VPython Functions

Written by Kevin Randrup

Claimed Chloe Choi

Introduction to functions in Python and applying them to write shorter and more understandable code. Assumes that VPython is installed and you understand the basics of programming in Python.

Summary

Functions at a high level are used to perform a certain task. Functions can accept a number of inputs (also "arguments" or "parameters") and can give back 0 or 1 output values. Furthermore, they make code much easier to understand by encapsulating a task in a single line of code instead of being repeated over and over again.

Whenever you type print(5), you are calling a function called print with an argument of 5. This page will describe the basics of functions and how to

Basic of Functions

Basic Python function syntax

Functions can be defined with the def keyword followed by the function name and a colon. The return keyword can be used for a function to "give back" a result.

def functionName(argumentOne, argumentTwo):
    functionReturnValue = argumentOne + argumentTwo
    return functionReturnValue

Example function

# This function adds three numbers together and gives back the result using the return keyword
def addNumbers(a, b, c):
    return a + b + c

Example use of a function

# Calls the function addNumbers with the arguments 1, 2 and 4
result = addNumbers(1, 2, 4)

Writing your own Functions

Writing a function for a task instead of copy and pasting code makes your program much easier to understand and debug. The best way to illustrate this is with an example.

For this example, we will create a function to calculate the electric field created by a point charge.

As a reminder, this is the formula we are modeling:

[math]\displaystyle{ \overrightarrow{E}=\frac{1}{4πε_0} \frac{q}{|\overrightarrow{r}|^2} \hat r }[/math]

First, we ask what do we need to calculate the electric field?

[math]\displaystyle{ q }[/math] - the charge of the source
[math]\displaystyle{ \overrightarrow{r} }[/math] - the distance from the source to the electric field

[math]\displaystyle{ q }[/math] and [math]\displaystyle{ \overrightarrow{r} }[/math] will be the two arguments to our function which will look like this:

# Calculates the electric field at a given vector away from the charge
def electricField(q, r):
    electricConstant = 9e9 # 1/(4 * π * e0)
    return electricConstant * q * r.norm() / r.mag2

Using the function

We can apply functions to make our code shorter and easier to understand. Here is some example code that we will shorten with functions.

# Calculate the eletric field in two different places
charge = 1.6e-19
origin = vector(0,0,0)

point1 = vector(-10, 5, 15)
point2 = vector(20, -5, 12)

field1 = 9e9 * charge * point1.norm() / point1.mag2
field2 = 9e9 * charge * point2.norm() / point2.mag2

We can use a function in the last 2 lines to reduce the duplicated code to the following

field1 = electricField(charge, point1)
field2 = electricField(charge, point2)

Frequently Used Functions

VPython already has a few predefined functions for your ease. The following functions are available for working with vectors. To better illustrate these functions, let's say we have a vector called exVector.

exVector = vector(-10, 2 ,5)

mag()

# Calculates the magnitude of a vector
magExVector = mag(exVector)
print magExVector    # will print 11.357

mag2(A)

# Calculates the magnitude squared of a vector
mag2ExVector = mag2(exVector)
print magExVector    # will print 129

norm(A)

# Calculates the unit vector of a vector
unitExVector = norm(exVector)
print unitExVector    # will print <-0.88, 0.17, 0.44>

dot(A, B)

# Calculates the scalar dot product between the two vectors
# exVector2 = vector(4, -2 ,8)
dotExVector = dot(exVector, exVector2)
print dotExVector     # will print 4

cross(A, B)

# Calculates the vector cross product between two vectors
# exVector2 = vector(4, -2 ,8)
crossExVector = cross(exVector, exVector2)
print crossExVector    # will print <26, 100, 12>

References