Calculate values of same distribution with given min, max and resolution

Question

I need some help to build a mathematical function, which takes three parameters (min, max, resolution) and returns values (nearly) in this distribution:

5
10.2
13.45
15.4
16.7
17.35
18

In this example, min is 5, max is 18 and there are 7 steps.

So I calculated the range, which is max - min (=13) and used these percentages (can be adjusted a bit, if calculation gets easier)

40%
65%
80%
90%
95%
100%

of the range, which is added to the min value.

13 * 0.4 + 5 = 10.2
13 * 0.65 + 5 = 13.45
...

The graph of these values, should be the same if the resolution is higher: If there are 100 instead of 7 steps, the distribution/graph should be the same. But how do I calculate the value of each step?

function calcValues(min, max, steps) {
    const data = []
    const range = max - min
    for (i = 0; i < steps; i++) {
        const value = range * whichValueIsNeededHere + min
        data.push(value)
    }
    return data
}

Answer 1

First Approach:

This graph seems close to the y = a(x^3) + b(x^2) + c(x) + d. I was able to retrieve the values of a, b, c and d with the help of the given (x,y) pairs. The values are:

a = 0.08125

b = -1.421875

c = 8.896875

d = -2.55625

Now, if you substitute different x values, you will be getting exact values (or close) to y. The minimal difference in the y values could be because of some constant which has not been taken into consideration in the equation (but like I said, the difference is very minimal).

The approach to use this equation is as follows:

1. Divide the max(x) - min(x) by steps to get the stepX.

2. Add the stepX to different values of x (within the range of x values i.e. [1,7]).

3. Substitute x values in the equation to get different y values.

Note - stepX is each step that needs to be taken to go from min to max in the X-axis.

This is a manual process for you to test the integrity of the graph for different (x,y) pairs.

Second Approach:

As you confirmed that you need the function to work only for a particular graph, we can use the given (x,y) pairs as the reference in the program. Well, this could be a trick or hack, whatever you say!!.

function traverseGraph(source, destination, steps) {
    // As the scenario is for a particular graph only, we can use the example for the reference
    const xValues = [1, 2, 3, 4, 5, 6, 7];
    const yPattern = [5, 10.2, 13.45, 15.4, 16.7, 17.35, 18];

    const diffX = destination[0] - source[0];
    const diffY = destination[1] - source[1];

    const stepX = diffX / (steps - 1);
    
    const ratio = (xValues.length - 1) / (steps - 1);

    const points = [];
    for (let i = 0; i < steps; i++) {
        const xIndex = Math.floor(i * ratio);
        const yIndex = Math.min(xIndex + 1, xValues.length - 1);

        const x = source[0] + stepX * i;
        const y = yPattern[xIndex] + (yPattern[yIndex] - yPattern[xIndex]) * (i * ratio - xIndex);

        points.push([x, y]);
    }

    return points;
}

function calcValues(min, max, steps) {
  const source = [1, min];
  const destination = [7, max];
  return traverseGraph(source, destination, steps);
}

console.log(calcValues(5, 18, 20))

I tested the output coming from the program and the equation for the same (x,y) pairs and again the difference is very minimal. So, I am not sure how much this has helped you but you can give it a try at least from your side using the approaches shared above.

PS - You can use this link to test the output from the equation.