How to smooth interpolation of a float array into a bigger array?

Question

I'm stuck with interpolation in Swift. Can anyone help me with that?

I want to interpolate the float array (say [0, 0, 100, 25, 0, 0, 0, 25, 0, 0, 0]) into another array with some given size (for example 128). I found an article (Use Linear Interpolation to Construct New Data Points) that shows, how to achieve this stuff.

There are two ways (you can see the results below, how they perform):

• Linear Interpolation using vDSP_vgenp and
• Smoother (but not for my purposes) Interpolation using vDSP_vlint

The problem is both techniques don't realize my expectations, which illustrated in Screenshot 3. How can I make my interpolated distribution smoother? I want to see a cube-like curve.

Initial Plot:

Linear Interpolation:

import Accelerate

let n = vDSP_Length(128)
let stride = vDSP_Stride(1)

let values: [Float] = [0, 0, 100, 25, 0, 0, 0, 25, 0, 0, 0]
let indices: [Float] = [0, 11, 23, 34, 46, 58, 69, 81, 93, 104, 116]

var result = [Float](repeating: 0, count: Int(n))

vDSP_vgenp(values, stride, indices, stride, &result, stride, n, vDSP_Length(values.count))

Smooth Interpolation:

import Accelerate
import AVFoundation

let n = vDSP_Length(1024)
let stride = vDSP_Stride(1)

let values: [Float] = [0, 0, 100, 25, 0, 0, 0, 25, 0, 0, 0]
let denominator = Float(n) / Float(values.count - 1)

let control: [Float] = (0 ... n).map {
    let x = Float($0) / denominator
    return floor(x) + simd_smoothstep(0, 1, simd_fract(x))
}

var result = [Float](repeating: 0, count: Int(n))

vDSP_vlint(values, control, stride, &result, stride, n, vDSP_Length(values.count))

Answer 1

It seems to me that the vDSP_vqint quadratic interpolation functions would solve the problem. See the discussion at https://developer.apple.com/documentation/accelerate/1449942-vdsp_vqint.