三角函数:
概念:用来描述三角形中某个角和对应的三条边的比例关系。
正弦:sin<θ>(sin<theta>)=对边/斜边
余弦:cos<θ>(cos<theta>)=邻边/斜边
正切:tan<θ>(tan<theta>)=对边/邻边
正弦函数曲线:随着θ角度不断增大,sinθ的值的变化周期
![](https://img2018.cnblogs.com/blog/1517599/201902/1517599-20190211182025667-1108388302.png)
余弦函数曲线:正弦函数曲线左移90度
![](https://img2018.cnblogs.com/blog/1517599/201902/1517599-20190211182949534-891988486.png)
反三角函数:已知比例关系,反推出角度或者弧度。
反正弦:Arcsin(0.5)=30度
反余弦:Arccos
反正切:Arctan
向量的乘法:
向量的点乘:a(ax,ay,az) · b(bx.by.bz)
数学运算:a·b = axbx + ayby + azbz,各分量分别相乘再相加
1、满足乘法交换律
2、结果是标量
几何意义:
a·b = |a| * |b| * cos<a,b>,<a,b>夹角范围0~180度,两个向量夹角越小,相似度越高
a·b = (|a| * cos<a,b>) * |b|,最重要的几何意义就是求投影
1、a向量在b向量方向上投影的长度再乘以b向量的模长
2、当b向量为单位向量的时候,结果就是:a向量在b向量方向上投影的长度
3、当a向量和b向量都是单位向量的时候,结果就是:两个向量的夹角的余弦
敌人的正前方和敌人与自己连线的夹角,小于90度,在敌人前方,大于90度,在敌人后方
API Vector3.Dot(Vector3 lhs,Vector3 rhs),两个向量点乘满足乘法交换律,但叉乘不行
API Vector3.Angle,直接计算两个向量之间的夹角
思考题:入射光线和反射光线不在一个水平线上
using System.Collections; using System.Collections.Generic; using UnityEngine; public class EnemyLook : MonoBehaviour { public Transform player; public float result; public float distance; // Use this for initialization void Start() { ////向量点乘的数学运算 //Vector3 enemy2Player = player.position - transform.position; //Vector3 enemyForward = transform.forward; //result = enemy2Player.x * enemyForward.x + enemy2Player.y * enemyForward.y + enemy2Player.z + enemyForward.z; //把向量变成单位向量 Vector3 enemy2Player = (player.position - transform.position).normalized; Vector3 enemyForward = transform.forward; //计算两个向量之间的夹角 result = Vector3.Dot(enemy2Player, enemyForward); //计算两个物体之间的距离 distance = Vector3.Distance(player.position, transform.position); //API:计算两个向量之间的夹角 //Vector3.Angle(); } // Update is called once per frame void Update() { } private void OnGUI() { //if (result > 0) //{ // GUILayout.Label("在敌人前方"); //} //else //{ // GUILayout.Label("在敌人后方"); //} if (result > Mathf.Cos(30 * Mathf.Deg2Rad) && distance < 5) { GUILayout.Label("在扇形范围内:" + Mathf.Acos(result) * Mathf.Rad2Deg + "度"); } else { GUILayout.Label("不在扇形范围内:" + Mathf.Acos(result) * Mathf.Rad2Deg + "度"); } } }
using System.Collections; using System.Collections.Generic; using UnityEngine; public class TestTrans : MonoBehaviour { public Transform Target; public float distance; private float SkillDistance = 5;//扇形距离 private float SkillJiaodu = 60;//扇形的角度 // Use this for initialization void Start () { ////偶然性编程 distance = Vector3.Distance(transform.position, Target.position);//距离 Vector3 norVec = transform.rotation * Vector3.forward; Vector3 temVec = Target.position - transform.position; Debug.DrawLine(transform.position, norVec, Color.red);//画出技能释放者面对的方向向量 Debug.DrawLine(transform.position, Target.position, Color.green);//画出技能释放者与目标点的连线 float jiajiao = Mathf.Acos(Vector3.Dot(norVec.normalized, temVec.normalized)) * Mathf.Rad2Deg; if (distance <= SkillDistance) { if (jiajiao <= SkillJiaodu) { Debug.Log("在扇形范围内"); } else { Debug.Log("不在扇形范围内"); } } } // Update is called once per frame void Update () { } }
using System.Collections; using System.Collections.Generic; using UnityEngine; public class CrystalMove : MonoBehaviour { //public Transform startTrans; //public float moveSpeed = 1; //public float rotSpeed = 1; public float rotateSpeed = 30; //调节上下频率和浮动 public float amplitude = 1f; public float frequency = 1f; // Use this for initialization void Start () { } // Update is called once per frame void Update () { // transform.Rotate(Vector3.up, Space.World); // Vector3 delta = Vector3.up * Mathf.Sin(Time.time) * moveSpeed*0.25F; // transform.position = startTrans.position + delta; transform.Rotate(Vector3.up * Time.deltaTime * rotateSpeed); float sin = Mathf.Sin(Time.time * frequency) * amplitude; transform.Translate(Vector3.up * sin, Space.World); } }