Add functionality to get_area() so it supports areas bounded by all axes

[JeroSQ]

Description of proposed feature

Modify the function so it allows you to get the area of a function bounded by any axis. For example, an integral from y0 to y1 (I don't know if there's a proper name for this). Like such:

How can the new feature be used?

Would improve the graphing tool and add functionality.

Additional comments

This may be regarded as too specific. Let me know what you think.

[JeroSQ]

One way I can think of doing this is the following (assuming the graph is on quadrants I or IV and the function increases, like the picture above):

Let the wanted area be the region next to the curve bounded by the y axis of the function f(x) from y0 to y1, then:

• Create a new function g(x) which is constant at y0 up to the first x0 which satisfies f(x0)=y0. (Constant until it reaches the function).
• After x0, the function would be the same as the original function f(x).
• Create another function h(x) constant at y1.
• Return get_area(h(x), x_range=[0, x1], bounded_graph=g(x)) where x1 satisfies f(x1)=y1

This method can be generalized to all functions on any quadrant as well as increasing or decreasing with some extra logic.

[nikolim]

Hi @JeroSQ
This sounds like a great feature.
Could you assign the issue to me?

[JeroSQ]

I can't assign issues but feel free to work on it. Devs need to decide if this feature can be implemented into the library or into manim-contrib

[Darylgolden]

I don't think this is too specific to be implemented, but it should be implemented by rewriting get_area such that it can be used on any axis, rather than implementing a different logic for the x and y axes.