1.y + parabola2.y) / 2.0
px = 1.0 * (parabola1.x ** 2 + (parabola1.y - py) ** 2 - sweep_line ** 2) / (2 * parabola1.x - 2 * sweep_line)
return Point(px, py)
elif parabola2.x == sweep_line:
py = parabola2.y
px = 1.0 * (parabola1.x ** 2 + (parabola1.y - py) ** 2 - sweep_line ** 2) / (2 * parabola1.x - 2 * sweep_line)
return Point(px, py)
elif parabola1.x == sweep_line:
py = parabola1.y
px = 1.0 * (parabola2.x ** 2 + (parabola2.y - py) ** 2 - sweep_line ** 2) / (2 * parabola2.x - 2 * sweep_line)
return Point(px, py)
else:
return calculate_parabolas_intersection(parabola1, parabola2, sweep_line)
def find_circle_center(a, b, c): # function from internet
# check if bc is a "right turn" from ab
if ((b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y)) > 0:
return None, None
# Joseph O'Rourke, Computational Geometry in C (2nd ed.) p.189
A = b.x - a.x
B = b.y - a.y
C = c.x - a.x
D = c.y - a.y
E = A * (a.x + b.x) + B * (a.y + b.y)
F = C * (a.x + c.x) + D * (a.y + c.y)
G = 2 * (A * (c.y - b.y) - B * (c.x - b.x))
if G == 0:
return None, None # Points are co-linear
# point o is the center of the circle
ox = 1.0 * (D * E - B * F) / G
oy = 1.0 * (A * F - C * E) / G
# o.x plus radius equals max x coord
x = ox + math.sqrt((a.x - ox) ** 2 + (a.y - oy) ** 2)
o = Point(ox, oy)
return x, o
def intersection_of_lines(line1, line2):
p1 = ((line1[0].x * line1[1].y - line1[0].y * line1[1].x) * (line2[0].x - line2[1].x) - (line1[0].x - line1[1].x)
* (line2[0].x * line2[1].y - line2[0].y * line2[1].x)) / \
((line1[0].x - line1[1].x) * (line2[0].y - line2[1].y) - (line1[0].y - line1[1].y) * (line2[0].x - line2[1].x))
p2 = ((line1[0].x * line1[1].y - line1[0].y * line1[1].x) * (line2[0].y - line2[1].y) - (line1[0].y - line1[1].y)
* (line2[0].x * line2[1].y - line2[0].y * line2[1].x)) / \
((line1[0].x - line1[1].x) * (line2[0].y - line2[1].y) - (line1[0].y - line1[1].y) * (line2[0].x - line2[1].x))
return Point(p1, p2)
def calculate_voronoi_diagram(self):
while not self.events.empty():
event = self.events.pop()
if isinstance(event, Circle):
self.handle_circle_event(event)
else:
self.handle_point_event(event)
self.scenes.append(Scene([PointsCollection(self.points, color='red'),
PointsCollection(self.get_voronoi_points(), color='blue')],
[LinesCollection(self.get_voronoi_lines()),
LinesCollection(lines_from_bounds(get_bounds(Point(0, 0), 30)), color='black'),
LinesCollection([[(event.x, -30), (event.x, 30)]], color='purple')]))
self.finish_edges()
self.bound(Point(0, 0), 30)
self.scenes.append(Scene([PointsCollection(self.points, color='red'),
PointsCollection(self.get_voronoi_points(), color='blue')],
[LinesCollection(self.get_voronoi_lines()),
LinesCollection(lines_from_bounds(get_bounds(Point(0, 0), 30)), color='black')]))
def calculate_parabolas_intersection(parabola1, parabola2, sweep_line):
z0 = 2.0 * (parabola1.x - sweep_line)
z1 = 2.0 * (parabola2.x - sweep_line)
a = 1.0 / z0 - 1.0 / z1
b = -2.0 * (parabola1.y / z0 - parabola2.y / z1)
c = 1.0 * (parabola1.y ** 2 + parabola1.x ** 2 - sweep_line ** 2) / z0 - 1.0 * (
parabola2.y ** 2 + parabola2.x ** 2 - sweep_line ** 2) / z1
py = 1.0 * (-b - math.sqrt(b * b - 4 * a * c)) / (2 * a)
px = 1.0 * (parabola1.x ** 2 + (parabola1.y - py) ** 2 - sweep_line ** 2) / (2 * parabola1.x - 2 * sweep_line)
return Point(px, py)
def create_bounding_box(self, points):
for pts in points:
point = Point(pts[0], pts[1])
self.events.push(point)
if point.x < self.LEFT:
self.LEFT = point.x
if point.y < self.BOTTOM:
self.BOTTOM = point.y
if point.x > self.RIGHT:
self.RIGHT = point.x
if point.y > self.TOP:
self.TOP = point.y
dx = (self.RIGHT - self.LEFT + 1) / 5.0
dy = (self.TOP - self.BOTTOM + 1) / 5.0
self.LEFT = self.LEFT - dx
self.RIGHT = self.RIGHT + dx
self.BOTTOM = self.BOTTOM - dy
self.TOP = self.TOP + dy
def intersect(point, arc):
if arc is None:
return None
if arc.point.x == point.x:
return None
y1 = 0.0
y2 = 0.0
if arc.prev is not None:
y1 = find_intersection_of_parabolas(arc.prev.point, arc.point, point.x).y
if arc.next is not None:
y2 = find_intersection_of_parabolas(arc.point, arc.next.point, point.x).y
if (arc.prev is None or y1 <= point.y) and (arc.next is None or point.y <= y2):
py = point.y
px = (arc.point.x ** 2 + (arc.point.y - py) ** 2 - point.x ** 2) / (2 * arc.point.x - 2 * point.x)
res = Point(px, py)
return res
return None
def insert_arc(self, point):
if self.beach_line is None:
self.beach_line = Arc(point)
return
if self.insert_arc_among_existing(point):
return
arc = self.beach_line
while arc.next is not None:
arc = arc.next
arc.next = Arc(point, arc)
x = self.LEFT
y = (arc.next.point.y + arc.point.y) / 2.0
start = Point(x, y)
seg = Edge(start)
arc.lower_edge = arc.next.upper_edge = seg
self.voronoi.append(seg)