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Problem 1 – Collision detection of balls
Many games have complex physics engines, and one major function of these engines is to figure out if two
objects are colliding. Weirdly-shaped objects are often approximated as balls. In this problem, we will figure
out if two balls are colliding.
We will think in 2D to simplify things, though 3D isn’t different conceptually. For calculating collision, we
only care about a ball’s position in space and its size. We can store position with its center x-y coordinates,
and we can use its radius for size. So a ball is a tuple of (x, y, r)
To figure out if two balls are colliding, we need to compute the distance between their centers, then see if
this distance is less than the sum of their radii. If so, they are colliding.
Write a function that takes two balls and computes if they are colliding. Then call the function with two sets
of balls. The first set is (0, 0, 1) and (3, 3, 1); these should not be colliding. The second set is (5, 5, 2) and (2,
8, 3); these should be colliding.
Problem 2 – Pig-Latin Converter
Write a program that lets the user enter in some English text, then converts the text to Pig-Latin. To review,
Pig-Latin takes the first letter of a word, puts it at the end, and appends “ay”. The only exception is if the
first letter is a vowel, in which case we keep it as it is and append “hay” to the end.
It will be useful to define a list or tuple at the top called VOWELS. This way, you can check if a letter x is a
vowel with the expression x in VOWELS.
Problem

It’s tricky for us to deal with punctuation and numbers with what we know so far, so instead, ask the user to
enter only words and spaces. You can convert their input from a string to a list of strings by calling split on
the string:
Using this list, you can go through each word and convert it to Pig-Latin. Also, to get a word except for the
first letter, you can use word[1:].
Hints: It will make your life much easier — and your code much better — if you separate tasks into
functions, e.g. have a function that converts one word to Pig-Latin rather than putting it into your main
program code.

# collision.py
# Example solution for Lab 6, problem 1
#
# Aseem Kishore
#
# 6.189 - Intro to Python
# IAP 2008 - Class 4
# Imports should usually go at the top of a program instead of in the main code.
from math import *
# These helper functions let me "abstract away" the syntax of getting a ball's
# x- and y- coordinates, or its radius. This makes my code more readable and
# also helps prevent bugs where I use x instead of y, etc.
def get_x(ball):
return ball[0]
def get_y(ball):
return ball[1]
def get_r(ball):
return ball[2]
Solution

# I got this function from the second day of class. We've been
trying to tell
# you guys the importance of functions; here's one -- reuse. There
are many
# applications for finding the distance between two points;
detecting collision
# is one, so we can reuse the function. This is also why we don't
ask for input
# or print our result inside the function.
def distance(x1, y1, x2, y2):
return sqrt((x2-x1)**2 + (y2-y1)**2)
# Here is my detect collision function. Note that I'm NOT taking six variables
# like x1, y1, r1, x2, y2, r2 -- that's the purpose of combining x, y, r into a
# tuple, as every ball has an x, y and r.
def collision(ball1, ball2):
d = distance(get_x(ball1), get_y(ball1), get_x(ball2), get_y(ball2))
sum_of_radii = get_r(ball1) + get_r(ball2)
return d < sum_of_radii
# My test cases
print "First test case:",

a = (0, 0, 1)
b = (3, 3, 1)
if collision(a, b):
print "Oops, we detected a collision!"
else:
print "Passed!"
print "Second test case:",
a = (5, 5, 2)
b = (2, 8, 3)
if collision(a, b):
print "Passed!"
else:
print "Oops, we didn't detect a collision!"

# piglatin.py
# Example solution for Lab 6, problem 2
#
# Aseem Kishore
#
# 6.189 - Intro to Python
# IAP 2008 - Class 4
VOWELS = ('a', 'e', 'i', 'o', 'u')
# Helper function that converts one word into Pig-Latin. Remember,
our word is
# the function's argument, like 4 is the argument in sqrt(4). We don't
need to
# know anything about the sentence from which the word came.
#
# Also, remember that strings are index-able, just like lists and tuples.
But,
# they are immutable, like tuples. So when we want to append "ay" or
"hay" to
# the end, we can't use append(). But, we can use the string
concatenation (+)
# operator to return a new string.
#
# e.g. we can't do "a".append("b"), but we can do "a" + "b".
def convert_word(word):
first_letter = word[0]
if first_letter in VOWELS: # if word starts with a vowel...
return word + "hay" # then keep it as it is and add hay to the
end

else:
return word[1:] + word[0] + "ay" # like the lab mentions,
word[1:]
# returns the word except word[0]
# From this function, it's easy to take a
sentence and convert it to Pig-Latin.
def convert_sentence(sentence):
list_of_words = sentence.split(' ')
new_sentence = "" # we'll keep
concatenating words to this...
for word in list_of_words:
new_sentence = new_sentence +
convert_word(word) # ...like this
new_sentence = new_sentence + " " #
but don't forget the space!
return new_sentence
# Now, let's write the main program code, to ask the user and convert.
print "Type in a sentence, and it'll get converted to Pig-
Latin!"
print "Please don't use punctuation or numbers."
print "Also, we can't handle uppercase/lowercase yet, so
lowers only please!"
print
text = raw_input() # nothing in the parentheses,
because there's nothing else
# extra to tell the user before he is allowed
to type
print
print convert_sentence(text)

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