[游戏开发]贝塞尔曲线在Unity里的简单例子实现

贝塞尔曲线一阶是线性曲线：

公式 : B1(t) = (1-t)* p0 + t* p1
二阶的贝塞尔曲线是建立在一阶的基础上，B2(t) = B1(t) * (1-t) + tB1(t)
化简后可得 : B2(t) = (1 - t) * ((1 - t) * p0 + t * p1) + t * ((1 - t) * p0 + t * p1)
注：一阶是(1-t) * p0 + tp1

c#代码如下所示

public class BezierMath
{
    /// <summary>
    /// 二阶贝塞尔曲线
    /// </summary>
    /// <param name="p0"></param>
    /// <param name="p1"></param>
    /// <param name="p2"></param>
    /// <param name="t"></param>
    /// <returns></returns>
    public static Vector3 Bezier_2(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        return (1 - t) * ((1 - t) * p0 + t * p1) + t * ((1 - t) * p0 + t * p1);
    }

    /// <summary>
    /// 三阶贝塞尔曲线
    /// </summary>
    /// <param name="p0"></param>
    /// <param name="p1"></param>
    /// <param name="p2"></param>
    /// <param name="p3"></param>
    /// <param name="t"></param>
    /// <returns></returns>
    public static Vector3 Bezier_3(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        return (1 - t) * (((1 - t) * p0 + t * p1) + t * ((1 - t) * p0 + t * p1)) + t * ((1 - t) * p0 + t * p1) + t * ((1 - t) * p0 + t * p1);
    }

    /// <summary>
    /// 递归实现贝塞尔曲线
    /// </summary>
    /// <param name="p"></param>
    /// <param name="t"></param>
    /// <returns></returns>
    public static Vector3 Bezier(List<Vector3> p, float t)
    {
        if (p.Count < 2)
            return p[0];
        List<Vector3> list2 = new List<Vector3>();
        for (int i = 0; i < p.Count - 1; i++)
        {
            Vector3 pos = (1 - t) * p[i] + t * p[i + 1];
            list2.Add(pos);
        }
        return Bezier(list2, t);
    }
}

public class Test : MonoBehaviour
{
    // Start is called before the first frame update
    public List<Transform> go;
    private List<Vector3> pos = new List<Vector3>();
    void Start()
    {
        for (int i = 0; i < go.Count - 1; i++)
        {
            pos.Add(go[i].position);
        }
    }

    // Update is called once per frame
    void Update()
    {
        for (float i = 0; i < 1; i += 0.1f)
        {
            Debug.DrawLine(BezierMath.Bezier(pos, i), BezierMath.Bezier(pos, i + 0.1f), Color.blue);
        }
    }
}

![

运行效果如下：