Question

Ok so I’ve been looking into interpolation lately. Sadly almost every article I’ve read only discusses interpolation at a decimal level 0.0 to 1.0 to be exact. I would like to interpolate whole number integers regardless of how big they are or if there negative or whatever. I’ve accomplished this with linear interpolation:

public int interpolate(int y1, int y2, int length, int x){
    return y1 + x * (y2 - y1) / (length-1);
}

However I’m stuck with cosine interpolation. This great article talks about cosine interpolation however it’s on a system of numbers from 0.0 to 1.0 as stated above. Here is what I have so far:

public int interpolate(int y1, int y2, int length, int x){
    int v = (int)(y2 - Mathf.Cos(x * 3.1415f))/2;
    return (y1 + x * (y2 - y1) / (length-1)) * v;
}

It doesn’t work though it returns an almost random number with no real direction making it not smooth at all. This is where I need your help. Long story short: How do I make a cosine interpolation function that deals with integers?

Answer 1

Output of cos θ varies from 1 to -1 to 1 as its input ranges from [0, 2π]. We need something from [0, 1]. So

1. Limit the domain to [0, π] to limit codomain to [1, -1]
2. Subtract from 1, for codomain to be [0, 2]
3. Divide by 2 to get a codomain of [0, 1]

You’ve get a nice function that goes from 0 to 1. The rest is transforming the argument.

Essentially you need

(int) ((1 - cos(pi*x / (length-1)))/2 * (y2-y1)+y2)