using System;
using UnityEngine;

namespace Bezier
{
    public class BezierCurve
    {
        private float[] valuesX;
        private float[] valuesY;
        private float[] valuesZ;

        public BezierCurve(Vector3[] vectors)
        {
            SetControlPoints(vectors);
        }

        public void SetControlPoints(Vector3[] vectors)
        {
            valuesX = new float[vectors.Length];
            valuesY = new float[vectors.Length];
            valuesZ = new float[vectors.Length];

            for (int i = 0; i < vectors.Length; i++)
            {
                valuesX[i] = vectors[i].x;
                valuesY[i] = vectors[i].y;
                valuesZ[i] = vectors[i].z;
            }
        }

        public Vector3 GetValue(float t)
        {
            return new Vector3(
                BezierMath.GetValueHorner(t, this.valuesX),
                BezierMath.GetValueHorner(t, this.valuesY),
                BezierMath.GetValueHorner(t, this.valuesZ)
                );
        }
    }

    public static class BezierMath
    {
        // Info
        // http://www.gamedev.net/page/resources/_/technical/math-and-physics/practical-guide-to-bezier-curves-r3166
        // http://pomax.github.io/bezierinfo/

        /// <summary>
        /// Точка кривой методом Горнера
        /// </summary>
        /// <param name="t">Параметр от 0.0 до 1.0</param>
        /// <param name="controlPoints">Управляющие точки по одной из координат</param>
        /// <returns>Координата точки</returns>
        static public float GetValueHorner(float t, float[] controlPoints)
        {
            if (controlPoints.Length == 0) // А для одной точки возвращается сама точка
                throw new ArgumentException("controlPoints.Length == 0.");
            float u = 1.0f - t;
            float bc = 1;
            float tn = 1;
            float tmp = controlPoints[0] * u;
            int order = controlPoints.Length - 1;

            for (int i = 1; i < order; i++)
            {
                tn *= t;
                bc *= (float)(order - i + 1) / i;
                tmp = (tmp + tn * bc * controlPoints[i]) * u;
            }
            return (tmp + tn * t * controlPoints[order]);
        }
    }
}

using UnityEngine;

[RequireComponent(typeof(LineRenderer))]
public class BezierDrawer : MonoBehaviour
{
    public Vector3[] ControlPoints = new Vector3[]{
        new Vector3(-3f, 0f, 0f),
        new Vector3(0f, 4f, 0f),
        new Vector3(0f, 4f, 0f),
        new Vector3(3f, 0f, 0f),
    };

    Bezier.BezierCurve curve;

    void Update()
    {
        curve = new Bezier.BezierCurve(ControlPoints);

        var lr = GetComponent<LineRenderer>();
        const int vertexCount = 100;
        lr.SetVertexCount(vertexCount);
        for (int c = 0; c < vertexCount; c++)
        {
            Vector3 currPos = curve.GetValue((float)c / (vertexCount - 1));
            lr.SetPosition(c, currPos);
        }
    }
}