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<Vector3> 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);}
}