# Project 1 — Fractions solution

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## Description

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Goal
Develop and implement a Fraction class and use it to calculate the intersection point of two
line segments.
Details
.The Fraction class
The first step in this project is to create a Fraction class that creates Fraction objects and
performs basic arithmetic on fractions. A Fraction object contains an integer numerator and
denominator with two properties:
• The numerator and denominator have no common factor other than 1;
• The numerator is always nonnegative.
A Fraction object must support the following actions:
• Initialize a fraction
– This can initialize to a default value (0/1), provide just a numerator (n/1) or provide both
a numerator and denominator
• Set a fraction to a specific value
– This has the same options as initialize
• Set one fraction equal to another
– This must be done with the = operator
• Add two fractions
– Fraction operator+(const Fraction &a)
• Subtract two fractions
• Multiply two fractions
• Divide two fractions
• Compare two fractions — all six comparisons
• Compare a fraction to an integer — all six comparisons
• Input and output fractions
– friend ostream& operator«(ostream &,const Fraction &)
Data Structures and Objects Project 1 — Fractions Fall 2017 — CRN 42034
– friend istream& operator»(istream &,Fraction &)
The arithmetic functions must use the arithmetic operators +, -, * and /.
.Source code layout
The project is also an exercise in separate compilation, where the source code is divided into multiple
parts. The project consists of four files:
• A header file that contains the class definition;
• A file containing the class methods (functions);
• A file containing a main function that performs the intersection calculations
• A Makefile that directs the process of creating the executable file
.Calculating intersections
Note: This is taken from https://stackoverflow.com/questions/563198/how-do-you-detect-wheretwo-line-segments-intersect
Also note: In the following calculations, bold names are points and other names are scalar values.
Given two line segments p1p2 and q1q2, first compute:
• r ← p2 − p1
• s ← q2 − q1
This parameterizes the line segments, so that any point on p1p2 can be written as p = p1 + t · r
where 0 ≤ t ≤ 1 and any point on q1q2 can be written as q = q1 +  · s where 0 ≤  ≤ 1. The
intersection problem can be recasted to solve for t and .
Next, let z ← q1 − p1 and calculate the following values:
• t ← z × s
•  ← z × r
• y ← r × s
The cross product of two points is given by  × b = x · by − y · bx. Note that it is a scalar (single)
value in our context.
The intersection is now given in the following scenarios:
• If y = 0 and t = 0, then the line segments are collinear.
• If y = 0 and t 6= 0, then the line segments are parallel.
• If y 6= 0, then calculate t ← t/y and  ← /y.
– If 0 ≤ t ≤ 1 and 0 ≤  ≤ 1, then the line segments intersect at p1 + t · r.
– Otherwise, the line segments do not intersect.
Your program must determine which case applies and output an appropriate message. If the
segments intersect, output the intersection point.
2 of ??
Data Structures and Objects Project 1 — Fractions Fall 2017 — CRN 42034
Extra Credit
For 10% extra credit, write a Point class that implements the following:
• Input and output of a point in the form (, y) where  and y are two Fraction objects
• Add and subtract two points using operator+ and operator-
• Multiply two points, computing the cross product
• Multiply a point by a Fraction, which multiplies both of the point’s coordinates by the given
fraction.
Note that both forms of multiply should use operator*; for cross product the parameter should
be a Point and for scaling it should be a Fraction.
Note that you must use your Point class in the project’s solution in order to receive the extra credit.
What to turn in
Turn in your source code and Makefile.