Utils.cs

using UnityEngine;

public static class Utils
{
    /*
     *  x       - value
     *  v       - velocity
     *  xt      - target value
     *  zeta    - damping ratio
     *  omega   - oscillation frequency
     *  h       - timestep
     */
    public static void Spring(ref float x, ref float v, float xt, float zeta, float omega, float h)
    {
        var f = 1.0f + 2.0f * h * zeta * omega;
        var oo = omega * omega;
        var hhoo = h * h * oo;
        var d = 1.0f / (f + hhoo);
        var numX = f * x + h * v + hhoo * xt;
        var numV = v + h * oo * (xt - x);
        x = numX * d;
        v = numV * d;
    }

    public static void Spring(ref Vector2 x, ref Vector2 v, Vector2 xt, float zeta, float omega, float h)
    {
        var f = 1.0f + 2.0f * h * zeta * omega;
        var oo = omega * omega;
        var hhoo = h * h * oo;
        var d = 1.0f / (f + hhoo);
        var numX = f * x + h * v + hhoo * xt;
        var numV = v + h * oo * (xt - x);
        x = numX * d;
        v = numV * d;
    }

    public static void Spring(ref Vector3 x, ref Vector3 v, Vector3 xt, float zeta, float omega, float h)
    {
        var f = 1.0f + 2.0f * h * zeta * omega;
        var oo = omega * omega;
        var hhoo = h * h * oo;
        var d = 1.0f / (f + hhoo);
        var numX = f * x + h * v + hhoo * xt;
        var numV = v + h * oo * (xt - x);
        x = numX * d;
        v = numV * d;
    }
}