## Description

Goal: In this assignment, you will design and implement two classes called point and line. There are four goals of this assignment: (1) Write a class that meets a precise specification; (2) Understand how to write a class that is separated into a header file and an implementation file; (3) Implement a class using another class; and (4) Gain experience in using a test program to track down bugs in a class implementation (there are two test programs provided with this homework, test1 is for point and test2 is for line). Point class: The point class implements a Cartesian coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. For example, the following figure shows four points, (2,3), (-3,1), (0,0), (-1.5,2.5) in a Cartesian coordinate system: The point class provides member functions for the following operations: (We will never actually draw these points and lines) Constructor: Two constructor functions: one that initializes a point object to (0, 0) and another that initializes a point object to (x, y) where x and y are provided by the programmer using the class. (recall the idea of “default arguments” in constructors) Copy Constructor: Initializes a point object to be a copy of an existing point object. Get x and y coordinates of a point: double get_x( ); double get_y( ); Set x and y coordinates of a point: void set_x (double x); void set_y (double y); Translation: Translating a point is equivalent to adding a fixed pair of numbers (X,Y) to the Cartesian coordinates of the point. That is, if the original coordinates of a point are (x,y), after the translation they will be (x + X, y + Y). void translate(double X, double Y); Scaling: Scaling a point is equivalent to multiplying the Cartesian coordinates of the point by a positive number m. If (x,y) are the coordinates of a point, the corresponding point after scaling has coordinates (mx, my). void scale(double m); Reflection: If (x, y) are the Cartesian coordinates of a point, then (x, -y) are the coordinates of its reflection across the X axis and (-x, y) are the coordinates of its reflection across the Y axis. void reflect_x( ); void reflect_y( ); Rotation: To rotate a point counterclockwise around the origin by some angle r radians is equivalent to (x cos r – y sin r, x sin r + y cos r). void rotate(double r); (remember to include math.h) Operators overloaded: assignment operator ( = ) and comparison operator ( == ). In addition, the point class provides two friend functions to overload the input and output operators. Input format: two real numbers Output format: (x, y). (i.e. for == if both points are equal return true, otherwise return false. Also remember for assignment that the object to the left of the equals is the calling object).

Line class: The line class is implemented using the point class. A line object is defined by (any) two distinct point objects through which the line passes. It provides the following member functions: (remember to include point.h, — our line class will just have two private variables which both points and all our member functions will act on those two private variables) Three constructor functions: (1) initializes the line to be same as X axis; (2) initializes the line to be passing through (0, 0) and a programmer provided point object; and (3) initializes the line to be passing through two programmer-provided point objects. Copy constructor: Initializes a line object to be a copy of an existing line object. Slope of the line: Slope of a line object passing through two different points, (x1, y1) and (x2, y2) is (y2 – y1)/(x2 – x1) provided x1 ≠ x2. Slope is ∞ if x1 = x2. double slope( ); Translation: Translating a line is equivalent to adding a fixed pair of numbers (X,Y) to the Cartesian coordinates of the points through which it passes. If the original line passes through points p1 and p2, the translated line will pass through points obtained by translating p1 and p2 by (X,Y). void translate(double X, double Y); (use the translate function you wrote for your point class to your advantage….) Reflection: Reflection of a line across the X axis is the line obtained by reflecting the points it passes through across X axis. Similarly, reflection across the Y axis is the line obtained by reflecting the points it passes through across Y axis. void reflect_x( ); void reflect_y( ); Operators overloaded: assignment operator ( = ) and comparison operator ( == ). In addition, the line class provides two friend functions to overload the input and output operators. Input format: x1 y1 x2 y2 Output format: The output operator prints out the linear equation of the line in one of the following three forms (m, a, b and c are real numbers): y = mx + c, y= b, x=a (ie: if our x’s are equal we have a vertical line (x=a) and if our y’s are equal we have a horizontal line (y=b)). Files you need to write/submit: 1. point.h and line.h: Header files for point and line classes. 2. point.cxx and line.cxx: Implementation files for point and line classes. 3.

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