18.6. Exercises¶

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)

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

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)

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)

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)

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)

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.

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.