Calculating integrer x and y coordinates around point by range variable

The problem didn't let me sleep at night.

Given floating point x and y coordinates of infinite 2D space, and the range variable, I need to get all possible intergrer coordinates that are in range.

The green blocks are in range, and the red ones are not.

Now, I have an answer, but I'm not sure if it's the best one. Make an 2D array with all the values in a square around the point (from -distance, distance to distance, -distance) and then iterate through the entire array, each time checking the distance if it is closer or further than needed, and if so then insert it into another array.