I want to generate a function which would non-linearly interpolate data. Let's say the fraction x (varies between 0 and 1) represents the distance from the Point A towards Point B. So, if x=0, we are at Point A and if x=1, we are at Point B. Now the condition I have if that at x=0.1, we would need to have travelled 90% of the distance from Point A towards Point B. Notice, I would not be able to connect this with the actual values of the parameter data at Point A or B unlink is the case in exponential interpolation techniques [https://www.mrmath.com/misfit/algebra-stuff/linear-and-non-linear-interpolation/#:~:text=ExponentialThe%20second%20most%20popular,smooth%2C%20concave%20curve%20between%20points].
The following resources are too tough for me and I am looking for the simplest solutions:-
- https://www.sciencedirect.com/science/article/pii/0022247X82901378
- https://ieeexplore.ieee.org/document/1054589
As an example of linear interpolation, let's say that the value of the parameter at Point A is 'a' and at Point B is 'b'. The linear interpolation formula is then given as:-
a+(b-a)*y
where y=x for linear interpolations. I wish to develop a non-linear function for y=f(x). Is there an easy general way for this?