Simple 3D Programming Using VPython

I. VPython: the Python/ Visual / IDLE environment

The interactive development environment you will use is called "IDLE."

The Display window

When using VPython the display window shows objects in 3D.

(0,0,0) is in the center of the display window . The +x axis runs to the right, the +y axis runs up, and the +z axis points out of the screen, toward you.

x, y, and z are measured in whatever units you choose; the display is automatically scaled appropriately. (You could, for example, create a sphere with a radius of 1E-15 m to represent a nucleus, or a sphere with a radius of 1E6 m to represent a planet, though it wouldn't make sense to put both of these objects in the same display!)

The Output window

The output of any -print- statements you execute in your program goes to the Output window, which is a scrolling text window. You can use this window to print values of variables, print lists, print messages, etc. Place it where you can see messages in it.

The Code window

If you type or copy the following simple program into the code window in IDLE and run it (press F5, or use the Run menu), you will see a display like the one shown in the figure.

from visual import *
redbox=box(pos=vector(4,2,3),
           size=(8,4,6),color=color.red)
ball=sphere(pos=vector(4,7,3),radius=2,color=color.green)

Visual is the name of the 3D graphics module used with the Python programming language. VPython is the name of the combination of the Python programming language, the Visual module, and the development environment IDLE.

Viewing the scene

In the display window, click and drag with the right mouse button (hold down the command key on a Macintosh). Drag left or right, and you rotate around the scene. To rotate around a horizontal axis, drag up or down. Click and drag up or down with the middle mouse button to move closer to the scene or farther away (on a 2-button mouse, hold down the left and right buttons; on a 1-button mouse, hold down the Option key).

II. Visual Entities

Objects, names, and attributes

The graphical objects you create, such as spheres, boxes, and curves, continue to exist for the duration of your program, and the Visual 3D graphics module will continue to display them, wherever they are. You must give each object a name (such as redbox or ball in the example above) if you wish to refer to it again later in your program. All objects have attributes: properties like ball.pos (the position of the sphere), ball.color, and radius or other size parameter. If you change an attribute of an object, such as its position or color, Visual will automatically display the object in its new location, or with its new color.

You can set the values of attributes in the "constructor" (the code used to create the object), and you can also modify attributes later:

ball.radius = 2.2

In addition to the built-in set of attributes, you may create new attributes. For example, you might create a sphere named moon; in addition to its radius and location, you might give it attributes such as mass (moon.mass) and momentum (moon.momentum).

Vectors

Not all objects in Visual are visible objects. For example, Visual allows you to create 3D vector quantities, and to perform vector operations on them. If you create a vector quantity called a, you may refer to its components as a.x, a.y, and a.z. To add two vectors, a and b, however, you do not need to add the components one by one; Visual will do the vector addition for you:

a = vector(1,2,3)
b = vector(4,5,6)
c=a+b

If you print c , you will find that it is a vector with components (5, 7, 9.).

Scalar multiplication

d = 3*a # d is a vector with components (3, 6, 9)

Vector magnitude

s = mag(c) # s is a scalar
z = mag(c)**2 # you can square the magnitude of a vector

Vector products

f = cross(a,b) # cross product
g = dot(a,b) # dot product
h = norm(a) # normalized (unit) vector; a/mag(a)

The attributes of Visual objects can be vectors, such as velocity or momentum.

III. Simple Python Programming

Importing the 3D Graphics Module (Visual)

The first line of your program must be:

from visual import *

Comments

A comment in a Python program starts with "#"

# this line is a comment

Variables

Variables can be created anywhere in a Python program, simply by assigning a variable name to a value. The type of the variable is determined by the assignment statement.

a = 3 # an integer
b = -2. # a floating-point number
c = vector(0.4, 3e3, -1e1) # a vector
Earth = sphere(pos=(0,0,0), radius=6.4e6) # an object
bodies = [ship, Earth, Moon] # a list of objects

Basic Visual objects such as sphere() and box() have a set of "attributes" such as color, and you can define additional attributes such as mass or velocity. Other objects, such as vector(), have built-in attributes but you cannot create additional attributes.

Warning about division

Division of integers will not come out the way you may expect, since the result is rounded down to the nearest integer. Thus:

a = 3/4
print a # a is 0

To avoid this, you can place a decimal point after every number, like this:

b = 3./4.
print b # b is 0.75, as expected

We recommend putting the following statement as the first line of your program, in which case 3/4 will be 0.75; there are two underscores before the word "future" and two after the word "future":

from __future__ import division

Exponentiation

x**2 # Not x^2, which is a bit operation in Python

Logical Tests

If, elif ("else if"), else:

if a == b: # see table of logical expressions below
    c = 3.5 # indented code executed if test is true
elif a < b:
    c = 0 # c will be set to zero only if a < b
else:
    c = -23.2

Logical expressions

==	equal
!=	not equal
<	less than
>	greater than
<=	less than or equal
>=	greater or equal
or	logical or
and	logical and
in	member of a sequence
not in	not sequence member

Lists

A list is an ordered sequence of any kind of object. It is delimited by square brackets.

moons = [Io, Europa, Ganymede, Callisto]

The function "arange" (short for "arrayrange") creates an array of numbers:

angles = arange (0., 2*pi, pi/100)
# from 0 to 2*pi-(pi/100) in steps of (pi/100)

numbers = arange(10) # integer argument -> integers
print numbers # [0,1,2,3,4,5,6,7,8,9]

Loops

The simplest loop in Python is a "while" loop. The loop continues as long as the specified logical expression is true:

while x < 23:
    x = x + vx*dt

To write an infinite loop, just use a logical expression that will always be true:

while True:
    ball.pos = ball.pos + (ball.momentum/ball.mass)*dt

Infinite loops are ok, because you can always interrupt the program by choosing "Stop Program" from the Run menu in IDLE.

It is also possible to loop over the members of a sequence:

moons = [Io, Europa, Ganymede, Callisto]
for a in moons:
    r = a.pos - Jupiter.pos
 
for x in arange(10):
# see "lists" above
...
 
for theta in arange(0., 2.*pi, pi/100.):
# see "lists" above

You can restart a loop, or terminate the loop prematurely:

if a == b: continue # go back to the start of the loop
if a > b: break # exit the loop

Printing results

To print a number, a vector, a list, or anything else, use the "print" option:

print Europa.momentum

To print a text message, enclose it in quotes:

print "We crashed on the Moon with speed", v, "m/s."

Python also offers a formatted print capability. Here price will be printed with 3 digits before the decimal place and 2 digits after, and num will be printed as an integer:

print "It's $%3.2f dollars for %d copies" % (price,num)

More Information about Python

We have summarized a small but important subset of the Python programming language. Extensive Python documentation is provided on the Help menu in IDLE, and there is additional information at the Python website, but much of this information assumes that you already have lots of programming experience in other languages. We recommend the following book to those who want to learn more about Python, and about programming in general: Python Programming: An Introduction to Computer Science by John M. Zelle (Franklin Beedle & Associates, 2003).