How to write equations from graphs?

Question

JavaScript

Hello.
Tell me please.
Here I came across work with animation in javascript learn.javascript.ru/js-animation , as for me, then I need to figure it out, which is what I'm trying to do.
I want to learn how to write equations based on given graphs, please tell me a specific textbook that describes such things, if I'm not mistaken - this is linear algebra for the initial courses of the institute, but I searched and did not find anything specific.
Please, can you tell me and give a specific link.
Thanks for the help.

Answer 1

I look at your bounceEasyOut example and understand that the task is more difficult than recognizing speech.
In the general case, any graph can be roughly described by a set of polynomials (even sinusoids) - break the graph into pieces that are continuous up to derivatives, count the number of inflection points and associate a straight line, a parabola, a cubic parabola, etc. This should be enough for game stuff and video effects.
It is not bad to construct derivatives of a function given graphically. This will give more food for thought.
This is not linear algebra, this is calculus.

Answer 2

This article simply describes the function, and then gives a graph illustrating the operation of this function.
But not vice versa.

Answer 3

Building a function from a graph is a very difficult task, and it seems that it is still unsolvable. You can try to approximate using the least squares method.

Answer 4

As already answered above, the task is not easy. If the graph should be from any arbitrary image, then only approximate. If the graph is drawn manually, then maybe it’s worth saving at least the parameters of the Bezier curves, for example?