3d 数学（叉乘、四元素、四元素旋转、四元素和四元素相乘、鼠标控制物体旋转、发射子弹、环形发射子弹、子弹缓冲池）

1、叉乘

2、四元素

3、四元素旋转

4、四元素和四元素相乘

5、鼠标控制物体旋转

6、发射子弹

7、环形发射子弹

8、子弹缓冲池

1、叉乘

两个向量叉乘，得到一个新的向量，新向量跟原始两个向量都垂直，也就是得到由两个向量所确定平面的法向量。

a(x, y , z) b(i , j , k)

a * b = (y * k - z * j , x * k - z * i , x * j - y * i)

public class CrossTest : MonoBehaviour
{public GameObject cube;public GameObject sphere;void Update(){Vector3 v = sphere.transform.position - cube.transform.position;Vector3 cross = Vector3.Cross(cube.transform.forward, v);Debug.DrawLine(cube.transform.position, cube.transform.forward * 10, Color.blue);Debug.DrawLine(cube.transform.position, sphere.transform.position , Color.red);Debug.DrawRay(cube.transform.position, cross, Color.green);if (cross.y > 0){Debug.Log("在右边");}else{Debug.Log("在左边");}}
}

2、四元素

万向节死锁 <x,y,z>

实数：分为有理数和无理数

虚数：i ^ 2 = -1

复数：实数 + 虚数

超复数：（x,y,z,w）

X = n * x * sin(/2)

Y = n * y * sin(/2)

Z = n * z * sin(/2)

W = cos(/ 2)

public class QuaternionTest : MonoBehaviour
{public GameObject cube;void Start(){cube.transform.rotation = new Quaternion(0, 0, Mathf.Sin(30 * Mathf.Deg2Rad),Mathf.Cos(30 * Mathf.Deg2Rad));//cube绕z轴旋转60度Quaternion q1 = Quaternion.Euler(0, 30, 0);cube.transform.rotation = q1;//cube绕y轴旋转30度Quaternion q2 = Quaternion.Euler(new Vector3(0, 30, 0));cube.transform.rotation = q2;Quaternion q3 = Quaternion.AngleAxis(30, Vector3.forward);cube.transform.rotation = q3;}}

3、四元素旋转

1）、cube位置rest,cube 从沿y轴从0度到60度旋转（Lerp(差值)）

public class QuaternionRotate : MonoBehaviour
{public GameObject cube;public Transform target;void Update(){Quaternion q2 = Quaternion.Euler(0, 60, 0);cube.transform.rotation = Quaternion.Lerp(cube.transform.rotation, q2, 0.1f);Debug.Log("旋转角度：" + cube.transform.rotation.eulerAngles.y);//0-60Debug.Log("cube.transform.rotation.y" + cube.transform.rotation.y);//0-0.5}
}

2）、用下面这个方法是错误的，q1的y值一直都是从0 - 32.975变化，没更新一次都执行：Quaternion q1 = Quaternion.Euler(0, 30, 0);

public class QuaternionRotate : MonoBehaviour
{public GameObject cube;void Update(){Quaternion q1 = Quaternion.Euler(0, 30, 0);Quaternion q2 = Quaternion.Euler(0, 60, 0);q1 = Quaternion.Lerp(q1, q2, 0.1f);cube.transform.rotation = q1;//cube.transform.rotation.eulerAngles.y = 32.975}
}

正确的做法：q1变量放方法外。

public class QuaternionRotate : MonoBehaviour
{public GameObject cube;Quaternion q1 = Quaternion.Euler(0, 30, 0);void Update(){Quaternion q2 = Quaternion.Euler(0, 60, 0);q1 = Quaternion.Lerp(q1, q2, 0.1f);cube.transform.rotation = q1;//0 - 60}
}

3）、旋转看向目标物体

1.LookAt


public class QuaternionLookRotate : MonoBehaviour
{public GameObject cube;public Transform target;void Update(){//cube主角z轴瞬间看向目标物体cube.transform.LookAt(target);}
}

2.public static Quaternion LookRotation(Vector3 forward);

public class QuaternionLookRotate : MonoBehaviour
{public GameObject cube;void Update(){Vector3 dir = new Vector3(30, 0, 0);//（30,0,0）相当于（1,0,0）//cube主角的z轴看向目标物体（dir）即x轴正方向cube.transform.rotation = Quaternion.LookRotation(dir);}
}

当改变dir的值时，cube的z轴正方向看向的位置也改变

public class QuaternionLookRotate : MonoBehaviour
{public GameObject cube;void Update(){Vector3 dir = new Vector3(0, 10, 0);cube.transform.rotation = Quaternion.LookRotation(dir);}
}

3.public static Quaternion LookRotation(Vector3 forward, [DefaultValue("Vector3.up")] Vector3 upwards);

public class QuaternionLookRotate : MonoBehaviour
{public GameObject cube;public Transform target;private void Start(){Debug.Log("Vector3.up:" + Vector3.up);//(0,1,0)}void Update(){Quaternion q1 = Quaternion.LookRotation(target.position - cube.transform.position);cube.transform.rotation = Quaternion.Lerp(cube.transform.rotation, q1, 0.1f);//最后cube的z轴指向targetDebug.DrawLine(cube.transform.position, target.position,Color.blue);}
}

4、四元素和四元素相乘

就是两个相加

    public GameObject cube;public Transform target;void Start(){Quaternion q1 = Quaternion.Euler(0, 30, 0);Quaternion q2 = Quaternion.Euler(0, 60, 0);Quaternion q3 = q1 * q2;cube.transform.rotation = q3;Debug.Log("cube.transfor.rotation.eulerAngles: " +                 cube.transform.rotation.eulerAngles);}

5、鼠标控制物体旋转

public class MouseRotate : MonoBehaviour
{public GameObject cube;private float mousex;void Update(){mousex = Input.GetAxis("Mouse X");Quaternion q = Quaternion.AngleAxis(mousex, Vector3.up);cube.transform.rotation *= q;}
}

6、发射子弹

biubullet类挂载在发射子弹的主角物体上，一定角度生成子弹

public class biubullet : MonoBehaviour
{public GameObject bullet;private float timer;void Start(){bullet = Resources.Load<GameObject>("Prefabs/bullet");}void Update(){timer += Time.deltaTime;if(timer > 3){Vector3 dir = Quaternion.AngleAxis(-15, Vector3.up) * transform.forward;GameObject go = Instantiate(bullet);go.transform.position = transform.position;go.transform.rotation = Quaternion.LookRotation(dir);timer = 0;}}
}

BulletController类挂载在子弹上，控制子弹的移动

public class BulletController : MonoBehaviour
{void Update(){transform.Translate(Vector3.forward * 0.01f, Space.Self);}
}

7、环形发射子弹

设置timer的时间，3秒后发射一次环形子弹，发射完一次环形子弹就将timer设置回0

public class biubullet : MonoBehaviour
{public GameObject bullet;private float timer;void Start(){bullet = Resources.Load<GameObject>("Prefabs/bullet");}void Update(){timer += Time.deltaTime;if(timer > 3){//for(int i = 0; i < 5; i++)//{//    Vector3 dir = Quaternion.AngleAxis(-30 + i *15, Vector3.up) * transform.forward;//    GameObject go = Instantiate(bullet);//    go.transform.position = transform.position;//    go.transform.rotation = Quaternion.LookRotation(dir);//}//timer = 0;for (int i = 0; i < 24; i++){Vector3 dir = Quaternion.AngleAxis(-30 + i * 15, Vector3.up) * transform.forward;GameObject go = Instantiate(bullet);go.transform.position = transform.position;go.transform.rotation = Quaternion.LookRotation(dir);}timer = 0;}}
}

public class BulletController : MonoBehaviour
{void Update(){transform.Translate(Vector3.forward * 0.01f, Space.Self);}
}

8、子弹缓冲池

1）、PoolMain 缓冲池单例；挂载在创建的缓冲池空物体上

public class PoolMain : MonoBehaviour
{public static PoolMain Instance;private void Awake(){Instance = this;}GameObject bulletPool;public GameObject GetBulletPool(){if(bulletPool == null){bulletPool = GameObject.Find("bulletPool");}return bulletPool;}
}

2）、biubullet 主角控制子弹的生成，缓冲池里没有子物体时克隆子弹（因为每3秒生成一圈子弹，而每5秒后将已生成的子弹设为缓冲池的子物体，所以克隆一圈子弹），缓冲池里有子物体时，就取出子物体。

public class biubullet : MonoBehaviour
{public GameObject bullet;private float timer;void Start(){bullet = Resources.Load<GameObject>("Prefabs/bullet");}void Update(){timer += Time.deltaTime;if(timer > 3){for (int i = 0; i < 24; i++){GameObject go = null;//找到缓冲池父物体GameObject pool = PoolMain.Instance.GetBulletPool();//判断缓冲池子物体数量是否足够if(pool.transform.childCount >0){//取缓冲池里的第一个子物体go = pool.transform.GetChild(0).gameObject;//把子弹物体迅速从缓冲池物体内取出go.transform.parent = null;//将游戏物体（子弹）设置为激活状态go.SetActive(true);}else{//缓冲池里没有子物体，就需要克隆子弹go = Instantiate(bullet);}Vector3 dir = Quaternion.AngleAxis(-30 + i * 15, Vector3.up) * transform.forward;go.transform.position = transform.position;go.transform.rotation = Quaternion.LookRotation(dir);}timer = 0;}}
}

3）、BulletController 控制子弹的移动，每5秒后将生成的子弹设置缓冲池物体的子物体，并失活

public class BulletController : MonoBehaviour
{private float timer;private GameObject pool;//缓冲池（空物体）private void Start(){pool = PoolMain.Instance.GetBulletPool();}void Update(){timer += Time.deltaTime;if(timer > 5){//将生成的子弹的父物体设置为缓冲池物体transform.parent = pool.transform;timer = 0;//作为缓冲池物体的子物体后失活gameObject.SetActive(false);}transform.Translate(Vector3.forward * 0.01f, Space.Self);}
}