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From what understand, a temporal auto Bezier keyframe automatically re-adjusts both of its direction handles whenever a neighboring keyframe is moved somehow and the influences of both of its incoming and outgoing velocities are always the same. Whereas a temporal continuous Bezier keyframe does not re-adjusts at all, and the influences are different. So those are the differences on how they work.

But what are the real benefits of auto Bezier keyframes over continuous Bezier keyframes? Most of the time, as far as I know, most people use Easy Ease (In/Out) keyframe assistants anyway, and end up manually adjusting the curves, which results only in continuous Bezier keyframes. What's the point of auto Bezier keyframes?

Difference is quite low :) Auto bezier will generate constrains automatically and continous bezier will allow that constrains to be streched in the axes (same line of auto generated constrains) and once you change constrains axis ( means u make shape like V) it'll become bezier

Auto Bezier : As it's name says; auto bezier stands for the smoothness of animation by adjusting all curves automatically.

Continous Bezier : same as Auto bezier in first perspective; does same thing when adjusting curves! Then what is the point??

Here it goes:

1. From my knowledge whenever keyframes are auto beziers if you changes the keyframes handles then this behaviour will FORCE all other relating (neighbour) handles to change their handles to in term to maintain the smoothness automatically so let me give you example. you want to make ball fall down and bounce animation then you can use this behavious since till collision of ball it's speed will be graduating constantly and then after collision it bounces upwards by applying pressure to surface and then it stops.

so in that case we had graduating changes in motion and to make it smooth we can use auto bezier since it will auto generate curves based on gravity(speed in our case) and even if you change one handle it'll change others too

2. now come in bezier handles. in continous bezier handles you have fully controls over each handles. so if you want to make your ball move down in illogical way(slowly comes down and then gets speed and again get very slow etc.) you can use continous bezier since it won't affect other handles while changing and then you can have your desired changes in motion speed

so basically if you doing natural movements like slope or fall or jump ; auto bezier will be best choice until you found that some keyframe really need change only then switch that frame to Continous Bezier :)

Edit : Watch Below image in which i drew constrains relation between auto ,continous and bezier and its effects by interpolation in graph

and not but least u can always read Official Docs if you want; Hope it helps :) Happy Animating time :)

Here Is Little More

About "influences of incoming and outgoing velocities" : it will only same when you've selected Auto Bezier or Continous Bezier in temporal interpolation and when we talk about spatial interpolation it doesn't effect on velocity at all. it just tells us about position : in short i think you will get all confusion clear by using graph.

first switch graph to Speed Graph and keep your Temporal interpolation linear.you will see that your speed isn't smooth at all but once you switch temporal interpolation to auto bezier the incoming and outgoing velocity will be equaled and now you can see smooth graph(curve)

now we comes to spatial interpolation: now it's all about values of position and so on so switch your graph from speed to value and set spatial interpolation from linear to auto or continuous bezier now it'll show you smooth curve instead of straight lines

In Short : "Use Auto Bezier unless you find some frames bad and fix it by only making it to continous :) to understand it more : no matter it's auto or continous the spatial interpolation reffers for values and temporal intepolation refers to velocity(speed over time) "

-Regards; Design Phoenix

Okay, after watching a bunch of physics lesson videos on how to read position-time graphs and lots of testing, I think I've finally understood how these different types of keyframes work.

Basically I've been looking at this at the wrong angle. The most obvious benefit of Auto Bezier keyframes are not over Continuous Bezier keyframes, but over Linear keyframes. With Auto Bezier keyframes (and Roving keyframes as well), you get more logical, or more realistic if you will, instantaneous speed at the keyframes. The problem about Linear keyframes is that you have an abrupt change of speed from before them to after them, which is impossible (unless you're Superman who can do something close to that). It's very obvious at the first or last keyframe, where an object goes straight from 0 speed to high speed or vice versa. Therefore, Auto Bezier keyframes introduce curves right at the keyframes ("smooth the corners out") so that you have feasible instantaneous speed at those keyframes (same speed before and after them). At the same time, you still get to keep the almost constant speed between keyframes that's almost indistinguishable from the true constant speed that Linear interpolation offers, with the influence of the keyframes on both sides about 16,666% (maybe a magical number that After Effects figured out somehow, I'm not sure). Basically, you get quite some decent easing right out of the box with Auto Bezier keyframes, plus the handles automatically readjust themselves whenever you move neighboring keyframes to maintain the proper smoothness and the influence of 16,666%.

As for Continuous Bezier keyframes, they cost you the automatic readjustment, but they offer even more fine adjustment to how the easing should work between keyframes. Maybe you don't want the easing happens only at 16,666% of the duration between 2 keyframes with Auto Bezier, or maybe you don't want the pseudo-constant speed between them. Maybe you want to really exaggerate the way your object accelerates by adjusting the positions of the tips of the angles of the handles (up and down for value, left and right for influence). However, exaggerating too much might result in very unrealistic motion, for example if the angles of the handles are wrong you may end up having overshoots of motion, in other words a case where temporal interpolation affects spatial interpolation.

That being said, Linear keyframes aren't useless. Sometimes it doesn't really make sense to try to achieve realism with a bunch of computer-generated motion graphics, especially when your object moves so slow that acceleration doesn't matter that much. And if you're relying on the Motion Sketch panel or the Convert Audio to Keyframes Keyframe Assistant for example, which may generate keyframes on a frame-by-frame basis, it's not very necessary to try to smooth them all out.

TL;DR: Auto Bezier's better than Linear because it's more logical and it offers simple automatic easing; Continuous Bezier's better than Auto Bezier's because you have more control over how your easing should be; Auto Bezier's better than Continuous Bezier because it offers easy and automatic (but more limited) easing.