Algodoo

nope, still doesn't work

Oh yes it does! It has a delay but at least it doesn't start from the 9th point lmao

huh, should work. Wait, I think it's this cursed algodoo configuration glitch.
Some scene messed your configurations, making your algodoo unable to read for(x,(i)=>{}) functions. That may be why it wont work, since it does work for me

Ah lol, alrighty then. It takes a while since the point interpolates, starting from -15, and needs to reach the first point before anything becomes visible xD

Is there any way to make it stop after it reaches the last point? it gets very hign and then resets itself

sure. Open the script menu of the little red blurry ball, and then, replace the whole _x> 15 ? {}: {} with:
_x > _px(10)+0.5 ? {sim.running = false} : {}

Please correct me if I am wrong, but in a "linear" interpolation, you basically connect-the-dots with interpolated points. But in a polynomial interpolation, the interpolated points still connect-the-dots, but not with straight lines. The new data points scribe either a sin or cos pattern, but they should "hug" the original data points rather closely. I noticed in this scene that the new data scribes a sinusoidal curve that swings quite far above and below the original data points, which, to me, doesn't seem quite right. Please explain.....

BTW - As I've mentioned many times in the past, although I love math and the things that can be accomplished with it, my math skills are rather weak. So, if I said anything above which sounds "dumb" or doesn't make sense mathematically, please excuse my ignorance.

The reason why the graph of this interpolation oszillates so irregularely, compared to a sine wave, is because this is'nt actually a sine or cosine function. Rather, this is a polynome (hence the name Polynomic interpolation). A polynome is any function made from powers of X, i.e: Y=2X+(3-X)*(X+1)+(X^3)/4...
The most common polynome is Y=X^2, aka. the parabola. This interpolation however forms a polynome of 9th grade, meaning the hightest power of X is the 9th power. It is constructed by puzzling together multiple polynomes of the same grade, which all hit only 1 point and hit 0 on all others instead, thus meaning that for each point, exactly 1 part polynome hits it, thus when adding all together, the complete interpolation graph hits all points. The way the parts only hit only 1 point is quite simple if one can decipher the variable conjunctions, which often takes a while on the first to third time:
Given you want to calculate the part polynome that hits the 3rd Points, P3. To construct it, use this chain of operations:
Py*(P1x-X)/(P1x-P3x)*(P2x-X)/(P2x-P3x)­*(P4x-X)/(P4x-P3x)*(P5x-X)/(P5x-P3X)...
What this basically does is, whenever X is the same as one of the Px's, for example x=P1x, the paranthesis containing (P1x-x) turn 0, thus multiplying the rest of the function with 0, and thus hitting 0 on that X value. Should you however have x=P3x, then we will hit 1*Py, since we dont have an element stating (P3x-x) which would turn all into 0. Instead all parantheses before the / are identical to each paranthesis after the /, causing every element to return 1. Multiply by Py, and you hit Py at Px, meaning you just hit that point.
All that remains is doing the same for the other 9 points and adding all parts. Since we dont multiply them with each other, the grade always remains 9(Not 10 since the paranthesis element of the hit point is missing). This also means that, just like in linear interpolation, the function perfectly hits each point, instead of just "hugging" it.