I want to write a mathematic formular that, given any number of monotonic arbitrary point, it will produce a monotonic smooth step function
Such as a figure below, I give it 2 point (the intersect point of red line and black curve). It will plot a graph as a function curve that pass all given points with derivative 0, so between each point will be like S curve
I want a function that was not being step, being a single function that could inverse and differentiate/integrate. So it could be use in forward and reverse calculation
Are there any function that fit this requirement?