D39_Vector

目录

1.Simple operations on vectors

1.向量简介

2.vector between two points

3.零向量

4.负向量

5.向量的大小

6.Addition and subtraction of vectors

7.Vector3 +- Vector3的几何意义

8.向量*标量

2.向量的乘法

1.向量的点乘

2.向量的叉乘

3.API

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1.Simple operations on vectors

1.向量简介

向量：具有大小和方向的量       标量（矢量）：只有大小没有方向的量

transform.position代表坐标        transform.forward代表向量

2.vector between two points

从起点A指向终点B的向量----用BThe coordinates of the point are subtractedA点的坐标

3.零向量

The zero vector is the only one of size 0的向量    Vector3.zero

4.负向量

If two vectors are equal in magnitude and opposite in direction, they are negative vectors of each other      （x,y,z）的负向量为（-x,-y,-z）

-transform.forwardMeaning is directly behind the object      -Vector3.forwardIt means right behind the world

5.向量的大小

|A|=（x²+y²+z²）½  向量的模长        几何意义：The distance between two endpoints

定义A为向量      Unity中使用  A.magnitude  Find the modulo length of a vector       平方模  A.sqrMagnitude

Using the square mode is more efficient than the mode length,Because it is easier for a computer to calculate a square than to take a square root

6.Addition and subtraction of vectors

A(x1,y1,z1)向量加B(x2,y2,z2)向量      |A|+|B|=（x1+x2,y1+y2,z1+z2）

A(x1,y1,z1)向量减B(x2,y2,z2)向量      |A|-|B|=（x1-x2,y1-y2,z1-z2）

7.Vector3 +- Vector3的几何意义

Vector3意义为  坐标  或者  向量

坐标+坐标  ：  无意义

坐标+向量  ：  得到新的位置----将一个点,in the direction of the vector,Modulo length of the motion vector,得到新的坐标点

向量+向量  ：  得到一个新的向量----将BThe start point of the vector is translated toAThe end point of the vector,就会得到  从AThe starting point of the vector points toBThe end point of the vector  of this new vector

坐标-坐标  ：  A-B  得到一个向量----得到一个从B指向A的向量

向量-向量  ：  得到一个新的向量----Connect the origins of two vectors by translation,Connect the endpoints of two vectors,The direction points to the subtracted vector          A-B相当于A+（-B）

位置-向量  ：  得到新的位置----位置+（-向量）  Place a point against the direction of the vector,The modulo length in the direction of movement,Get the coordinates of the new point

向量-位置  ：  无意义

8.向量*标量

A（x,y,z）*M    得到    B（x*M,y*M,z*M）

得到一个新的向量  ：  Increase the modulo length of the vector by a multiple of the scalar,Scalar is a positive number,方向不变,Scalar is negative,方向相反

2.向量的乘法

1.向量的点乘

A（x1,y1,z1）    B(x2,y2,z2)      AB=x1*x2+y1*y2+z1*z2     What is obtained is a new value

几何意义：AB=|A|*|B|*cosθ 

                  θ是A  BThe vector is less than180°的夹角

                  cosθ=AB/|A|*|B|

                  θ=ArcCos(AB/|A|*|B|)

                  If the two vectors are unit vectors--------AB=cosθ -------- θ=ArcCos(AB)

        By vector dot product,The angle between the two vectors can be obtained

It only makes sense to dot-multiply a vector,Position dot-multiply vector,Position multiplication by position is meaningless

2.向量的叉乘

A（x1,y1,z1）    B(x2,y2,z2)      A×B=（y1z2-z1y2,z1x2-x1z2,x1y2-y1x2）     

几何意义：A叉乘BThe resulting new vector is also perpendicular to A B向量

                  A叉乘BThe resulting new vector is perpendicular to A Bformed plane

                  A叉乘B得到的就是A B face normal

                  Use the left-hand rule to determine direction,Four-finger wrapping direction from left multiplier to right multiplier,The thumb points in the direction of the cross

3.API

开根号：Mathf.Sqrt();

指数：Mathf.Pow();

向量的模: 向量.magnitude;

The square modulo of the vector：向量.sqrMagnitude;

反三角：Mathf.Acos();  Mathf.Asin();  

绝对值：Mathf.Abs();

向量的归一化：向量.normalized;

向量点乘：Vector3.Dot();

算夹角：Vector3.Angle();

向量叉乘：Vector3.Cross();

弧度转角度：弧度* Mathf.Rad2Deg

角度转弧度：角度* Mathf.Deg2Red