Moving Items Along Bezier Curves with CSS Animation (Part 1: Constructions)

TLDR: This article is NOT about cubic-bezier(), and it is not about layered CSS animations (for X and Y axes respectively). It is about carefully crafted combined animation, that moves an element along any quadratic/cubic Bezier curve.

UPDATE: Here's the link to part 2.

Following my previous post, I continued investigating competing CSS animations, which are two or more CSS animations affecting the same property.

I observed that two animations may "compete". In the following example, the box has two simple linear animations, move1 and move2. It turns out the box actually moves along a curved path:

So clearly it must be the combined effects from both animations. Note that in move2, the `from` keyframe was not specified. It'd look like this if it is specified:

In this case, it seems only the second animation takes effects.

Actually this is not surprising, in the first case, the starting point of move2 would be "the current location from move1".  But in the second case, move2 does not need any "current location", so move1 would take no effect.

I further examined the actual behavior of the first case. If move1 is "move from \(P_0\) to \(P_1\)" and move2 is "move to \(P_2\)". At time \(t\):

- The animated location of move1 is \(Q_1=(1-t)P_0 + tP_1\)

- The animated location of move1+move2 is \(Q_2=(1-t)Q_1 + tP_2\)

This formula actually looks very similar to the Bezier curve, but I just double checked from Wikipedia, they are not the same.

Fun fact: I came up with this string art pattern during high school, I realized that it is not a circle arc, but I didn't know what kind of curve it is. Now I understand that it is a Bezier curve.

Quadratic Beziers in string art

Build a quadratic Bezier animation path with two simple animations

The quadratic Bezier curve is defined by this formula:

\[B(t) = (1-t)^2P_0 + 2(1-t)tP_1 + t^2P_2, 0\le t \le 1\]

But our curve looks like \(f(t) = (1-t)^2 P_0 + t(1-t)P_1' + tP_2\). Note that I use \(P_1'\) to distinguish it from P1 above.

If we set \(P_1'=2P_1-P_2\), we'll see that f(t)=B(t) for all t. So it is a Bezier curve, just the control point is a bit different.

Here's an interactive demo, which is based on this codepen.

An Alternative Version

Another option is to follow the construction of a Bezier curve:

Bézier 2 big

This version needs slightly more code, but it does not require much math. Just observe that a quadratic Bezier curve is a linear interpolation of two moving points, which are in turn obtained by another two linear interpolations.

All these linear interpolation can be easily implemented with CSS animation on custom properties. Here is an example:

Here I just have one animation, which does multiple linear interpolation at the same time. In this case I have to make sure all animated custom properties are defined with @property, which was not the case in the previous example.

How about cubic Bezier curves?

Both versions can be extended to make animation along cubic Bezier paths.

The first version needs a bit more math, but doable. 

\[ P_1' = 3P_1 - 3P_2 + P_3\]
\[ P_2' = 3P_2 - 2P_3\]

The second version just involves more custom properties.

Actually both versions may be extended to even higher-degree Bezier curves, and 3D versions.

For the first version, I suppose there would be a generic formula for any \(P_i'\) for any \(N\)-order curve, but I did not spend time in it.


Studying CSS Animation State and Multiple (Competing) Animations

[2022-08-04 Update] Most of my observations seems confirmed in the CSS animation spec.

I stumped upon this youtube video. Then after some discussion with colleages,  I was really into CSS-only projects.

Of course I'd start with a rotating cube:

Then I built this CSS-only first person (rail) shooter:

It was lots of fun. Especially I learned about the checkbox hack

However there were two problems that took me long to solve.

1. Move from in the middle of an animation

The desired effect is:
  • An element is moving from point A to point B.
  • If something is clicked, the element should move from its current state (somewhere between A and B, in the middle of the animation/transition) to another point C.
This is for the last hit of the boss, the boss is fastly moving. I'd like the boss to slowly move to the center if being hit.

The first try: just set a new animation "move-to-new-direction" when triggered, but it does not work. The new animation starts with the "original location" instead of the "current location".

This is because the old animation was removed in the new rule, so the animation state would be instantly lost.

As a side note, it turned out this is easier to achieve with CSS transition:

However transition does not well for me because I need non-trivial scripted animation.

In order to let the browser "remember the state", I tried to "append a new animation" instead of "setting new animations". Which kind of works.

However it is clear that the first animation is not stopped. Both animations are competing with the transform property, and eventually the box will always stop, due to the second animation. It'd be obvious that the order of the animation matters.

Then I tried to play with the first animation in the triggerd rule. 

The original first animation is "default-move 2s infinite 0s". It turns out that it does not matter too much if I
  • change infinite to 100 (or another large number), and I trigger the change before the animation finished
  • change delay from 0s to 2s (or another multiple of 2s), and I trigger the change after that delay.
However it will be an obvious change if I modify the duration, or change the delay to 1s:

So I figured that the browser will keep the state of "animation name" and "play time". It'd re-compute the state once the new value is set for the animation property. 

To stop the first animation from "competing", I figured that I could just set the state to paused, which works well:

And similary, I should keep all the setting (duration, delay etc) of the first animation, of carefully change it to a "compatible" set.

This basically solves my problem. And finally, actually I realized that the boss should just die at where he's shot, so I'd just pause the current animation. It's also easier than copying all existing animations and adding a new one, in the CSS ruleset.

2. Replaying Animation with Multiple Triggers

This is needed for the weapon firing animation, whenever an enemy is being shot, the "weapon firing" animation should play.

This simple implementation does not work well:

Both input elements work individually, however if the first checkbox is checked before clicking on the second, the animation does not replay.

Now it should be clear why this happens: the browser would remember the state of "animation name" and "play time". This can be verified by tweaking duration and delay:

Especially, it would be a good solution, if I know exactly when the animation should be played (despite of the trigger time). This is not the case for my game, because I want to play the weapon-firing animation immediately after the trigger.

To make both triggers work, one solution is to "append the animation":

But this could be repetitive and hard to maintain for a large number of triggers (on the same element).

A better solution is to define multiple identical @keyframes with different names. Then different triggers can just set individual animation names. The browser would replay the animation because the animation name changes:

I think this one is better because the animation rules can be written with a @for loop in SCSS.

In my game I ended up using multiple (duplicate) elements with individual triggers. All elements are hidden by default. Upon triggered, each element would show up, play the animation, then hide.

One nice thing about this solution, I can still control the "non-firing weapon" with scripted animations, because the triggers will not override the animation CSS property.

Note that here it is assumed the triggers will start in a pre-defined order, otherwise the CSS rules would not work properly.


I find most CSS-only projects fascinating. Pure animatoin is one thing, but some interactive projects, especially games, are quite inspiring.

I'm also wondering if there is any practical value besides the "fun factor". It'd be interesting if we can export some simple 3D models/animations from Blender to CSS.