diff -r 659ab465152e -r f9788970fa46 geometry.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/geometry.py	Wed Jul 29 23:45:53 2020 +0300
@@ -0,0 +1,124 @@
+from math import sqrt, hypot, radians, sin, cos, atan2
+
+class Location:
+	def __init__(self, latitude, longitude):
+		self.latitude, self.longitude = latitude, longitude
+	def distance(self, other):
+		# https://stackoverflow.com/a/365853
+		a = sin(radians(self.latitude - other.latitude) / 2) ** 2
+		a += sin(radians(self.longitude - other.longitude) / 2) ** 2 * cos(radians(self.latitude)) * cos(radians(other.latitude))
+		return 6371 * 2 * atan2(sqrt(a), sqrt(1 - a))
+	def __repr__(self):
+		return '%s(%r, %r)' % (type(self).__name__, self.latitude, self.longitude)
+	def __str__(self):
+		return '%.5f, %.5f' % (self.latitude, self.longitude)
+	@property
+	def x(self):
+		return self.latitude
+	@property
+	def y(self):
+		return self.longitude
+	@property
+	def link_to_map(self):
+		return 'http://www.openstreetmap.org/#map=19/%f/%f' % (self.latitude, self.longitude)
+
+class Ring:
+	def __init__(self, container):
+		self.container = container
+	def __getitem__(self, i):
+		while i < 0:
+			i += len(self.container)
+		while i >= len(self.container):
+			i -= len(self.container)
+		return self.container[i]
+	def __iter__(self):
+		return iter(self.container)
+	def __len__(self):
+		return len(self.container)
+
+class Polygon:
+	def __init__(self, *points):
+		self.points = points
+	def __repr__(self):
+		return '%s(%s)' % (type(self).__name__, ', '.join(map(repr, self.points)))
+	def area(self):
+		ring = Ring(self.points)
+		return sum(
+			ring[i].x * ring[i + 1].y - ring[i + 1].x * ring[i].y
+			for i in range(len(ring))
+		) / 2
+	def circumference(self):
+		ring = Ring(self.points)
+		return sum(
+			sqrt((ring[i + 1].x - ring[i].x)**2 + (ring[i + 1].y - ring[i].y)**2)
+			for i in range(len(ring))
+		)
+	def centroid(self):
+		ring = Ring(self.points)
+		x = sum(
+			(ring[i].x + ring[i + 1].x) * (ring[i].x * ring[i + 1].y - ring[i + 1].x * ring[i].y)
+			for i in range(len(ring))
+		) / 6 / self.area()
+		y = sum(
+			(ring[i].y + ring[i + 1].y) * (ring[i].x * ring[i + 1].y - ring[i + 1].x * ring[i].y)
+			for i in range(len(ring))
+		) / 6 / self.area()
+		return self.point_type()(x, y)
+	def point_type(self):
+		if len(self.points):
+			return type(self.points[0])
+		else:
+			return Point
+	def segments(self):
+		ring = Ring(self.points)
+		for i in range(len(ring)):
+			yield LineSegment(ring[i], ring[i + 1])
+	def contains_point(self, point):
+		outer_point = self.point_type()(
+			min(point.x for point in self.points) - 1,
+			min(point.y for point in self.points) - 1
+		)
+		outer_segment = LineSegment(point, outer_point)
+		intersections = 0
+		for segment in self.segments():
+			if segment.intersection(outer_segment) is not None:
+				intersections += 1
+		return bool(intersections & 1)
+
+class LineSegment:
+	def __init__(self, p1, p2):
+		self.p1, self.p2 = p1, p2
+	def __repr__(self):
+		return 'LineSegment(%r, %r)' % (self.p1, self.p2)
+	def length(self):
+		return hypot(self.p1.x - self.p2.x, self.p1.y - self.p2.y)
+	def intersection(self, other):
+		point_type = type(self.p1)
+		x = (self.p1.x, self.p2.x, other.p1.x, other.p2.x)
+		y = (self.p1.y, self.p2.y, other.p1.y, other.p2.y)
+		try:
+			denominator = (x[0] - x[1]) * (y[2] - y[3]) - (y[0] - y[1]) * (x[2] - x[3])
+			Px = ((x[0] * y[1] - y[0] * x[1]) * (x[2] - x[3]) - (x[0] - x[1]) * (x[2] * y[3] - y[2] * x[3])) / denominator
+			Py = ((x[0] * y[1] - y[0] * x[1]) * (y[2] - y[3]) - (y[0] - y[1]) * (x[2] * y[3] - y[2] * x[3])) / denominator
+			distance = lambda n: hypot(Px - x[n], Py - y[n])
+			if max(distance(0), distance(1)) <= self.length() and max(distance(2), distance(3)) <= other.length():
+				return point_type(Px, Py)
+			else:
+				return None
+		except ZeroDivisionError:
+			return None
+
+class Point:
+	def __init__(self, x, y):
+		self.x, self.y = x, y
+	def __repr__(self):
+		return 'Point(%r, %r)' % (self.x, self.y)
+
+A = Polygon(
+	Point(2,3),
+	Point(1,1),
+	Point(4,0),
+	Point(6,2),
+	Point(4,4))
+L1 = LineSegment(Point(1, 1), Point(-1, 5))
+L2 = LineSegment(Point(1, 5), Point(5, 1))