Specify, design, and implement a class that can be used to keep track of the pos

Question

Specify, design, and implement a class that can be used to keep track of the position of a point in three-dimensional space. For example, consider the point drawn at the top of the next column. The point shown there has three coordinates: x = 2.5, y = 0, and z 2.0. Include member functions to set a point to a specified location, to shift a point a given amount along one of the axes, and to retrieve the coordinates of a point. Also provide member functions that will rotate the point by a specified angle around a specified axis. To compute these rotations, you will need abit of trigonometry. Suppose you have a point with coordinates, x, y, and z. After rotating this point (counter-clockwise) by an angle theta, the point will have new coordinates, which we'll call x', y', and z'. The equations for the new coordinates use the c math library functions sin and cos, as shown here: After a a rotation around the x-axis: x' = x y' y cos(theta)-z sin(theta) z' = y sin(theta) +z cos(theta)

Explanation / Answer

// Please see comments given with code .

// angle to be passed in PI terms +ve for anticlock and -ve for clock

// axis value to be passed for axis of rotation : x = 1 , y = 2 , z = 3

#include <iostream>
#include <cmath>

using namespace std;

#include <iostream>
using namespace std;

class TDPR

{

private :

// coordinates
double x,y,z;

// default constructor
public : TDPR()

{

}

// constructor to initialize coordinates passing x,y,z in sequence
public : TDPR

(double xc,double yc,double zc)

{

x = xc ;

y = yc ;

z = zc

;

}

// to set coordinates passing x,y,z in sequence
public : void setPoint(double xc,double yc,double zc)

{

x = xc ;

y = yc ;

z = zc ;

}

// to rotate angle in PI value ,+ve for counterclockwise and -ve for clockwise and axis as 1 for x , 2 for y and 3 for z   
public : void rotate(double angle , int axis )

{
if(axis==1)
{
y = y*cos(angle) -

z*sin(angle);
z = y*sin(angle) + z*cos(angle);
}
else

if(axis==2)
{
x = x*cos(angle) + z*sin(angle);

  
z = z*cos(angle) - x*sin(angle);
}
else if

(axis==3)
{
  
x = x*cos(angle) - y*sin(angle);
y =

x*sin(angle) + y*cos(angle);
}
}
public : void showPoint

()
{
cout << " x = " << x <<" y = " << y <<" z = " <<

z << endl;
}
} ;

// Main Function

int main()
{
TDPR T1 ; // T1 object created without coordinates
TDPR T2(1.5,2.0,3.0); // T2 object created with coordinates
  

T1.setPoint(3.0,0.0,1.0); // setting coordinates for T1
T1.showPoint(); // show coordinates for T1
  

T2.showPoint(); // show coordinates for T2
T1.rotate(1,2); // rotate T1
T2.rotate(-1,1); // rotate T2
  

T1.showPoint(); // show coordinates for T1
T2.showPoint(); // show coordinates for T2
return 0;
}

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