I have two points in the 2D space, e.g. point A is (3, 2) and point B is (30, 20)
I want to get some points in between, aka, interpolating between A and B. But I don't want linear interpolation, I want something like exponential interpolation.
I've found the following formula for exponential interpolation:
$$y = c * (d/c)^{(x-a) / (b-a)}$$
Where $a$ is the starting value in the $Y$axis and b the end value in the $Y$ axis too
$c$ is the starting value in the $X$ axis and $d$ the end value in the $X$ axis too
In the example I stated above: $a = 2, b = 20, c = 3, d = 30$
Using this formula, this is the interpolation I get (I drawed a line for demonstration purposes, but I get some points)
But the curve is not very steep, I would like to have something like this
What formula should I use?
Best Answer
You can try
$$f(x) = \alpha \exp(\beta x^n)$$
Use points $A$ and $B$ to find $\alpha$ and $\beta$. For instance, $n=2$ gives a steeper curve than $n=1$.