Algorithm to rotate an image 90 degrees in place? (No extra memory)

Question

In an embedded C app, I have a large image that I'd like to rotate by 90 degrees. Currently I use the well-known simple algorithm to do this. However, this algorithm requires me to make another copy of the image. I'd like to avoid allocating memory for a copy, I'd rather rotate it in-place. Since the image isn't square, this is tricky. Does anyone know of a suitable algorithm?

Edited to add clarification, because people are asking:

I store an image in the usual format:

// Images are 16 bpp
struct Image {
    int width;
    int height;
    uint16_t * data;
};

uint16_t getPixel(Image *img, int x, int y)
{
    return img->data[y * img->width + x];
}

I'm hoping to move the contents of the data array around, then swap over the width and height member variables. So if I start with a 9x20 pixel image, then rotate it, I'll end up with a 20x9 pixel image. This changes the stride of the image, which complicates the algorithm a lot.

Answer 1

This might help: In-place matrix transposition.

(You might also have to do some mirroring after the transposition, as rlbond mentions).