Question

I’ve got a vector of samples that form a curve. Let’s imagine there are 1000 points in it. If I want to stretch it to fill 1500 points, what is the simplest algorithm that gives decent results? I’m looking for something that is just a few lines of C/C++.

I’ll always want to increase the size of the vector, and the new vector can be anywhere from 1.1x to 50x the size of the current vector.

Thanks!

Answer 1

Here’s C++ for linear and quadratic interpolation.
interp1( 5.3, a, n ) is a[5] + .3 * (a[6] – a[5]), .3 of the way from a[5] to a[6];
interp1array( a, 1000, b, 1500 ) would stretch a to b.
interp2( 5.3, a, n ) draws a parabola through the 3 nearest points a[4] a[5] a[6]: smoother than interp1 but still fast.
(Splines use 4 nearest points, smoother yet; if you read python, see
basic-spline-interpolation-in-a-few-lines-of-numpy.

// linear, quadratic interpolation in arrays
// from interpol.py denis 2010-07-23 July

#include <stdio.h>
#include <stdlib.h>

// linear interpolate x in an array
// inline
float interp1( float x, float a[], int n )
{
    if( x <= 0 )  return a[0];
    if( x >= n - 1 )  return a[n-1];
    int j = int(x);
    return a[j] + (x - j) * ( a[j+1] - a[j] );
}

// linear interpolate array a[] -> array b[]
void interp1array( float a[], int n, float b[], int m )
{
    float step = float( n - 1 ) / (m - 1);
    for( int j = 0; j < m; j ++ )
    {
        b[j] = interp1( j*step, a, n );
    }
}

//..................................................................
// parabola through 3 points, -1 < x < 1
float parabola( float x, float f_1, float f0, float f1 )
{
    if( x <= -1 )  return f_1; 
    if( x >= 1 )  return f1; 
    float l = f0 - x * (f_1 - f0);
    float r = f0 + x * (f1 - f0);
    return (l + r + x * (r - l)) / 2;
}

// quadratic interpolate x in an array
float interp2( float x, float a[], int n )
{
    if( x <= .5  ||  x >= n - 1.5 )
        return interp1( x, a, n );
    int j = int( x + .5 );
    float t = 2 * (x - j);  // -1 .. 1
    return parabola( t, (a[j-1] + a[j]) / 2, a[j], (a[j] + a[j+1]) / 2 );
}

    // quadratic interpolate array a[] -> array b[]
void interp2array( float a[], int n, float b[], int m )
{
    float step = float( n - 1 ) / (m - 1);
    for( int j = 0; j < m; j ++ ){
        b[j] = interp2( j*step, a, n );
    }
}

int main( int argc, char* argv[] )
{
        // a.out [n m] --
    int n = 10, m = 100;
    int *ns[] = { &n, &m, 0 },
        **np = ns;
    char* arg;
    for( argv ++;  (arg = *argv) && *np;  argv ++, np ++ )
        **np = atoi( arg );
    printf( "n: %d  m: %d\n", n, m );

    float a[n], b[m];
    for( int j = 0; j < n; j ++ ){
        a[j] = j * j;
    }
    interp2array( a, n, b, m );  // a[] -> b[]

    for( int j = 0; j < m; j ++ ){
        printf( "%.1f ", b[j] );
    }
    printf( "\n" );
}