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 = sinA + ycosA
Rotational Matrix Equation:-
C
// C program to rotate an object by // a given angle about a given point #include<stdio.h> #include<math.h> // 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 void rotate(float a[][2], 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][0] - x_pivot; int y_shifted = a[i][1] - y_pivot; // Calculating the rotated point co-ordinates // and shifting it back a[i][0] = x_pivot + (x_shifted*COS(angle) - y_shifted*SIN(angle)); a[i][1] = y_pivot + (x_shifted*SIN(angle) + y_shifted*COS(angle)); printf("(%f, %f) ", a[i][0], a[i][1]); i++; } } // Driver Code int 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[][2] = {{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[][2] = {{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<iostream> #include<math.h> 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[][2], 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][0] - x_pivot; int y_shifted = a[i][1] - y_pivot; // Calculating the rotated point co-ordinates // and shifting it back a[i][0] = x_pivot + (x_shifted*COS(angle) - y_shifted*SIN(angle)); a[i][1] = y_pivot + (x_shifted*SIN(angle) + y_shifted*COS(angle)); cout << "(" << a[i][0] << ", " << a[i][1] << ") "; i++; } } // Driver Code int 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[][2] = {{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[][2] = {{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
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