I implemented a formula from this link https://www.dcode.fr/lagrange-interpolating-polynomial to calculate some kind of score between coordinates.
The result value worked as expected with coordinates like
const coordinates = [
[0, 100],
[2.5, 70],
[10, 30],
]where y axis are even numbers but with y value like 67, 33 is not working as expected.
function getScore (thresholds, macro) {
let value = 0
for (let j = 0; j < thresholds.length; j++) {
let temp = 1
for (let i = 0; i < thresholds.length; i++) {
if (i !== j) {
temp *= (macro - thresholds[i][0]) / (thresholds[j][0] - thresholds[i][0])
}
}
value += thresholds[j][1] * temp
}
return value
}
console.log(
'Expecting Something above 33 but get 31',
getScore(
[
[0, 100],
[2.5, 66],
[10, 33],
],
9
)
)
console.log(
'Expecting Something above 30 but and got 31',
getScore(
[
[0, 100],
[2.5, 70],
[10, 30],
],
9
)
)Did I make a mistake with my code?
Thank you,
The algorithm is working as it should, though not as you expect.
That algorithm fits a polynomial to the points. If you have 3 points, it will be a parabola. Because it falls so fast over the first 2 points, that parabola will have its minimum between the second two, and therefore gives values below the numbers you gave.
If this is not the kind of interpolation that you want, I would suggest that you use a non-polynomial. For example you could play around with a weighted average that looks something like this:
sum(point.y * f(x - point.x) for point in points)
/
sum(f(x - point.x) for point in points)
Make f(x) be a function that has f(x) = f(-x) and blows up at 0. Of course if you're at that point, just enter the value of that point. For example 1/x^2. This will cause you to every be close to a reasonable average of the nearby points.