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HTML5 Canvas interactive animations of menu with bubbles


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Need make animated menu with bubbles.
Like here:

On vanilla js. Third-party libs and frameworks cannot be used. 
Only base jquery.

I looked, it's done on canvas.

Need guides/books/tutorials/articles on the topic.
How to make animations on canvas?

How to calculate the trajectory of the balls immediately after
loading a web page?
How to calculate the trajectory and behavior of the balls when they are dragged with the mouse?
How to calculate the trajectory and behavior of the balls when clicking on the ball and opening the submenu?
How to implement the effect of soap bubbles?

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