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Array interpolation

Before I begin, please accept my apologies that I am not a mathematician and I donโ€™t know the names for what Iโ€™m trying to do ...;) Pointers to any simple English explanations that may help (since at the moment I am purely Googling on based on what, in my opinion, could be a solution).

If you have a multi-parameter array of source values โ€‹โ€‹and you want to increase the size of the array by n times, I think I will need Bicubic interpolation Of course, the image at the top right of this page is representative of what I aim for - to create a graduated stream of values โ€‹โ€‹between the basic starting points of the data, based on the value (s) of their surrounding neighbors, I completely agree that, without increasing the amount of data, I do not increase the resolution of the data; just blurring the edges.

Something like this:

Source grid

to this (and beyond);

Target grid

, () , , , , . getValue (, 0.5, 0.5) BicubicInterpolator, ? , x/y of (0.0,0.0), , (1,1), , .

double[][] source  = new double[][] {{1, 1, 1, 2}, {1, 2, 2, 3}, {1, 2, 2, 3}, {1, 1, 3, 3}};
BicubicInterpolator bi = new BicubicInterpolator();
for (double idx = 0; idx <= 1; idx += 0.1) {
  LOG.info("Result (" + String.format("%3.1f", idx) + ", " + String.format("%3.1f", idx) + ") : " + bi.getValue(source, idx, idx));         
}

, , :

Result (0.0, 0.0) : 2.0
Result (0.1, 0.1) : 2.08222625
Result (0.2, 0.2) : 2.128
Result (0.3, 0.3) : 2.13747125
Result (0.4, 0.4) : 2.11424
Result (0.5, 0.5) : 2.06640625
Result (0.6, 0.6) : 2.00672
Result (0.7, 0.7) : 1.9518312500000001
Result (0.8, 0.8) : 1.92064
Result (0.9, 0.9) : 1.93174625
Result (1.0, 1.0) : 2.0

, 1 3 1 2; 2 2 () . ?

: , quick'n'dirty highscale 30x30;

Grid from Peter's answer

, , , , :

  • ( , 2, 2.2)
  • , ,
  • , , .
  • , , , " ".
+5
1

, "" , , , ...

public static void main(String... args) {
    double[][] source = new double[][]{{1, 1, 1, 2}, {1, 2, 2, 3}, {1, 2, 2, 3}, {1, 1, 3, 3}};
    BicubicInterpolator bi = new BicubicInterpolator();
    for (int i = 0; i <= 30; i++) {
        double idx = i / 10.0;
        System.out.printf("Result (%3.1f, %3.1f) : %3.1f%n", idx, idx, bi.getValue(source, idx, idx));
    }
}

public static class CubicInterpolator {
    public static double getValue(double[] p, double x) {
        int xi = (int) x;
        x -= xi;
        double p0 = p[Math.max(0, xi - 1)];
        double p1 = p[xi];
        double p2 = p[Math.min(p.length - 1,xi + 1)];
        double p3 = p[Math.min(p.length - 1, xi + 2)];
        return p1 + 0.5 * x * (p2 - p0 + x * (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3 + x * (3.0 * (p1 - p2) + p3 - p0)));
    }
}

public static class BicubicInterpolator extends CubicInterpolator {
    private double[] arr = new double[4];

    public double getValue(double[][] p, double x, double y) {
        int xi = (int) x;
        x -= xi;
        arr[0] = getValue(p[Math.max(0, xi - 1)], y);
        arr[1] = getValue(p[xi], y);
        arr[2] = getValue(p[Math.min(p.length - 1,xi + 1)], y);
        arr[3] = getValue(p[Math.min(p.length - 1, xi + 2)], y);
        return getValue(arr, x+ 1);
    }
}


Result (0.0, 0.0) : 1.0
Result (0.1, 0.1) : 1.0
Result (0.2, 0.2) : 1.0
Result (0.3, 0.3) : 1.1
Result (0.4, 0.4) : 1.1
Result (0.5, 0.5) : 1.3
Result (0.6, 0.6) : 1.4
Result (0.7, 0.7) : 1.6
Result (0.8, 0.8) : 1.7
Result (0.9, 0.9) : 1.9
Result (1.0, 1.0) : 2.0
Result (1.1, 1.1) : 2.1
Result (1.2, 1.2) : 2.1
Result (1.3, 1.3) : 2.1
Result (1.4, 1.4) : 2.1
Result (1.5, 1.5) : 2.1
Result (1.6, 1.6) : 2.0
Result (1.7, 1.7) : 2.0
Result (1.8, 1.8) : 1.9
Result (1.9, 1.9) : 1.9
Result (2.0, 2.0) : 2.0
Result (2.1, 2.1) : 2.1
Result (2.2, 2.2) : 2.3
Result (2.3, 2.3) : 2.5
Result (2.4, 2.4) : 2.7
Result (2.5, 2.5) : 2.8
Result (2.6, 2.6) : 2.9
Result (2.7, 2.7) : 3.0
Result (2.8, 2.8) : 3.0
Result (2.9, 2.9) : 3.0
Result (3.0, 3.0) : 3.0

, , 2x2 4x4 . (0.0, 0.0) - (1.0, 1.0) 2 ( 2,2) 2 ( 3,3), , .

double[][] source = new double[][]{{1, 1, 1, 2}, {1, 2, 2, 3}, {1, 2, 2, 3}, {1, 1, 3, 3}};
BicubicInterpolator bi = new BicubicInterpolator();
for (int i = -10; i <= 20; i++) {
    double idx = i / 10.0;
    System.out.printf("Result (%3.1f, %3.1f) : %3.1f%n", idx, idx, bi.getValue(source, idx, idx));
}


Result (-1.0, -1.0) : -5.0
Result (-0.9, -0.9) : -2.8
Result (-0.8, -0.8) : -1.2
Result (-0.7, -0.7) : -0.2
Result (-0.6, -0.6) : 0.5
Result (-0.5, -0.5) : 1.0
Result (-0.4, -0.4) : 1.3
Result (-0.3, -0.3) : 1.5
Result (-0.2, -0.2) : 1.7
Result (-0.1, -0.1) : 1.9
Result (0.0, 0.0) : 2.0
Result (0.1, 0.1) : 2.1
Result (0.2, 0.2) : 2.1
Result (0.3, 0.3) : 2.1
Result (0.4, 0.4) : 2.1
Result (0.5, 0.5) : 2.1
Result (0.6, 0.6) : 2.0
Result (0.7, 0.7) : 2.0
Result (0.8, 0.8) : 1.9
Result (0.9, 0.9) : 1.9
Result (1.0, 1.0) : 2.0
Result (1.1, 1.1) : 2.1
Result (1.2, 1.2) : 2.3
Result (1.3, 1.3) : 2.5
Result (1.4, 1.4) : 2.7
Result (1.5, 1.5) : 2.8
Result (1.6, 1.6) : 2.7
Result (1.7, 1.7) : 2.1
Result (1.8, 1.8) : 0.9
Result (1.9, 1.9) : -1.4
Result (2.0, 2.0) : -5.0
+5

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