unity学习2——基于物理模拟的太阳系模型
游戏对象运动的本质是什么？
游戏对象的运动，在本质上是在离散的时间点上，物体按照物理引擎说运算出的，呈现出不同的位置。
请用三种方法以上方法，实现物体的抛物线运动。（如，修改Transform属性，使用向量Vector3的方法…）
方法一：矢量叠加法
众所周知，一个抛物运动由水平方向的匀速和竖直方向的匀加速运动构成。
方法二：collider 的gravity 模拟
类似于上面，但云加速运动部分采用collider组件自带的gravity功能。
方法三：transform.position 描述表达式法
写一个程序，实现一个完整的太阳系， 其他星球围绕太阳的转速必须不一样，且不在一个法平面上。
实现思路：利用transform的rotate、lookat、等方法，看上去像但并不真实的模拟出太阳系的运动。
另一种实现思路：使用万有引力定律和牛顿第二运动定律，列出物体动力学方程。
第二种方法的优点：可以模拟出水星的章动（椭圆周期运动上叠加小周期简谐振动）、各行星的椭圆轨道、冥王星和海王星的引力影响轨道。
引力模拟代码如下
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class GravitySimulate : MonoBehaviour {
public List graviEffectWith;
public Vector3 TotalGravitationalForce;
// Use this for initialization
void Start () {
// this.GetComponent().speed=startsetspeed();
}
public Vector3 startsetspeed()
{
this.GetComponent().speed.z = Mathf.Sqrt(graviEffectWith[0].GetComponent().mass /
Vector3.Distance(this.transform.position, graviEffectWith[0].transform.position)
);
return new Vector3(0, 0, this.GetComponent().speed.z);
}
public void setSpeed(Vector3 input)
{
this.GetComponent().speed = input;
}
// Update is called once per frame
void FixedUpdate () {
TotalGravitationalForce.Set(0, 0, 0);
foreach (GameObject i in graviEffectWith)
{
TotalGravitationalForce += -(i.GetComponent().mass) /
(Vector3.Distance(this.transform.position, i.transform.position) * Vector3.Distance(this.transform.position, i.transform.position) * Vector3.Distance(this.transform.position, i.transform.position))
* (this.transform.position - i.transform.position);
}
this.GetComponent().speed += TotalGravitationalForce*Time.deltaTime;
this.transform.position+=(this.GetComponent().speed)*Time.deltaTime;
}
}
我们可以看到，简单的使用牛顿第二定律就可以画出真实的椭圆轨道。
然后我们用一个PhysicalModel组件存储一些物理数据，此处略过
在gameController里，我们储存了九大行星的数据（重点是距离、黄道交角）
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class SolarController : MonoBehaviour {
public GameObject SunPrefabs;
public GameObject Sun;
public GameObject[] SolarPlanetPrefabs;
public GameObject[] SolarPlanet;
public GameObject MoonPrefab;
public GameObject Moon;
Quaternion q;
// Use this for initialization
void Awake () {
SolarPlanet = new GameObject[9];
Sun = GameObject.Instantiate(SunPrefabs);
for (int i=0; i < SolarPlanetPrefabs.Length; ++i)
{
SolarPlanet[i] = GameObject.Instantiate(SolarPlanetPrefabs[i]);
SolarPlanet[i].GetComponent().graviEffectWith.Add(Sun);
// SolarPlanet[i].GetComponent().startsetspeed();
}
/*此处初始化行星*/
SolarPlanet[0].GetComponent().SetPara(0.0553f,0.383f,3.87f);//质量半径距离
SolarPlanet[1].GetComponent().SetPara(0.815f,0.950f,7.23f);
SolarPlanet[2].GetComponent().SetPara(1,1,10);
SolarPlanet[3].GetComponent().SetPara(0.107f, 0.532f, 15.24f);
// SolarPlanet[4].GetComponent().SetPara(95.159f,9.14f,52.03f);
// SolarPlanet[5].GetComponent().SetPara(317.83f,10.97f,95.39f);
// SolarPlanet[6].GetComponent().SetPara(14.536f,3.98f,191.8f);
//Sun.GetComponent().SetPara(332837f, 109.25f, 0);
Sun.GetComponent().SetPara(33237f, 10.25f, 0);
/*下面设定初始速度*/
for (int i = 0; i < SolarPlanetPrefabs.Length; ++i)
{
SolarPlanet[i].GetComponent().setSpeed(planetspeed(i));
SolarPlanet[i].GetComponent().setRotateAxis(selfrotateAxis(i));
}
/*下面设定月球相关*/
Moon = Instantiate(MoonPrefab);
Moon.GetComponent().graviEffectWith.Add(SolarPlanet[2]);
Moon.GetComponent().graviEffectWith.Add(Sun);
SolarPlanet[2].GetComponent().graviEffectWith.Add(Moon);
Moon.GetComponent().GetComponent().SetPara(0.18f, 0.1f, 10 + 0.0256f);
Moon.GetComponent().setSpeed(Moon.GetComponent().startsetspeed()+SolarPlanet[2].GetComponent().startsetspeed());
}
Vector3 planetspeed(int index)//这个函数用来存储各种行星的初始速度
{
Vector3 theplanetspeed=SolarPlanet[index].GetComponent().startsetspeed();
switch (index)
{
case 0:
q = Quaternion.AngleAxis(7.01f,new Vector3(1,0,0));
break;
case 1:
q = Quaternion.AngleAxis(3.39f, new Vector3(1, 0, 0));
break;
case 2:
q = Quaternion.AngleAxis(0.00f, new Vector3(1, 0, 0));
break;
case 3:
q = Quaternion.AngleAxis(1.85f, new Vector3(1, 0, 0));
break;
case 4:
q = Quaternion.AngleAxis(1.31f, new Vector3(1, 0, 0));
break;
case 5:
q = Quaternion.AngleAxis(2.49f, new Vector3(1, 0, 0));
break;
case 6:
q = Quaternion.AngleAxis(0.77f, new Vector3(1, 0, 0));
break;
case 7:
q = Quaternion.AngleAxis(1.77f, new Vector3(1, 0, 0));
break;
case 8:
q = Quaternion.AngleAxis(1.85f, new Vector3(1, 0, 0));
break;
}
Debug.Log(q * theplanetspeed);
return (q*theplanetspeed);
}
Vector3 selfrotateAxis(int index)//这个函数用来存储各种行星的初始自传角
{
switch (index)
{
case 0:
q = Quaternion.AngleAxis(28f, new Vector3(1, 0, 0));
break;
case 1:
q = Quaternion.AngleAxis(177f, new Vector3(1, 0, 0));
break;
case 2:
q = Quaternion.AngleAxis(23.45f, new Vector3(1, 0, 0));
break;
case 3:
q = Quaternion.AngleAxis(23.98f, new Vector3(1, 0, 0));
break;
case 4:
q = Quaternion.AngleAxis(3.08f, new Vector3(1, 0, 0));
break;
case 5:
q = Quaternion.AngleAxis(26.73f, new Vector3(1, 0, 0));
break;
case 6:
q = Quaternion.AngleAxis(97.92f, new Vector3(1, 0, 0));
break;
case 7:
q = Quaternion.AngleAxis(28.8f, new Vector3(1, 0, 0));
break;
case 8:
q = Quaternion.AngleAxis(1.85f, new Vector3(1, 0, 0));
break;
}
Debug.Log(q * new Vector3(0, 1, 0));
return (q * new Vector3(0,1,0));
}
}
这个项目我会持续完善的，下一步时添加所有的行星、小行星带
项目地址：https://github.com/kotomineshiki/cosmos.git