Unity - 3D mathematics -vector3

Reissue yesterday's , Continue today and tomorrow 3D mathematics , Learn spoilers ：25、26 Will release a different version of “ Synthetic watermelon ” Detailed explanation of , Look forward to it ！ There are colored eggs at the end ！

One sentence per day ： Young people are Utopian , The heart is still growing towards the sun

Catalog

Vector3

vector

The size of the vector

The direction of the vector

Vector operations

Vector subtraction 、 Add up

  demand ：t3 Along t1-t2 Direction of movement

Multiplication and division of vector and scalar

Angle measurement ：

angle Degree And radians Radin

Conversion of angle and radian

Trigonometric functions

Anti trigonometric function

practice ： Calculate the right front of the object 30 degree ,10 Meter distant coordinates

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Vector3

vector

The size of the vector

API：float dis=Vector.magnitude

Vector3 pos=this.transform.position;

// There are three forms of representing the size of a vector

float  m01=Mathf.Sqrt(Mathf.Pow(pos.x,2)+Mathf.Pow(pos.y,2）+Mathf.Pow(pos.z,2));

// The formula

float  m02=pos.magnitude;//API

float  m03=Vector3.Distance(Vector3.zero,pos);// distance

The direction of the vector

Getting vector direction is also called “ Normalized vectors ”,“ Normalized vectors ” or “ Unit vector ”, That is, the vector is lengthened or shortened , Make the die length equal to 1

API:Vector3 n02=vector.normalized;

n02 by vector Unit vector

private void Update()

    {

        Vector3 pos = this.transform.position;

        Vector3 n01 = pos / pos.magnitude;

        Vector3 n02 = pos.normalized;

        Debug.DrawLine(Vector3.zero, pos);

        Debug.DrawLine(Vector3.zero, n02, Color.red);

}

 

Vector operations

Vector subtraction 、 Add up

Vector3 relativeDirection=t1.position-t2.position;

size ： Distance between two points

Direction ： Point to the subtracted vector

because t1,t2 It's the world coordinates , therefore t1-t2 The actual position is translated to the world Coordinate origin

  demand ：t3 Along t1-t2 Direction of movement

 

public Transform t1, t2, t3;

    private void Update()

    {

        Vector3 relativeDirection = t1.position - t2.position;

        if (Input.GetKeyDown(KeyCode.A))

        {

            t3.Translate(relativeDirection.normalized);

        }

        Debug.DrawLine(Vector3.zero, relativeDirection, Color.red);

}

t3.Translate(relativeDirection.normalized);// Get directions , Avoid the influence of the distance between two objects on the speed

=t3.position = t3.position + relativeDirection.normalized;

 

Multiplication and division of vector and scalar

Multiplication ： Each component of the vector is multiplied by the scalar k[x,y,z]=[kx,ky,kz]

Geometric meaning ： Scale vector length

demand ： There is a length of 8 Vector , How to get a length of 13 Vector

Let's take the vector normalized, cube 13

Angle measurement ：

angle Degree And radians Radin

Two rays shoot out from the center of the circle , Form an included angle and an arc directly opposite to the included angle .

1 radian ： When the arc length is equal to the radius of the circle , The included angle is 1 radian

Half circle =π（3.14159） radian

Conversion of angle and radian

1 radian =180 degree /π    1 angle =π/180 degree

API radian = Angle degrees *Mathf.Deg2Rad;

API angle = Radians *MAthf.Rad2Deg;

angle —> radian

float d1=60;

float r1=d1*Mathf.PI/180;

float r2=d1*Mathf.Deg2Rad;

radian —> angle

float r1=3;

float d1=r1*180/Mathf.PI;

float d2=r1*Marhf.Rad2Deg;

Trigonometric functions

The relationship between the ratio of the middle angle to the side length of a right triangle is established

It can be used according to one corner , Calculate the length of the other side

The formula ：sin x=a/c  cos x=b/c  tan x=a.b

API:

Mathf.Sin(float radian radian );

Mathf.Cos(float radian radian );

Mathf.Tan(float radian radian );

30 degree —> radian ：30*Mathf.Deg2Rad// Radian to degree conversion constant

· Given the angle x And adjacent edges a, Find the opposite side

float x = 50, b = 20;

float a = Mathf.Tan(Mathf.Deg2Rad * x) * b;

Anti trigonometric function

It can be used to calculate the angle according to the length of both sides

The formula ： Anti sine arcsin a/c=x  arccos b/c=x  arctan a/b=x

API:

Mathf.Asin(float radin);

Mathf.Acos(float radin);

Mathf.Atan(float radin);

· Known side length a and b, Find the angle angle

float a = 30, b = 20;

float angle = Mathf.Atan(a / b) * Mathf.Rad2Deg;

practice ： Calculate the right front of the object 30 degree ,10 Meter distant coordinates

Vector3 worldPoint=this.transform.TransformPoint(Vector3 point)// Convert the point from its own coordinate system to the world coordinate system

public static void DrawLine (Vector3 start, Vector3 end, Color color= Color.white, float duration= 0.0f, bool depthTest= true);// Draw a straight line between the specified start point and end point .

private void Update()

    {

        float x = Mathf.Sin(30 * Mathf.Deg2Rad) * 10;

        float z = Mathf.Cos(30 * Mathf.Deg2Rad) * 10;

        Vector3 worldPoint = transform.TransformPoint(x, 0, z);

        Debug.DrawLine(this.transform.position, worldPoint, Color.blue);

}

Colored eggs ！！！

Three characteristics of object-oriented ： encapsulation 、 inheritance 、 polymorphism

1. encapsulation ： Hide object properties and implementation details , Only public interfaces , Control the access level of property reading and modification in the program , Will abstract the resulting data and behavior （ Or function ） Combination , Form an organic whole （“ class ”）.（ Combine data and behavior , Modify data through behavior constraint code ; Wrap some complex logic , Others only need to pass in the required parameters , You can get the results you want ）

2. inheritance ： That is, the subclass inherits the characteristics and behavior of the parent class , Make subclass objects （ example ） Instance fields and methods with parents , Or subclasses inherit methods from their parents , Make subclasses have the same behavior as the parent .

3. polymorphism ： The ability of a behavior to have multiple forms or forms of expression . An instance of a class （ object ） The same method has different forms in different situations . Polymorphism mechanism enables objects with different internal structures to share the same external interface . signify , Although specific operations for different objects are different , But through a public class , they （ Those operations ） It can be called in the same way .

Polymorphism exists Three necessary conditions ：

• Inherit
• rewrite （ After the subclass inherits the parent class, redefine the parent class method ）
• The parent class reference points to the subclass object

　　 Polymorphism is actually based on inheritance .

encapsulation Can enhance the enhanced type of data , Hide implementation details , Making code modular ; Inherit You can extend the functions of the original class , It improves the code repeatability and development efficiency , An important means to enhance software maintainability , Comply with opening and closing principle ; and polymorphic Is to achieve another purpose —— Interface reuse ！

* The meaning of the opening and closing principle is ： When the requirements of the application change , Without modifying the source code or binary code of the software entity , It can extend the function of the module , Make it meet new needs .