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File: infinizoom0266.png (1.08 MB, 1920x1080)
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I made this simple animated thingy in c4d:


It's a recursive scene - think infinite zoom, like zooming into a picture that contains a smaller version of itself, and that smaller version also contains a yet smaller version, etc. - just in 3d.
Read the clip description on YT if you don't get it, or watch the clip.

It's not the final product or anything, just a test.

The ratio of the bigger scene to the smaller scene is 10:1. Meaning, each consecutive level of zoom is 10 times smaller, for simplicity sake. The camera zooms in. At frame 0, it has a keyframe that points its zoom level to, say, 1. And the last keyframe of each zooming makes the zoom level, say, 0.1.

Problem is perspective, though. If the F-curve connecting the two keyframes was set to linear, it would look like the zoom speeds up and then suddenly stops when it reaches the next zoom level, and repeating that pattern, instead of a relatively smooth-looking camera movement you see in the clip. I am not sure how I achieved that, but I set the F-curve to spline and fiddled about with the curve shape until I was like "Guess that has to do, I can't possibly do a better job", which took me a while.

But look at the blue car. It too has keyframes at 0 and the last frame of 1 zoom sequence: for position and size. Position changes in this fashion: 10 + 1 + 0.1 + 0.001 + ... etc, each level of zoom "adding" a 1/10th of its actual coordinates - since every consecutive iteration is 10 times smaller, right? Thus its size decreases from the factor of 1 to 0.1 to 0.01 to 0.001 ... etc. Since the camera's APPARENT movement is linear (while its ACTUAL movement, to zoom in, is this fucking spline that took me forever), the blue car's size should stay roughly the same throughout the whole animation. But with its F-curves set to linear (size & position), it doesn't look to smooth.

How do I compensate for the camera's movement?
waste of your/my time. AWFUL
Lol, the "art" is obviously just a placeholder. I didn't bother with textures or anything, I spent literally 2 hours modelling everything. Another 2 hours to render. That's not the focus.

I just want to figure out proper camera / movement splines when dealing with powers of 10 while zooming in - perhaps there's a function for that? Exponential, logarythmic etc? - so I can then use them to zoom into something way better.
File: cam f curve.png (225 KB, 1021x919)
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Oh and here's how the spline currently looks. That has to be a crude approximation of a real math function I could use to figure out the shape of the spline. I just know it.
But what does the car's spline look like?
If your camera is splined, your car's scale/position also has to be splined the exact same way if you want to achieve this effect.
Your car has to scale and move exactly with the camera, or else you're going to get the effect you're getting in the current render, where it looks like the car is independent of the camera.
File: car f curve.png (155 KB, 1285x970)
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Like this. Somehow I don't see a way to copy just the spline shape (i.e. what the not-perfect-but-will-certainly-do curve shape I attached in my previous post looks like) between two sets of unrelated keyframed values. Cinema 4D if nobody noticed. So the blue car's spline had to be done manually, and when I tried to re-create the shape of the camera's curve, it just looked wonky, so I gave up and decided to ask here

Perhaps I should be asking a mathematician. Obviously the car's scale / postition progression has to be splined in the same fashion as the camera. The problem is, I think I'm approaching it from the wrong angle. I shouldn't be trying to approximate the shape of a function that already exists, I should be able to utilize whatever tools are available to generate the spline curve from a function/plugin...

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