XiuXianGame/Assets/Scripts/Core/Utility/Parabola3DPath.cs

using UnityEngine;

namespace Core.Utility
{
    public class Parabola3DPath
    {
        public Vector3 startPos;
        public Vector3 targetPos;
        public float gravity = 9.8f;
        public Vector3 initialVelocity; // 物体的初始速度

        public float totalFlightTime;

        public Parabola3DPath(Vector3 startPos,Vector3 targetPos)
        {
            this.startPos = startPos;
            this.targetPos = targetPos;
            CalculateInitialVelocity();
        }

        // 计算发射物体的初始速度和飞行时间
        void CalculateInitialVelocity()
        {
            Vector3 startPosition = startPos;
            Vector3 targetPosition = targetPos;

            // 计算目标的水平距离和垂直高度差
            float deltaX = targetPosition.x - startPosition.x;
            float deltaY = targetPosition.y - startPosition.y;
            float deltaZ = targetPosition.z - startPosition.z;

            // 计算水平距离（包括 X 和 Z 轴）
            float horizontalDistance = Mathf.Sqrt(deltaX * deltaX + deltaZ * deltaZ);

            // 计算飞行所需的时间
            totalFlightTime = CalculateFlightTime(horizontalDistance, deltaY);

            // 计算发射的初速度
            initialVelocity = CalculateInitialVelocityVector(deltaX, deltaZ, deltaY, totalFlightTime);
        }

        // 计算飞行时间
        float CalculateFlightTime(float horizontalDistance, float deltaY)
        {
            // 使用物理公式来计算飞行时间：竖直分量的运动方程
            // time = sqrt(2 * (deltaY + horizontalDistance * tan(45))) / gravity
            float time = Mathf.Sqrt((2 * (deltaY + horizontalDistance * Mathf.Tan(Mathf.Deg2Rad * 45f))) / gravity);
            return time;
        }

        // 计算初速度向量
        Vector3 CalculateInitialVelocityVector(float deltaX, float deltaZ, float deltaY, float timeToTarget)
        {
            // 计算水平速度分量
            float v_x = deltaX / timeToTarget; // X轴速度
            float v_z = deltaZ / timeToTarget; // Z轴速度

            // 垂直速度
            float v_y = (deltaY + 0.5f * gravity * timeToTarget * timeToTarget) / timeToTarget;

            // 初速度向量
            Vector3 velocity = new Vector3(v_x, v_y, v_z);
            return velocity;
        }

        public Vector3 GetPositionAtTime(float t)
        {
            // 计算每个轴的位移
            float deltaX = initialVelocity.x * t;
            float deltaY = initialVelocity.y * t - 0.5f * gravity * t * t;
            float deltaZ = initialVelocity.z * t;
            // 返回当前位置
            return new Vector3(startPos.x + deltaX, startPos.y + deltaY, startPos.z + deltaZ);
        }
    }
}