Multivariate interpolation error in GML

Question

everybody. I am using Game Maker, a program with syntax somewhat similar to Python (aside from spacing) to implement interpolation between multiple data values, as described here. Imagine a scatterplot with x = 0 at the origin and x = 100 at the end, with equal spacing between each data value. The x-positions are constant, but the y-positions may have any value. If lines were connected between each data point, then ideally, a script would be able to find the y for a given x-position. Here was my original implementation:

// This is executed once.

nums = 3; // the number of values to interpolate between
t = 0; // the position along the "scatterplot" of values

// Values may be decimals with any sign.  There should be values >= nums.
ind[0] = 100;
ind[1] = 0;
ind[2] = 100;

//This is executed each step.

intervals = 100 / (nums - 1);
index = round(percent / intervals);
if percent != 0 {newpercent=  (intervals / (percent - index)) / 100;}
else {newpercent = 0;}
newval = ind[index] * (1 - newpercent) + ind[index + 1] * newpercent;

This should've used a lerp() after finding which two points surround the given x-position to return an interpolation between their two values, but it didn't, so my question is:
What went wrong and how could I fix it? Thanks in advance.

Edit: Here is the finished and working code:

// This is executed once.

nums = 3; // the number of values to interpolate between
t = 0; // the position along the "scatterplot" of values

// Values may be decimals with any sign.  There should be values >= nums.
ind[0] = 100;
ind[1] = 0;
ind[2] = 100;

// This is executed each step; setting the result to 'alpha'.

if (nums > 1) {
    if (t != 1) {
        _temp1 = 1 / (nums - 1);
        _temp2 = floor(t / _temp1);
        _temp3 = (t - (_temp1 * _temp2)) * (nums - 1);
        alpha = ind[_temp2] + _temp3 * (ind[_temp2 + 1] - ind[_temp2]);
    }
    else {
        alpha = ind[nums - 1];
    }
}

Answer 1

What you want to do is interpolate the value of property of your game (sound volume, danger level, gravity etc.) let's call the variable you want to caluculate y as some other property changes (like time, x-position etc.) let's call it t.

We have n points where we know the value of y. Let's call each of these points p0, p1 ... pn-1 where each number is the index of that point. Lets call the values in these points y0, y1 ... yn-1. So for any given value of t we want to do the following:

First we find the two points closest to t. Since all points are evenly spaced out we know that the value of t for a given point is t = index/(n-1) and by reordering this equation we can get the "index" of any given t like this index = t*(n-1). When t isn't exactly in the same position as one of our points it's going to be a number in between the index values of the two closest points pk and pk1. So pk = floor(index) gets you the index previous to your t and pk1 = pk + 1 is the next point.

Then we have to find out how close t is to each of these two points (value between 0 and 1) as that determines how much influence the value from each point will get in out interpolation. Let's call this measurement alpha. Then alpha = (t - pk)/(pk1 - pk).

Finally if pk and pk1 have values yk and yk1 you get your interpolated value y like this

y = (1-alpha)*yk + alpha*yk1;