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.