def __nearest_distance(seg: LineSegment, p: Point):
a = p.get_x() - seg.get_a().get_x()
b = p.get_y() - seg.get_a().get_y()
c = seg.get_b().get_x() - seg.get_a().get_x()
d = seg.get_b().get_x() - seg.get_a().get_y()
dot = a * c + b * d
q = c ** 2 + d ** 2
param = -1
if q != 0:
param = dot / q
if param < 0:
xx = seg.get_a().get_x()
yy = seg.get_a().get_y()
elif param > 1:
xx = seg.get_b().get_x()
yy = seg.get_b().get_y()
else:
xx = seg.get_a().get_x() + param * c
yy = seg.get_a().get_y() + param * d
dx = p.get_x() - xx
dy = p.get_y() - yy
return math.sqrt(dx ** 2 + dy ** 2)
def distance_between_two_points(pa: Point, pb: Point):
"""
Get a distance between two points
:param pa - Point A
:param pb - Point B
:return distance between point A and B
"""
return math.sqrt(pow(pb.get_x() - pa.get_x(), 2) + pow(pb.get_y() - pa.get_y(), 2))
def distance_between_one_line_and_one_point(p: Point, l: Line):
"""
Get a distance between one line and one point
:param p: one point
:param l: one line
:return: distance between p and l
"""
return (math.fabs(l.get_a() * p.get_x() + l.get_a() * p.get_y() + l.get_c())) / \
math.sqrt(pow(l.get_a(), 2) + pow(l.get_b(), 2))
def __point_in_segment(p: Point, s: LineSegment):
px = p.get_x()
py = p.get_y()
sa_x = s.get_a().get_x()
sa_y = s.get_a().get_y()
sb_x = s.get_b().get_x()
sb_y = s.get_b().get_y()
if px <= max(sa_x, sb_x) and px >= min(sa_x, sb_x) and \
py <= max(sa_y, sb_y) and py >= min(sa_y, sb_y):
return True
else:
return False
def point_in_polygon(p: Point, polygon: Polygon):
cn = 0
v = copy.deepcopy(polygon.get_list_points())
v.append(v[0])
for i in range(len(v)-1):
if (v[i].get_y() <= p.get_y() and v[i+1].get_y() > p.get_y()) or \
(v[i].get_y() > p.get_y() and v[i+1].get_y() <= p.get_y()):
vt = (p.get_y() - v[i].get_y()) / float(v[i+1].get_y() - v[i].get_y())
if p.get_x() < (v[i].get_x() + vt * (v[i+1].get_x() - v[i].get_x())):
cn += 1
return True if (cn % 2) == 1 else False
def remove_point(self, p: Point):
remove_seg = []
for i in self.__segments.get_iterator():
if i.get_a().comparable(i.get_a(), p) == 0 or i.get_b().comparable(
i.get_b(), p) == 0:
remove_seg.append(i)
for i in remove_seg:
self.__segments.delete(i)
for i in self.__list_points:
if i.get_x() == p.get_x() and i.get_y() == p.get_y():
self.__list_points.remove(i)
break
def _make_circle_two_points(points: list, p: Point, q: Point):
circ = make_diameter(p, q)
left = None
right = None
px = p.get_x()
py = p.get_y()
qx = q.get_x()
qy = q.get_y()
# para cada ponto que nao está no circulo
for r in points:
if classics.side_of_circle(circ, r) >= 0:
continue
# Formar uma circunferência e classificá-la no lado esquerdo ou direito
cross = _cross_product(px, py, qx, qy, r.get_x(), r.get_y())
c = make_circumcircle(p, q, r)
if c is None:
continue
elif cross > 0.0 and (left is None
or _cross_product(px, py, qx, qy,
c.get_centre().get_x(),
c.get_centre().get_y()) >
_cross_product(px, py, qx, qy,
left.get_centre().get_x(),
left.get_centre().get_y())):
left = c
elif cross < 0.0 and (right is None
or _cross_product(px, py, qx, qy,
c.get_centre().get_x(),
c.get_centre().get_y()) <
_cross_product(px, py, qx, qy,
right.get_centre().get_x(),
right.get_centre().get_y())):
right = c
# selecionar qual circulo vai retornar
if left is None and right is None:
return circ
elif left is None:
return right
elif right is None:
return left
else:
return left if (left.get_radius() <= right.get_radius()) else right
def ears_clipping(points, ears):
if len(ears) == 0:
return []
edges = []
length = len(points)
e = ears[0]
while len(points) > 3:
ind = points.index(e)
prev_pred = points[(ind - 2) % length]
pred = points[(ind - 1) % length]
succ = points[(ind + 1) % length]
next_succ = points[(ind + 2) % length]
edges.append(LineSegment(Point(pred[0], pred[1]), Point(succ[0], succ[1])))
points.remove(e)
length -= 1
ears.remove(e)
if EarClipping.__is_ear(points, prev_pred, pred, succ):
if pred not in ears:
ears.append(pred)
else:
if pred in ears:
ears.remove(pred)
if EarClipping.__is_ear(points, pred, succ, next_succ):
if succ not in ears:
ears.append(succ)
else:
if succ in ears:
ears.remove(succ)
if len(ears) > 0:
e = ears[0]
else:
return []
return edges
def __points_orientation(p: Point, q: Point, r: Point):
value = (q.get_y() - p.get_y()) * (r.get_x() - q.get_x()) - (q.get_x() - p.get_x()) * (r.get_y() - q.get_y())
if value == 0:
return 0
elif value > 0:
return 1
else:
return 2
def orient_2d(a: Point, b: Point, c: Point):
"""
Orientation of tree points
Algorithm based in http://www.geeksforgeeks.org/orientation-3-ordered-points/
:param a: point 1
:param b: point 2
:param c: point 3
:return: orientation
"""
first = (b.get_y() - a.get_y()) * (c.get_x() - b.get_x())
second = (c.get_y() - b.get_y()) * (b.get_x() - a.get_x())
det = first - second
if det == 0:
return 0
elif det > 0:
return 1
else:
return -1
def closest_point(seg: LineSegment, points: list):
"""
Algorithm for get closest point between a line segment
Algorithm based in https://goo.gl/PkLqhe
:param seg: one line segment
:param points: a list of points
:return: a point more closest
"""
distance = math.inf
point = None
for i in points:
value = __nearest_distance(seg, i)
if value < distance:
distance = value
point = Point(i.get_x(), i.get_y())
return point
def convex_polygon(poly: Polygon):
if len(poly.get_list_points()) < 3:
return False
list_points = poly.get_list_points()
res = 0
for i in range(len(list_points)):
p = list_points[i]
tmp = list_points[((i+1) % len(list_points))]
vx = tmp.get_x() - p.get_x()
vy = tmp.get_y() - p.get_y()
v = Point(vx, vy)
u = list_points[((i+2) % len(list_points))]
if i == 0:
res = u.get_x() * v.get_y() - u.get_y() * v.get_x() + v.get_x() * p.get_y() - v.get_y() * p.get_x()
else:
new_res = u.get_x() * v.get_y() - u.get_y() * v.get_x() + v.get_x() * p.get_y() - v.get_y() * p.get_x()
if (new_res > 0 and res < 0) or (new_res < 0 and res > 0):
return False
return True
new_set = Set()
Set.__add_difference(self.__binTree.get_root(), b, new_set)
return new_set
def __len__(self):
return len(self.__binTree)
def get_iterator(self):
return self.__binTree.get_root()
if __name__ == '__main__':
set1 = Set()
set2 = Set()
p1 = Point(1, 2)
p2 = Point(3, 4)
p3 = Point(5, 6)
p4 = Point(7, 8)
p1_copy = Point(1, 2)
set1.insert(p1)
set1.insert(p2)
set1.insert(p3)
set2.insert(p3)
set2.insert(p4)
set3 = set1.union(set2)
set4 = set1.intersection(set2)
def make_circumcircle(p0: Point, p1: Point, p2: Point):
ax = p0.get_x()
ay = p0.get_y()
bx = p1.get_x()
by = p1.get_y()
cx = p2.get_x()
cy = p2.get_y()
ox = (min(ax, bx, cx) + max(ax, bx, cx)) / 2.0
oy = (min(ay, by, cy) + max(ay, by, cy)) / 2.0
ax -= ox
ay -= oy
bx -= ox
by -= oy
cx -= ox
cy -= oy
d = (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)) * 2.0
if d == 0.0:
return None
x = ox + ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) *
(cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d
y = oy + ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) *
(ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d
ra = math.hypot(x - p0.get_x(), y - p0.get_y())
rb = math.hypot(x - p1.get_x(), y - p1.get_y())
rc = math.hypot(x - p2.get_x(), y - p2.get_y())
return Circle(Point(x, y), max(ra, rb, rc))
return self.__list_points
def remove_point(self, p: Point):
remove_seg = []
for i in self.__segments.get_iterator():
if i.get_a().comparable(i.get_a(), p) == 0 or i.get_b().comparable(
i.get_b(), p) == 0:
remove_seg.append(i)
for i in remove_seg:
self.__segments.delete(i)
for i in self.__list_points:
if i.get_x() == p.get_x() and i.get_y() == p.get_y():
self.__list_points.remove(i)
break
def get_list(self):
return self.__list_tuple
if __name__ == '__main__':
p = Polygon()
p.add_segment(LineSegment(Point(1, 2), Point(2, 3)))
p.add_segment(LineSegment(Point(2, 3), Point(5, 6)))
p.add_segment(LineSegment(Point(5, 6), Point(1, 2)))
p.remove_point(Point(1, 2))
print('aaa')
def onClick(self, event):
if not self.LOCK:
self.w.create_oval(event.x - self.RADIUS,
event.y - self.RADIUS,
event.x + self.RADIUS,
event.y + self.RADIUS,
fill="black")
self.pts.append((event.x, event.y))
if self.btnCirculo['state'] == tk.NORMAL:
if len(self.pts) == 2:
p1 = Point(self.pts[0][0], self.pts[0][1])
p2 = Point(self.pts[1][0], self.pts[1][1])
distance = classics.distance_between_two_points(p1, p2)
circle = Circle(p1, int(distance))
self.circles.append(circle)
self.draw_circle(p1.get_x(), p1.get_y(),
circle.get_radius())
nome = "Circ" + str(len(self.circles))
self.w.create_text(p1.get_x(),
p1.get_y() + circle.get_radius() + 7,
text=nome)
self.liberaTodosBotoes()
self.LOCK = True
self.pts.clear()
elif self.btnLinha['state'] == tk.NORMAL:
if len(self.pts) == 2:
p1 = Point(self.pts[0][0], self.pts[0][1])
p2 = Point(self.pts[1][0], self.pts[1][1])
line = Line.generate_by_two_points(p1, p2)
self.lines.append(line)
p1_x_canvas = line.get_x_from_y(0)
p2_x_canvas = line.get_x_from_y(500)
self.w.create_line(int(p1_x_canvas),
0,
int(p2_x_canvas),
500,
fill="RoyalBlue2")
nome = "Lin" + str(len(self.lines))
self.w.create_text((p1_x_canvas + p2_x_canvas) / 2,
(0 + 500) / 2,
text=nome)
self.liberaTodosBotoes()
self.LOCK = True
self.pts.clear()
elif self.btnSegmento['state'] == tk.NORMAL:
if len(self.pts) == 2:
p1 = Point(self.pts[0][0], self.pts[0][1])
p2 = Point(self.pts[1][0], self.pts[1][1])
seg = LineSegment(p1, p2)
self.segments.append(seg)
self.w.create_line(p1.get_x(),
p1.get_y(),
p2.get_x(),
p2.get_y(),
fill='red')
nome = "Seg" + str(len(self.segments))
self.w.create_text((p1.get_x() + p2.get_x()) / 2,
(p1.get_y() + p2.get_y()) / 2,
text=nome)
self.liberaTodosBotoes()
self.LOCK = True
self.pts.clear()
elif self.btnPonto['state'] == tk.NORMAL:
p = Point(self.pts[0][0], self.pts[0][1])
self.points.append(p)
nome = "Ptn" + str(len(self.points))
self.w.create_text(p.get_x(), p.get_y() + 10, text=nome)
self.pts.clear()
elif self.btnPolygon['state'] == tk.NORMAL:
if len(self.pts) == 2:
p1 = Point(self.pts[0][0], self.pts[0][1])
p2 = Point(self.pts[1][0], self.pts[1][1])
seg = LineSegment(p1, p2)
self.polygons[len(self.polygons) - 1].add_segment(seg)
self.w.create_line(p1.get_x(),
p1.get_y(),
p2.get_x(),
p2.get_y(),
fill='blue')
del self.pts[0]
def make_diameter(p0: Point, p1: Point):
cx = (p0.get_x() + p1.get_x()) / 2.0
cy = (p0.get_y() + p1.get_y()) / 2.0
r0 = math.hypot(cx - p0.get_x(), cy - p0.get_y())
r1 = math.hypot(cx - p1.get_x(), cy - p1.get_y())
return Circle(Point(cx, cy), max(r0, r1))
strip.append(py[i])
return min(d, ClosestPair.strip_closest(strip, len(strip), d, points))
def get_closest_points(self):
points = self.points
px = copy.deepcopy(self.p)
py = copy.deepcopy(self.p)
px.sort(key=cmp_to_key(ClosestPair.compare_x))
py.sort(key=cmp_to_key(ClosestPair.compare_y))
ClosestPair.closest_util(px, py, len(px), points)
return points.minDistance, points.point_1, points.point_2
if __name__ == '__main__':
a = []
a.append(Point(2, 3))
a.append(Point(12, 30))
a.append(Point(40, 50))
a.append(Point(5, 1))
a.append(Point(12, 10))
a.append(Point(3, 4))
asd = ClosestPair(a)
print(asd.get_closest_points())
def compare_y(p1: Point, p2: Point):
return p1.get_y() - p2.get_y()
cy -= oy
d = (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)) * 2.0
if d == 0.0:
return None
x = ox + ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) *
(cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d
y = oy + ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) *
(ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d
ra = math.hypot(x - p0.get_x(), y - p0.get_y())
rb = math.hypot(x - p1.get_x(), y - p1.get_y())
rc = math.hypot(x - p2.get_x(), y - p2.get_y())
return Circle(Point(x, y), max(ra, rb, rc))
def make_diameter(p0: Point, p1: Point):
cx = (p0.get_x() + p1.get_x()) / 2.0
cy = (p0.get_y() + p1.get_y()) / 2.0
r0 = math.hypot(cx - p0.get_x(), cy - p0.get_y())
r1 = math.hypot(cx - p1.get_x(), cy - p1.get_y())
return Circle(Point(cx, cy), max(r0, r1))
# Retorna duas vezes a área assinada do triângulo definido por (x0, y0), (x1, y1), (x2, y2).
def _cross_product(x0, y0, x1, y1, x2, y2):
return (x1 - x0) * (y2 - y0) - (y1 - y0) * (x2 - x0)
if __name__ == '__main__':
points = [Point(1, 1), Point(4, 3), Point(5, 3), Point(3, 1)]
c = make_circle(points)