geometry.py

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))