18.6. Exercises

7. We can represent a rectangle by knowing three things: the location of its lower left corner, its width, and its height. Create a class definition for a Rectangle class using this idea. To create a Rectangle object at location (4,5) with width 6 and height 5, we would do the following:

   r = Rectangle(Point(4, 5), 6, 5)
   

   class Point: """ Point class for representing and manipulating x,y coordinates. """ def __init__(self, initX, initY): self.x = initX self.y = initY def getX(self): return self.x def getY(self): return self.y def __str__(self): return "x=" + str(self.x) + ", y=" + str(self.y) class Rectangle: """Rectangle class using Point, width and height""" def __init__(self, initP, initW, initH): self.location = initP self.width = initW self.height = initH loc = Point(4, 5) r = Rectangle(loc, 6, 5) print(r)

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8. Add the following accessor methods to the Rectangle class: getWidth, getHeight, __str__.

9. Add a method area to the Rectangle class that returns the area of any instance:

   r = Rectangle(Point(0, 0), 10, 5)
   test(r.area(), 50)
   

   class Point: """ Point class for representing and manipulating x,y coordinates. """ def __init__(self, initX, initY): self.x = initX self.y = initY def getX(self): return self.x def getY(self): return self.y def __str__(self): return "x=" + str(self.x) + ", y=" + str(self.y) class Rectangle: """Rectangle class using Point, width and height""" def __init__(self, initP, initW, initH): self.location = initP self.width = initW self.height = initH def area(self): return self.width * self.height

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10. Write a perimeter method in the Rectangle class so that we can find the perimeter of any rectangle instance:

    r = Rectangle(Point(0, 0), 10, 5)
    test(r.perimeter(), 30)
    

11. Write a transpose method in the Rectangle class that swaps the width and the height of any rectangle instance:

    r = Rectangle(Point(100, 50), 10, 5)
    test(r.width, 10)
    test(r.height, 5)
    r.transpose()
    test(r.width, 5)
    test(r.height, 10)
    

    class Point: """ Point class for representing and manipulating x,y coordinates. """ def __init__(self, initX, initY): self.x = initX self.y = initY def getX(self): return self.x def getY(self): return self.y def __str__(self): return "x=" + str(self.x) + ", y=" + str(self.y) class Rectangle: """Rectangle class using Point, width and height""" def __init__(self, initP, initW, initH): self.location = initP self.width = initW self.height = initH def transpose(self): temp = self.width self.width = self.height self.height = temp

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12. Write a new method in the Rectangle class to test if a Point falls within the rectangle. For this exercise, assume that a rectangle at (0,0) with width 10 and height 5 has open upper bounds on the width and height, i.e. it stretches in the x direction from [0 to 10), where 0 is included but 10 is excluded, and from [0 to 5) in the y direction. So it does not contain the point (10, 2). These tests should pass:

    r = Rectangle(Point(0, 0), 10, 5)
    test(r.contains(Point(0, 0)), True)
    test(r.contains(Point(3, 3)), True)
    test(r.contains(Point(3, 7)), False)
    test(r.contains(Point(3, 5)), False)
    test(r.contains(Point(3, 4.99999)), True)
    test(r.contains(Point(-3, -3)), False)
    

13. Write a new method called diagonal that will return the length of the diagonal that runs from the lower left corner to the opposite corner.

    class Point: """ Point class for representing and manipulating x,y coordinates. """ def __init__(self, initX, initY): self.x = initX self.y = initY def getX(self): return self.x def getY(self): return self.y def __str__(self): return "x=" + str(self.x) + ", y=" + str(self.y) class Rectangle: """Rectangle class using Point, width and height""" def __init__(self, initP, initW, initH): self.location = initP self.width = initW self.height = initH def diagonal(self): d = (self.width**2 + self.height**2) ** 0.5 return d

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14. In games, we often put a rectangular “bounding box” around our sprites in the game. We can then do collision detection between, say, bombs and spaceships, by comparing whether their rectangles overlap anywhere.

    Write a function to determine whether two rectangles collide. Hint: this might be quite a tough exercise! Think carefully about all the cases before you code.

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