Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Rotation of a point about another point in C++

  • Last Updated : 06 Jul, 2017

We have already discussed the rotation of a point P about the origin in the Set 1 and Set 2. The rotation of point P about origin with an angle θ in the anti-clockwise direction is given as under:

Rotation of P about origin: P * polar(1.0, θ)

Rotation of P about point Q

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Now, we have to rotate the point P not about origin but about a general point Q. This can be easily understood by the method of translation which is quite a common technique adopted in geometric analysis.
What is Translation?
In Euclidean geometry, translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction.

How to Perform Translation?
Translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.
After the translation, required computations are made and the translation is nullified by subtracting the constant vector to every point or shifting the origin back.

Translation of Coordinate Axes

So, for rotating P about Q, we shift the origin at Q i.e. we subtract the vector equivalent of Q from every point of the coordinate plane. Now the new point P – Q has to be rotated about the origin and then translation has to be nullified.
These steps can be described as under:

  1. Translation (Shifting origin at Q): Subtract Q from all points. Thus, P becomes P – Q
  2. Rotation of (P – Q) about origin: (P – Q) * polar(1.0, θ)
  3. Restoring back the Origin: Add Q to all the points.


 Rotation of P about Q : (P – Q) * polar(1.0, θ) + Q

// CPP example to illustrate the rotation 
// of a point about another point
#include <iostream>
#include <complex>
using namespace std;
typedef complex<double> point;
#define x real()
#define y imag()
// Constant PI for providing angles in radians
#define PI 3.1415926535897932384626
// Function used to display X and Y coordinates of a point
void displayPoint(point P)
    cout << "(" << P.x << ", " << P.y << ")" << endl;
//Function for Rotation of P about Q by angle theta
point rotate(point P, point Q, double theta)
    return (P-Q) * polar(1.0, theta) +  Q;
int main()
    // Rotate P about Q
    point P(4.0, 3.0);
    point Q(2.0, 2.0);
    // Angle of rotation = 90 degrees
    double theta = PI/2;
    point P_rotated = rotate(P, Q, theta);
    cout << "The point P on rotating 90 degrees anti-clockwise about Q becomes:";
    cout << "P_rotated"; displayPoint(P_rotated);
    return 0;


The point P on rotating 90 degrees anti-clockwise about Q becomes: P_rotated(1, 4)

This article is contributed by Aanya Jindal. If you like GeeksforGeeks and would like to contribute, you can also write an article using or mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up
Recommended Articles
Page :