Associated Reading

User-defined types

We have used many of Python’s built-in types; now we are going to define a new type. As an example, we will create a type called Point that represents a point in two-dimensional space.

In mathematical notation, points are often written in parentheses with a comma separating the coordinates. For example, (0,0) represents the origin, and (x,y) represents the point x units to the right and y units up from the origin.

There are several ways we might represent points in Python:

We could store the coordinates separately in two variables, x and y. We could store the coordinates as elements in a list or tuple. We could create a new type to represent points as objects. Creating a new type is (a little) more complicated than the other options, but it has advantages that will be apparent soon.

A user-defined type is also called a class. A class definition looks like this:

class Point(object):
    """Represents a point in 2-D space."""

This header indicates that the new class is a Point, which is a kind of object, which is a built-in type. The body is a docstring that explains what the class is for. You can define variables and functions inside a class definition, but we will get back to that later.

Defining a class named Point creates a class object.

>>> print Point
<class '__main__.Point'>

Because Point is defined at the top level, its “full name” is main.Point. The class object is like a factory for creating objects. To create a Point, you call Point as if it were a function.

>>> blank = Point()
>>> print blank
<__main__.Point instance at 0xb7e9d3ac>

The return value is a reference to a Point object, which we assign to blank. Creating a new object is called instantiation, and the object is an instance of the class. When you print an instance, Python tells you what class it belongs to and where it is stored in memory (the prefix 0x means that the following number is in hexadecimal).

Attributes

You can assign values to an instance using dot notation:

>>> blank.x = 3.0
>>> blank.y = 4.0

This syntax is similar to the syntax for selecting a variable from a module, such as math.pi or string.whitespace. In this case, though, we are assigning values to named elements of an object. These elements are called attributes. As a noun, “AT-trib-ute” is pronounced with emphasis on the first syllable, as opposed to “a-TRIB-ute,” which is a verb.

You can read the value of an attribute using the same syntax:

>>> print blank.y
4.0
>>> x = blank.x
>>> print x
3.0

The expression blank.x means, “Go to the object blank refers to and get the value of x.” In this case, we assign that value to a variable named x. There is no conflict between the variable x and the attribute x. You can use dot notation as part of any expression. For example:

>>> print '(%g, %g)' % (blank.x, blank.y)
(3.0, 4.0)
>>> distance = math.sqrt(blank.x**2 + blank.y**2)
>>> print distance
5.0

You can pass an instance as an argument in the usual way. For example:

def print_point(p):
    print '(%g, %g)' % (p.x, p.y)

print_point takes a point as an argument and displays it in mathematical notation. To invoke it, you can pass blank as an argument:

>>> print_point(blank)
(3.0, 4.0)

Inside the function, p is an alias for blank, so if the function modifies p, blank changes.

Exercises

Exercise 1
Write a function called distance_between_points that takes two Points as arguments and returns the distance between them.

Rectangles

Sometimes it is obvious what the attributes of an object should be, but other times you have to make decisions. For example, imagine you are designing a class to represent rectangles. What attributes would you use to specify the location and size of a rectangle? You can ignore angle; to keep things simple, assume that the rectangle is either vertical or horizontal.

There are at least two possibilities:

You could specify one corner of the rectangle (or the center), the width, and the height. You could specify two opposing corners. At this point it is hard to say whether either is better than the other, so we’ll implement the first one, just as an example. Here is the class definition:

class Rectangle(object):
    """Represents a rectangle. 

    attributes: width, height, corner.
    """

The docstring lists the attributes: width and height are numbers; corner is a Point object that specifies the lower-left corner. To represent a rectangle, you have to instantiate a Rectangle object and assign values to the attributes:

box = Rectangle()
box.width = 100.0
box.height = 200.0
box.corner = Point()
box.corner.x = 0.0
box.corner.y = 0.0

The expression box.corner.x means, “Go to the object box refers to and select the attribute named corner; then go to that object and select the attribute named x.”

Instances as return values

Functions can return instances. For example, find_center takes a Rectangle as an argument and returns a Point that contains the coordinates of the center of the Rectangle:

def find_center(rect):
    p = Point()
    p.x = rect.corner.x + rect.width/2.0
    p.y = rect.corner.y + rect.height/2.0
    return p

Here is an example that passes box as an argument and assigns the resulting Point to center:

>>> center = find_center(box)
>>> print_point(center)
(50.0, 100.0)

Objects are mutable

You can change the state of an object by making an assignment to one of its attributes. For example, to change the size of a rectangle without changing its position, you can modify the values of width and height:

box.width = box.width + 50
box.height = box.width + 100

You can also write functions that modify objects. For example, grow_rectangle takes a Rectangle object and two numbers, dwidth and dheight, and adds the numbers to the width and height of the rectangle:

def grow_rectangle(rect, dwidth, dheight):
    rect.width += dwidth
    rect.height += dheight

Here is an example that demonstrates the effect:

>>> print box.width
100.0
>>> print box.height
200.0
>>> grow_rectangle(box, 50, 100)
>>> print box.width
150.0
>>> print box.height
300.0

Inside the function, rect is an alias for box, so if the function modifies rect, box changes.

Exercises

Exercise 2
Write a function named move_rectangle that takes a Rectangle and two numbers named dx and dy. It should change the location of the rectangle by adding dx to the x coordinate of corner and adding dy to the y coordinate of corner.