BezierCurve.cs

using UnityEngine;

public class BezierCurve
{

    public Vector2[] ControlPoints { get; set; }

    public BezierCurve(Vector2[] controlPoints)
    {
        ControlPoints = controlPoints;
    }

    public Vector2 Evaluate(float t)
    {
        if (ControlPoints == null)
        {
            return Vector2.zero;
        }

        var result = Vector2.zero;
        int n = ControlPoints.Length;
        for (int i = 0; i < n; i++)
        {
            result += ControlPoints[i] * Bernstein(n - 1, i, t);
        }

        return result;
    }

    static float Bernstein(int n, int i, float t)
    {
        return Binomial(n, i) * Mathf.Pow(t, i) * Mathf.Pow(1 - t, n - i);
    }

    static float Binomial(int n, int k)
    {
        return Factorial(n) / (Factorial(k) * Factorial(n - k));
    }

    static float Factorial(int a)
    {
        float result = 1f;
        for (int i = 2; i <= a; i++)
        {
            result *= i;
        }

        return result;
    }

}