Bezier.cs

using UnityEngine;

public static class Bezier
{
    public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        t = Mathf.Clamp01(t);
        float oneMinusT = 1f - t;
        return oneMinusT * oneMinusT * p0 + 2f * oneMinusT * t * p1 + t * t * p2;
    }

    public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        return 2f * (1f - t) * (p1 - p0) + 2f * t * (p2 - p1);
    }

    public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        t = Mathf.Clamp01(t);
        float oneMinusT = 1f - t;
        return oneMinusT * oneMinusT * oneMinusT * p0 + 3f * oneMinusT * oneMinusT * t * p1 + 3f * oneMinusT * t * t * p2 + t * t * t * p3;
    }

    public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        t = Mathf.Clamp01(t);
        float oneMinusT = 1f - t;
        return 3f * oneMinusT * oneMinusT * (p1 - p0) + 6f * oneMinusT * t * (p2 - p1) + 3f * t * t * (p3 - p2);
    }
}