二阶贝塞尔曲线公式

 三阶贝塞尔曲线公式

C++ 三维坐标点  二阶到N阶源码

//二阶公式：
FVector BezierUtils::CalculateBezierPoint(float t, FVector startPoint, FVector controlPoint, FVector endPoint)
{
	 float t1 = (1 - t) * (1 - t);
	 float t2 = 2 * t * (1 - t);
	 float t3 = t * t;
	 return t1 * startPoint + t2 * controlPoint + t3 * endPoint;
}

// 三阶贝塞尔曲线
FVector BezierUtils::BezierCurve(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
{
    Vector3 B = Vector3.zero;
    float t1 = (1 - t) * (1 - t) * (1 - t);
    float t2 = 3 * t * (1 - t) * (1 - t);
    float t3 = 3 * t * t * (1 - t);
    float t4 = t * t * t;
    return t1 * p0 + t2 * p1 + t3 * p2 + t4 * p3;
}
 
/// n阶贝塞尔曲线
FVector BezierUtils::BezierCurve(List<FVector3> pointList, float t)
{
    FVector B = FVector(0,0,0);
    if (pointList == null)
    {
        return B;
    }
    if (pointList.Count < 2)
    {
        return pointList[0];
    }
 
    List<Vector3> tempPointList = new List<Vector3>();
    for (int i = 0; i < pointList.Count - 1; i++)
    {
        Vector3 tempPoint = BezierCurve(pointList[i], pointList[i + 1], t);
        tempPointList.Add(tempPoint);
    }
    return BezierCurve(tempPointList, t);
}

C# 三维坐标点  二阶到N阶源码

using UnityEngine;
using System.Collections.Generic;
 
/// <summary>
/// 贝塞尔工具类
/// </summary>
public static class BezierUtils
{
    /// <summary>
    /// 线性贝塞尔曲线
    /// </summary>
    public static Vector3 BezierCurve(Vector3 p0, Vector3 p1, float t)
    {
        Vector3 B = Vector3.zero;
        B = (1 - t) * p0 + t * p1;
        return B;
    }
 
    /// <summary>
    /// 二阶贝塞尔曲线
    /// </summary>
    public static Vector3 BezierCurve(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        Vector3 B = Vector3.zero;
        float t1 = (1 - t) * (1 - t);
        float t2 = 2 * t * (1 - t);
        float t3 = t * t;
        B = t1 * p0 + t2 * p1 + t3 * p2;
        return B;
    }
 
    /// <summary>
    /// 三阶贝塞尔曲线
    /// </summary>
    public static Vector3 BezierCurve(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        Vector3 B = Vector3.zero;
        float t1 = (1 - t) * (1 - t) * (1 - t);
        float t2 = 3 * t * (1 - t) * (1 - t);
        float t3 = 3 * t * t * (1 - t);
        float t4 = t * t * t;
        B = t1 * p0 + t2 * p1 + t3 * p2 + t4 * p3;
        return B;
    }
 
    /// <summary>
    /// n阶贝塞尔曲线
    /// </summary>
    public static Vector3 BezierCurve(List<Vector3> pointList, float t)
    {
        Vector3 B = Vector3.zero;
        if (pointList == null)
        {
            return B;
        }
        if (pointList.Count < 2)
        {
            return pointList[0];
        }
 
        List<Vector3> tempPointList = new List<Vector3>();
        for (int i = 0; i < pointList.Count - 1; i++)
        {
            Vector3 tempPoint = BezierCurve(pointList[i], pointList[i + 1], t);
            tempPointList.Add(tempPoint);
        }
        return BezierCurve(tempPointList, t);
    }
}