Question

c++ program

Create the "point" class as shown in the text with (private and public sections)

        a.   data members are the one listed in the text book plus the new ones below

              Methods in the text:  shift,  rotate90,  rotations_needed,  distance,  middle

        b.   Default "constructor" with two arguments for x and y coordinates

        c.  Add the following methods:  

                        Translation:   (x,y) translated to (x’,y’) by adding x’ to x and y’ to y value
                                    (x’,y’) = (x+x’, y+y’) where x’ & y’ are int + or – or 0 values

                        Scaling:  (x’, y’) = (x’x, y’y)  (multiply) where m > 1 makes larger,
                                                            m 0.0 to 1.0 makes smaller

                        Rotation: ( d) = ( x cos d– y sin d,  x sin d+ y cos d)
                                                            whered is the degrees to rotate.

                        Shearing: (x’, y’) = (x+x’, y)  to shear in the x direction

                                                        (x, y’+y) to shear in the y direction

Write a main program that will test the above implementation of ‘points’ class and that will convince me your points class is correct.  Test all methods in the Points class and show results.

Also, set up a box with 4 points:  (2,2) (2,5)  (4,5)  (4,2)

1. Print out the points for the box.

2. Print out the points for the box after Translating it x’=2 and y’=1 distance.

3. Continuing with new set of box points,
            print out the box after scaling x by 2 and y by 0.5

4. Original box pts: print out the box after rotating the box by 30 degrees then
            print again after rotation another 60 degrees.  
            (Note: degrees may need to be converted to radians?)

5. Original box pts: print out the box after
            shearing in the x direction 1.5

6. Original box pts:
            print out the box after shearing in the y direction 1.7

Print out and label each of the outputs above.

For each output of each box, also draw a picture of the new box (nice accurate boxes)

Answer 1

Short Summary:

• Overridden the operator "<<" for Point class to print the co ordinates in (X, Y) format.
• Shown the boxes for every output.

Source Codes:

Point.cpp file

#include<iostream>
#include<cmath>

using namespace std;

/**
* Point class
*/
class Point{

public:
//Member variables to store co ordinates (x and y)
double X, Y;
  
/**
* Constructor
* Accepts co ordinates (x, y)
* And assings them to Member variables
*/
Point(double x, double y){
X = x;
Y = y;
}
  
/**
* Translation:   
* (x,y) translated to (x’,y’) by adding x’ to x and y’ to y value
(x’,y’) = (x+x’, y+y’) where x’ & y’ are int + or – or 0 values
*
*/
void Translation(double _x, double _y){
X += _x;
Y += _y;
}
  
/**
* Scaling:
* (x’, y’) = (x’x, y’y) (multiply) where m > 1 makes larger,
m 0.0 to 1.0 makes smaller
*
*/
void Scaling(double _x, double _y){
X = (X * _x);
Y = (Y * _y);
}
  
/**
* Rotation: ( d) = ( x cos d– y sin d, x sin d+ y cos d)
where d is the degrees to rotate.
*
*/
void Rotation(double d){
//create temp variables to hold the new co ordinates
double rx=X, ry=Y;
//Calculate new co ordinates using the given formula
rx = (X * cos(d) - Y * sin(d));
ry = (X * sin(d) + Y * cos(d));
  
//Assign the new co ordinates back to Member variables
X = rx;
Y = ry;
}
  
/**
* ShearingX: in X direction
* (x+x’, y) to shear in the x direction
*
*/
void ShearingX(double _x){
X += _x;
}
  
/**
* ShearingY: in y direction
* (x, y’+y) to shear in the y direction
*
*/
void ShearingY(double _y){
Y += _y;
}
  
/**
* Overriding << operator
* Prints co ordinates in the format (X, Y)
*/
friend ostream& operator<<(ostream& out, const Point& P){
return out << "(" << P.X << ", " << P.Y << ")";
}
};

Main.cpp file:

#include <iostream>
#include "Point.cpp"

using namespace std;

int main()
{
  
//set up a box with 4 points: (2,2) (2,5) (4,5) (4,2)
Point point1(2,2);
Point point2(2,5);
Point point3(4,5);
Point point4(4,2);

//1.Print out the points for the box.
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;



//2. Print out the points for the box after Translating it x’=2 and y’=1 distance.
// translate each point at x=2 and y=1
cout << "\nTranslating x = 2 , y = 1" << endl;
point1.Translation(2, 1);
point2.Translation(2, 1);
point3.Translation(2, 1);
point4.Translation(2, 1);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;
  
//3.Continuing with new set of box points,
//print out the box after scaling x by 2 and y by 0.5
cout << "\nScaling x = 2 , y = .5" << endl;
point1.Scaling(2, .5);
point2.Scaling(2, .5);
point3.Scaling(2, .5);
point4.Scaling(2, .5);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;
  
//4. Original box pts: print out the box after rotating the box by 30 degrees then
// print again after rotation another 60 degrees.
// (Note: degrees may need to be converted to radians?)
  
// rotate 30 degree PI/6
cout<<"\nRotate 30 degree" << endl;
point1.Rotation(22/(double)42);
point2.Rotation(22/(double)42);
point3.Rotation(22/(double)42);
point4.Rotation(22/(double)42);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;

// rotate 60 degree PI/3
cout<<"\nRotate 60 degree" << endl;
point1.Rotation(22/(double)21);
point2.Rotation(22/(double)21);
point3.Rotation(22/(double)21);
point4.Rotation(22/(double)21);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;
  

//5. Original box pts: print out the box after
// shearing in the x direction 1.5
cout<<"\nShearing x direction 1.5" << endl;
point1.ShearingX(1.5);
point2.ShearingX(1.5);
point3.ShearingX(1.5);
point4.ShearingX(1.5);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;

  
//6. Original box pts:
// print out the box after shearing in the y direction 1.7
cout<<"\nShearing y direction 1.7" << endl;
point1.ShearingY(1.7);
point2.ShearingY(1.7);
point3.ShearingY(1.7);
point4.ShearingY(1.7);
//Print out the points
cout << "Point 1: " << point1 << endl;
cout << "Point 2: " << point2 << endl;
cout << "Point 3: " << point3 << endl;
cout << "Point 4: " << point4 << endl;
  

return 0;
}

Refer the following screen shots for code indentations:

Sample Output:

Boxes:

Point 1 - A : (2, 2)
Point 2 - B: (2, 5)
Point 3 - C: (4, 5)
Point 4 - D: (4, 2)

Translating x = 2 , y = 1
Point 1 - A: (4, 3)
Point 2 - B: (4, 6)
Point 3 - C: (6, 6)
Point 4 - D: (6, 3)

Scaling x = 2 , y = .5
Point 1 (A) : (8, 1.5)
Point 2 (B) : (8, 3)
Point 3 (C) : (12, 3)
Point 4 (D): (12, 1.5)

Rotate 30 degree
Point 1: (6.17709, 5.30034)
Point 2: (5.42681, 6.59922)
Point 3: (8.89049, 8.59995)
Point 4: (9.64077, 7.30107)

Rotate 60 degree
Point 1: (-1.50506, 7.99905)
Point 2: (-3.00506, 7.9981)
Point 3: (-3.00759, 11.9981)
Point 4: (-1.50759, 11.999)

Shearing x direction 1.5
Point 1: (-0.00505766, 7.99905)
Point 2: (-1.50506, 7.9981)
Point 3: (-1.50759, 11.9981)
Point 4: (-0.00758664, 11.999)

Shearing y direction 1.7
Point 1: (-0.00505766, 9.69905)
Point 2: (-1.50506, 9.6981)
Point 3: (-1.50759, 13.6981)
Point 4: (-0.00758664, 13.699)

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Happy Studying!!!