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Exercises 18.6 Exercises

1.

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)
Solution.
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)

2.

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

3.

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)
Solution.
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

4.

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)

5.

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)
Solution.
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

6.

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)

7.

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.

Solution.
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

8.

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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