Question

See also: Why is my image rotation algorithm not working?

This question isn’t language specific, and is a math problem. I will however use some C++ code to explain what I need as I’m not experienced with the mathematic equations needed to express the problem (but if you know about this, I’d be interested to learn).

Here’s how the image is composed:

ImageMatrix image; image[0][0][0] = 1; image[0][1][0] = 2; image[0][2][0] = 1; image[1][0][0] = 0; image[1][1][0] = 0; image[1][2][0] = 0; image[2][0][0] = -1; image[2][1][0] = -2; image[2][2][0] = -1; 

Here’s the prototype for the function I’m trying to create:

ImageMatrix rotateImage(ImageMatrix image, double angle); 

I’d like to rotate only the first two indices (rows and columns) but not the channel.

Answer 1

The usual way to solve this is by doing it backwards. Instead of calculating where each pixel in the input image ends up in the output image, you calculate where each pixel in the output image is located in the input image (by rotationg the same amount in the other direction. This way you can be sure that all pixels in the output image will have a value.

output = new Image(input.size())  for each pixel in input: {   p2 = rotate(pixel, -angle);   value = interpolate(input, p2)   output(pixel) = value } 

There are different ways to do interpolation. For the formula of rotation I think you should check https://en.wikipedia.org/wiki/Rotation_matrix#In_two_dimensions

But just to be nice, here it is (rotation of point (x,y) angle degrees/radians):

 newX = cos(angle)*x - sin(angle)*y  newY = sin(angle)*x + cos(angle)*y