How do you rotate a image clockwise?

Answer 1

A picture is just a two-dimensional matrix of pixel colour values. However, the element type is of no importance to the algorithm so, for the purpose of this answer, we'll use a matrix of characters to better illustrate the steps required.

Given the following matrix:

A B C

X Y Z

The rotated matrix would be:

X A

Y B

Z C

Thus given a matrix M[X][Y], the rotated matrix N will be N[Y][X]. In other words, the dimensions are transposed. So before we can rotate we first need to transpose the matrix:

for a = 0 to X

for b = 0 to Y

N[b][a] = M[a][b]

next b

next a

At this point, N has the following layout:

A X

B Y

C Z

To complete the rotation, we simply reverse each row:

for a = 0 to Y

for b = 0 to X / 2

swap (N[a][b], N[a][X-b])

next b

next a

To rotate 270 degrees clockwise (or 90 degrees anti-clockwise), we reverse the columns after transposing:

for b = 0 to X

for a = 0 to Y / 2

swap (N[a][b], N[Y-a][b])

next a

next b

To rotate by 180 degrees, we reverse each row and then reverse each column (without transposing).

Note that all these rotations have a time complexity of O(X*Y*2) because every element has to be written twice. Space complexity is O(X*Y) for transposes and O(1) for reversals. However, when X is equal to Y (square matrix), transposing can be achieved in-place by reversing elements across the primary diagonal.

Answer 2

To rotate an image clockwise, you can use an image editing software like Adobe Photoshop or online tools like Canva. Look for the option to rotate the image, usually found in the editing tools or menu. Select the image and then choose the rotation direction (clockwise) to rotate the image.