Unity中贝塞尔曲线(Bezier)，实现二阶和三阶

下图为贝塞尔曲线一阶，二阶，三阶，四阶。

  图片来自 https://www.jasondavies.com/animated-bezier/

刚开始知道贝塞尔曲线的时候觉得这东西好难，今天花了点时间想了一下

发现在Unity中实现贝塞尔曲线还是很容易的。

贝塞尔曲线二阶的原理：

 p0到p1的点（红色0到1），与p1到p2的点（黄色0到1）连接成的线（蓝色0到1），这条线经过的轨迹就是贝塞尔曲线。

先上动图：

 

代码如下：

/// <summary>
    /// 曲线圆滑度
    /// </summary>
    public int nultiple = 5;
    public List<Vector3> allPoints = new List<Vector3>();

    public RectTransform p1;
    public RectTransform p2;
    public RectTransform p3;

    private void Update()
    {
        CreatTwoBezierCurve(p1.position, p2.position, p3.position);
        for (int i = 1; i < allPoints.Count; i++)
        {
            Debug.DrawLine(allPoints[i - 1], allPoints[i], Color.blue);
        }
    }

    /// <summary>
    ///二阶贝塞尔
    /// </summary>
    /// <param name="startPoint"></param>
    /// <param name="endPoint"></param>
    /// <param name="middlePoint"></param>
    public void CreatTwoBezierCurve(Vector3 startPoint, Vector3 endPoint, Vector3 middlePoint)
    {
        allPoints.Clear();
        for (int i = 0; i < nultiple; i++)
        {
            float tempPercent = (float)i / (float)nultiple;
            float dis1 = Vector3.Distance(startPoint, middlePoint);
            Vector3 point1 = startPoint + Vector3.Normalize(middlePoint - startPoint) * dis1 * tempPercent;
            float dis2 = Vector3.Distance(middlePoint, endPoint);
            Vector3 point2 = middlePoint + Vector3.Normalize(endPoint - middlePoint) * dis2 * tempPercent;
            float dis3 = Vector3.Distance(point1, point2);
            Vector3 linePoint = point1 + Vector3.Normalize(point2 - point1) * dis3 * tempPercent;
            allPoints.Add(linePoint);
        }
        allPoints.Add(endPoint);
    }

其中p1是起点，p2是终点，p3是中间控制点。

三阶原理跟二阶相同：

先上动图：

再上代码：

    /// <summary>
    /// 曲线圆滑度
    /// </summary>
    public int nultiple = 5;
    public List<Vector3> allPoints = new List<Vector3>();

    public RectTransform p1;
    public RectTransform p2;
    public RectTransform p3;
    public RectTransform p4;

    private void Update()
    {
        // CreatTwoBezierCurve(p1.position, p2.position, p3.position);
        CreatThreeBezierCurve(p1.position, p2.position, p3.position, p4.position);
        for (int i = 1; i < allPoints.Count; i++)
        {
            Debug.DrawLine(allPoints[i - 1], allPoints[i], Color.blue);
        }
    }

    /// <summary>
    /// 三阶贝塞尔
    /// </summary>
    /// <param name="startPoint"></param>
    /// <param name="endPoint"></param>
    /// <param name="middlePoint1"></param>
    public void CreatThreeBezierCurve(Vector3 startPoint, Vector3 endPoint, Vector3 middlePoint1, Vector3 middlePoint2)
    {
        allPoints.Clear();
        for (int i = 0; i < nultiple; i++)
        {
            float tempPercent = (float)i / (float)nultiple;
            float dis1 = Vector3.Distance(startPoint, middlePoint1);
            Vector3 pointL1 = startPoint + Vector3.Normalize(middlePoint1 - startPoint) * dis1 * tempPercent;
            float dis2 = Vector3.Distance(middlePoint1, middlePoint2);
            Vector3 pointL2 = middlePoint1 + Vector3.Normalize(middlePoint2 - middlePoint1) * dis2 * tempPercent;
            float dis3 = Vector3.Distance(pointL1, pointL2);
            Vector3 pointLeft = pointL1 + Vector3.Normalize(pointL2 - pointL1) * dis3 * tempPercent;


            float dis4 = Vector3.Distance(middlePoint2, endPoint);
            Vector3 pointR1 = middlePoint2 + Vector3.Normalize(endPoint - middlePoint2) * dis4 * tempPercent;
            float dis5 = Vector3.Distance(pointL2, pointR1);
            Vector3 pointRight = pointL2 + Vector3.Normalize(pointR1 - pointL2) * dis5 * tempPercent;


            float disLeftAndRight = Vector3.Distance(pointLeft, pointRight);
            Vector3 linePoint = pointLeft + Vector3.Normalize(pointRight - pointLeft) * disLeftAndRight * tempPercent;
            allPoints.Add(linePoint);
        }
        allPoints.Add(endPoint);
    }

就这样。拜拜~