一阶贝塞尔曲线

使用两个点绘制线段
p3=p1+(p2-p1)*t

p1:起点;
p2:终点;
t:0-1;
p3:线段L12上的点
两个点和t的变化(0-1)可得到一条线段

二阶贝塞尔曲线

使用三个点绘制曲线
p12=p1+(p2-p1)*t
p23=p2+(p3-p2)*t
p123=p12+(p23-p12)*t
p12是线段L12上的点，
p23是线段L23上的点，
p123是线段L12 23上的点
控制p2的位置，可改变曲线的弯曲程度

示例

一阶贝塞尔，二阶贝塞尔

using UnityEngine;
public static class Curve
{
    public static Vector3 CurveOne(Vector3 begin, Vector3 end, float percentage)
    {
        return begin + (end - begin) * Mathf.Clamp01(percentage);
    }
    public static Vector3 CurveTwo(Vector3 begin, Vector3 center, Vector3 end, float percentage)
    {
        return CurveOne(CurveOne(begin, center, percentage), CurveOne(center, end, percentage), percentage);
    }
}

绘制曲线

using UnityEngine;
public class DrawCurve : MonoBehaviour
{
    public Transform point;//位置1
    public Transform point2;
    public Transform point3;
    [Range(1, 1000)]
    public int length;//曲线平滑程度
    float t;
    public LineRenderer line;//显示曲线
    private void Update()
    {
        if (line.positionCount != length + 1)
            line.positionCount = length + 1;
        for (int i = 0; i <= length; i++)
        {
            t = i;
            line.SetPosition(i, Curve.CurveTwo(point.position, point2.position, point3.position, t / length));
        }
    }
}

改变p2位置

using UnityEngine;
public class ChangePos : MonoBehaviour
{
    [SerializeField] float moveSpeed = 10;
    private void Update()
    {
        transform.position += transform.up * Input.GetAxis("Vertical") * Time.deltaTime * moveSpeed;
    }
}