The image quality suffers if the mapping functions X(x,y) and Y(x,y) of the position (x,y) of a pixel of the output image to the position (X,Y) of the sampled input image pixel are strongly contracting or expanding.
For contracting mappings many pixels of the output image are mapped to the same single pixel of the input image. Without interpolation such a pixel appears magnified in the output image as a large patch of uniform color. You can see an example in “How to generate rosettes“. With cubic interpolation we can remove this defect , see the post “interpolation of pixels“.
For strongly expanding mappings neighboring output pixels are mapped to input pixels that lie far away from each other. If they are further apart than the size of characteristic details of the input image, then we get artifacts in the output image. An example are the nearly random pixels at the center of this spiral image:
This is essentially aliasing. We can improve the image by averaging, see “Smoothing and anti-aliasing“. Using four sampling points for each output pixel gives a much nicer image:
Obviously, interpolation and averaging slows down image generation and should only be used where needed. Often, we need neither of them. And never both. The generating program should analyze the mapping and choose the image improvement.