XiuXianGame/Assets/Scripts/Core/Utility/QuinticBezierCurve.cs

using UnityEngine;

namespace Core.Utility
{
    public class QuinticBezierCurve: MonoBehaviour
    {
        // 5个控制点
        public Vector3 p0; // 起点
        public Vector3 p1; // 控制点1
        public Vector3 p2; // 控制点2
        public Vector3 p3; // 控制点3
        public Vector3 p4; // 终点

        // 计算四阶贝塞尔曲线上的点
        // t: 参数，范围 [0, 1]
        public Vector3 CalculatePoint(float t)
        {
            // 确保 t 在 0-1 范围内
            t = Mathf.Clamp01(t);

            // 四阶贝塞尔曲线公式
            // B(t) = (1-t)^4 * P0 + 4(1-t)^3 * t * P1 + 6(1-t)^2 * t^2 * P2 + 4(1-t) * t^3 * P3 + t^4 * P4
            float u = 1 - t;
            float t2 = t * t;
            float t3 = t2 * t;
            float t4 = t3 * t;
            float u2 = u * u;
            float u3 = u2 * u;
            float u4 = u3 * u;

            Vector3 point = (u4 * p0) +
                            (4 * u3 * t * p1) +
                            (6 * u2 * t2 * p2) +
                            (4 * u * t3 * p3) +
                            (t4 * p4);

            return point;
        }

        // 示例：在场景中绘制曲线
        void OnDrawGizmos()
        {
            Gizmos.color = Color.yellow;
        
            // 绘制控制点
            Gizmos.DrawSphere(p0, 0.1f);
            Gizmos.DrawSphere(p1, 0.1f);
            Gizmos.DrawSphere(p2, 0.1f);
            Gizmos.DrawSphere(p3, 0.1f);
            Gizmos.DrawSphere(p4, 0.1f);

            // 绘制曲线
            Vector3 previousPoint = p0;
            int segments = 50;
        
            for (int i = 1; i <= segments; i++)
            {
                float t = i / (float)segments;
                Vector3 currentPoint = CalculatePoint(t);
                Gizmos.DrawLine(previousPoint, currentPoint);
                previousPoint = currentPoint;
            }
        }

        // 获取曲线的切线（导数）
        public Vector3 GetTangent(float t)
        {
            t = Mathf.Clamp01(t);
            float u = 1 - t;
        
            // 四阶贝塞尔曲线的导数
            Vector3 tangent = 4 * (u * u * u * (p1 - p0) +
                                   3 * u * u * t * (p2 - p1) +
                                   3 * u * t * t * (p3 - p2) +
                                   t * t * t * (p4 - p3));
        
            return tangent.normalized;
        }
    }
}