Related Articles
2D Transformation | Rotation of objects
• Difficulty Level : Medium
• Last Updated : 02 Nov, 2020

We have to rotate an object by a given angle about a given pivot point and print the new co-ordinates.
Examples:

Input : {(100, 100), (150, 200), (200, 200),
(200, 150)} is to be rotated about
(0, 0) by 90 degrees
Output : (-100, 100), (-200, 150), (-200, 200), (-150, 200) Input : {(100, 100), (100, 200), (200, 200)}
is to be rotated about (50, -50) by
-45 degrees
Output : (191.421, 20.7107), (262.132, 91.4214),
(332.843, 20.7107) In order to rotate an object we need to rotate each vertex of the figure individually.
On rotating a point P(x, y) by an angle A about the origin we get a point P'(x’, y’). The values of x’ and y’ can be calculated as follows:- We know that,
x = rcosB, y = rsinB
x’ = rcos(A+B) = r(cosAcosB – sinAsinB) = rcosBcosA – rsinBsinA = xcosA – ysinA
y’ = rsin(A+B) = r(sinAcosB + cosAsinB) = rcosBsinA + rsinBcosA = xsinA + ycosA
Rotational Matrix Equation:- ## C

 // C program to rotate an object by// a given angle about a given point#include #include  // Using macros to convert degree to radian// and call sin() and cos() as these functions// take input in radians#define SIN(x) sin(x * 3.141592653589 / 180)#define COS(x) cos(x * 3.141592653589 / 180) // To rotate an objectvoid rotate(float a[], int n, int x_pivot, int y_pivot,            int angle){    int i = 0;    while (i < n) {        // Shifting the pivot point to the origin        // and the given points accordingly        int x_shifted = a[i] - x_pivot;        int y_shifted = a[i] - y_pivot;         // Calculating the rotated point co-ordinates        // and shifting it back        a[i] = x_pivot                  + (x_shifted * COS(angle)                     - y_shifted * SIN(angle));        a[i] = y_pivot                  + (x_shifted * SIN(angle)                     + y_shifted * COS(angle));        printf("(%f, %f) ", a[i], a[i]);        i++;    }} // Driver Codeint main(){    // 1st Example    // The following figure is to be    // rotated about (0, 0) by 90 degrees    int size1 = 4; // No. of vertices     // Vertex co-ordinates must be in order    float points_list1[] = { { 100, 100 },                                { 150, 200 },                                { 200, 200 },                                { 200, 150 } };    rotate(points_list1, size1, 0, 0, 90);     // 2nd Example    // The following figure is to be    // rotated about (50, -50) by -45 degrees    /*int size2 = 3;//No. of vertices    float points_list2[] = {{100, 100}, {100, 200},                                {200, 200}};    rotate(points_list2, size2, 50, -50, -45);*/    return 0;}

## CPP

 // C++ program to rotate an object by// a given angle about a given point#include #include using namespace std; // Using macros to convert degree to radian// and call sin() and cos() as these functions// take input in radians#define SIN(x) sin(x * 3.141592653589 / 180)#define COS(x) cos(x * 3.141592653589 / 180) // To rotate an object given as order set of points in a[]// (x_pivot, y_pivot)void rotate(float a[], int n, int x_pivot, int y_pivot,            int angle){    int i = 0;    while (i < n) {        // Shifting the pivot point to the origin        // and the given points accordingly        int x_shifted = a[i] - x_pivot;        int y_shifted = a[i] - y_pivot;         // Calculating the rotated point co-ordinates        // and shifting it back        a[i] = x_pivot                  + (x_shifted * COS(angle)                     - y_shifted * SIN(angle));        a[i] = y_pivot                  + (x_shifted * SIN(angle)                     + y_shifted * COS(angle));        cout << "(" << a[i] << ", " << a[i] << ") ";        i++;    }} // Driver Codeint main(){    // 1st Example    // The following figure is to be    // rotated about (0, 0) by 90 degrees    int size1 = 4; // No. of vertices    // Vertex co-ordinates must be in order    float points_list1[] = { { 100, 100 },                                { 150, 200 },                                { 200, 200 },                                { 200, 150 } };    rotate(points_list1, size1, 0, 0, 90);     // 2nd Example    // The following figure is to be    // rotated about (50, -50) by -45 degrees    /*int size2 = 3;//No. of vertices    float points_list2[] = {{100, 100}, {100, 200},                                {200, 200}};    rotate(points_list2, size2, 50, -50, -45);*/    return 0;}

Output:

(-100, 100), (-200, 150), (-200, 200), (-150, 200)


References: Rotation matrix

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