# smooth zoom animation formulas (and rounding numbers)

I need to generate an easy animation video in Python (I use PIL to create every frame, then combine them using avconv). The animation is just an image being zoomed out.

That's my code:

for i in xrange(zoom_length):

# zoom level on this step
zoom = 1.0 - 1.0 * i * (max_zoom / zoom_length)

# "size" is the resulting video frame size
# "img.size" is the source image size (around 2.5x bigger than the frame)
anti_zoomed_frame_size = int(size[0] / zoom), int(size[1] / zoom)
anti_zoomed_frame_margins = (img.size[0] - anti_zoomed_frame_size[0]) / 2, (img.size[1] - anti_zoomed_frame_size[1]) / 2

anti_zoomed_frame = img.crop(anti_zoomed_frame_margins +
(anti_zoomed_frame_size[0] + anti_zoomed_frame_margins[0],
anti_zoomed_frame_size[1] + anti_zoomed_frame_margins[1]))

frame = anti_zoomed_frame.resize(size, resample=Image.BILINEAR)

print i, img.size, anti_zoomed_frame_size, anti_zoomed_frame_margins

# frame No for debugging
draw = ImageDraw.Draw(frame)
draw.text((size[0] - 200, size[1] - 100), str(i), (0,0,0), font=font)

yield frame


So what happens is I crop out of the source image a rectangle of size frame_size / zoom , then I resize it zoom times to get the needed frame size. zoom <= 1.0 so doing it in this order seems to be a good idea, though I also tried doing it the other way (resize, then crop).

Anyway in both cases the resulting video is kind of shaking at times. It seems that the problem is in rounding the numbers. The math I'm doing inevitably leads to non-integers, yet PIL requires integers everywhere (also the resulting frame size is obviously a pair of integer constants). This rounding operation seems to affect the smoothness of the animation badly.

How smooth zooming is implemented in real life?

• I'm voting to close this question as off-topic because it doesn't seem to be about computer graphics, but rather video/image/signal processing. Jan 16 '17 at 14:04
• I think it's an interesting question. Essentially temporal aliasing problem which is too often ignored by CG people. There are a huge number of algorithms out there which look cool on still frames but break down when you start animating input parameters. Jan 16 '17 at 19:20
• I meant quantization, not aliasing, but I still think it's worth discussing why this fails to be smooth and what can be done about it besides the obvious "get a toolkit with the proper floating point zoom support". Jan 16 '17 at 19:30
• We have a tag for image-processing, and there is support for the place of image processing in our scope on Meta here and here. Jan 17 '17 at 15:06