added exam exercise 16

exam/ex16/geometry.py

@@ -0,0 +1,122 @@
+from abc import abstractmethod, ABCMeta
+from itertools import permutations
+import numpy as np
+
+class Point(object):
+	__slots__ = ["x", "y"]
+	def __init__(self, x, y):
+		self.x = x
+		self.y = y
+
+	def __abs__(self):
+		return (self.x**2 + self.y**2)**0.5
+	def __add__(self, other):
+		if(isinstance(self, Point)):
+			return Point(self.x + other.x, self.y + other.y)
+		raise TypeError("cannot add {} and {}".format(type(other), type(self)))
+	def __sub__(self, other):
+		if(isinstance(self, Point)):
+			return Point(self.x - other.x, self.y - other.y)
+		raise TypeError("cannot subtract {} and {}".format(type(other), type(self)))
+
+	def rotate(self, angle):
+		return Point(self.x * np.cos(angle) - self.y * np.sin(angle)
+				, self.x * np.sin(angle) + self.y * np.cos(angle))
+	def __repr__(self):
+		return "{}({}, {})".format(type(self).__name__, self.x, self.y)
+
+
+class TwoDimensionalObject(metaclass=ABCMeta):
+	@abstractmethod
+	def contains_point(self, point: Point):
+		pass
+
+	def __contains__(self, other):
+		if(isinstance(other, Point)):
+			return self.contains_point(other)
+		raise TypeError("unable to check if {} is in {}".format(type(other), type(self)))
+	
+
+class Circle(TwoDimensionalObject):
+	def __init__(self, origin: Point, radius):
+		self.origin = origin
+		self.radius = radius
+
+	def contains_point(self, point: Point):
+		return abs(self.origin - point) < self.radius
+
+	def __repr__(self):
+		return "{}({}, {})".format(type(self).__name__, self.origin, self.radius)
+
+class Rectangle(TwoDimensionalObject):
+	"""
+	A Rectangle is constructed as follows:
+	The Points p1, p2 are connected using orthogonal lines::
+
+		p1  +-------+
+		    |       |
+		    |       |
+		    |       |
+		    +-------+ p2
+
+	and then the Rectangle is rotated ``angle`` degrees around ``p1``.
+
+	"""
+	def __init__(self, p1: Point, p2: Point, angle=0):
+		self.p1 = p1
+		self.p2 = p2
+
+		self.local_p1 = Point(0, 0)
+		self.local_p2 = (p2 - p1).rotate(angle)
+
+		self.angle = angle
+
+	def contains_point(self, point: Point):
+		point_in_eigen_frame = (point - self.p1).rotate(self.angle)
+		
+		if(self.local_p1.x < self.local_p2.x):
+			if(point_in_eigen_frame.x < self.local_p1.x or point_in_eigen_frame.x > self.local_p1.x):
+				return False
+		else:
+			if(point_in_eigen_frame.x > self.local_p1.x or point_in_eigen_frame.x < self.local_p1.x):
+				return False
+
+		if(self.local_p1.y < self.local_p2.y):
+			if(point_in_eigen_frame.y < self.local_p1.y or point_in_eigen_frame.y > self.local_p1.y):
+				return False
+		else:
+			if(point_in_eigen_frame.y > self.local_p1.y or point_in_eigen_frame.y < self.local_p1.y):
+				return False
+
+		return True
+	def __repr__(self):
+		return "{}({}, {}, angle={})".format(type(self).__name__, self.p1, self.p2, self.angle)
+
+
+class Triangle(TwoDimensionalObject):
+	def __init__(self, p1: Point, p2: Point, p3: Point):
+		self.p1 = p1
+		self.p2 = p2
+		self.p3 = p3
+	def contains_point(self, point: Point):
+		points = [self.p1, self.p2, self.p3]
+		triangle_surface = abs(sum([points[i].x * (points[(i + 1) % 3].y - points[(i + 2) % 3].y) for i in range(3)]))
+
+		points = [point, self.p1, self.p2, self.p3]
+		surfaces = [abs(sum([p[i].x * (p[(i + 1) % 4].y - p[(i + 2) % 4].y) for i in range(4)])) for p in permutations(points)]
+
+		return max(surfaces) < triangle_surface
+	def __repr__(self):
+		return "{}({}, {}, {})".format(type(self).__name__, self.p1, self.p2, self.p3)
+
+
+
+class CollectionOfFigures(object):
+	def __init__(self, figures):
+		self.figures = figures
+
+	def containing(self, point: Point):
+		return [f for f in self.figures if point in f]
+
+	def __repr__(self):
+		return "{}({})".format(type(self).__name__, repr(self.figures))

exam/ex16/main.py

@@ -0,0 +1,21 @@
+
+from geometry import Point, Rectangle, Triangle, Circle, CollectionOfFigures
+
+
+c1 = Circle(Point(0, 0), 1)
+c2 = Circle(Point(4, 4), 2)
+r1 = Rectangle(Point(0, 0), Point(4, 4))
+r2 = Rectangle(Point(-3, -3), Point(-1, -1))
+t1 = Triangle(Point(-1, -1), Point(-1, 1), Point(0, 1))
+t2 = Triangle(Point(0, 0), Point(6, 0), Point(0, 6))
+t3 = Triangle(Point(-5, -5), Point(0, 6), Point(5, -5))
+
+collection = CollectionOfFigures([c1, c2, r1, r2, t1, t2, t3])
+
+p1 = Point(4, 4)
+p2 = Point(-1, 0)
+p3 = Point(0, 0)
+
+print(p1, "is in", collection.containing(p1))
+print(p2, "is in", collection.containing(p2))
+print(p3, "is in", collection.containing(p3))