[unity] several ideas about circular motion of objects

The first one is

Without the foundation of Mathematics , Use it directly Unity Provided API：

Transform.RotateAround Move around . The object surrounded is the center of the circle , If you don't understand, you can check Manual links

Only need Update Put a line of code inside

this.transform.RotateAround(targetTrans.position, Vector3.forward, 180 * Time.deltaTime);
// targetTrans.position  Is the position of the center of the circle , Here I use an empty object , You can visually edit the position of the center of the circle .
// Vector3.forward Is the axis of rotation , the reason being that 2D So I use z Axis .
// 180 Indicates rotation per second 180 Degree is half a circle .

We can do it in 2D Place a small ball in the scene to observe the movement , Attach this script to the ball . Put another empty object , Set to targetTrans object . It indicates the position of the center of the circle .

The ball will make a uniform circular motion around the center of the circle .

 

The second kind

Ideas ： Use  Quaternion.AngleAxis（） The method of rotating a vector , Imagine a dial , The second hand rotates 360 degree , It will draw a circle at the end .

Then you only need to have “ center of a circle ”（ Location ）、“ radius ”（ vector ）, Add the two together , You can get the position of the point on the circle .

Keep rotating this “ radius ”, Get circular motion .

    Vector3 CenterPosition = Vector3.zero; // The position of the center , I set it at （0,0） spot 
    Vector3 r; // Circle radius , That is, the vector to rotate .
    

    private void Awake()
    {
        r = transform.position - CenterPosition; // The center of the circle points “ I ” Vector , That's the radius 
    }

    public void Update()
    {
        // Per second 180 The speed of degrees “ radius ” vector , Because I do 2D game , So the axis of rotation is Z Axis .
        r = Quaternion.AngleAxis(180 * Time.deltaTime, Vector3.forward) * r;
        // Center position  +  radius  =  Points on the circle 
        transform.position = CenterPosition + r;
    }

The third kind of

Mathematical methods , Using trigonometric functions . You can find many references , I'm not going to go into the code

Important functions used ：

• Mathf.Sin () Get an angle sin value , Parameters use radians
• Mathf.Cos() ditto ,cos value .
• May be used ：Mathf.Deg2Rad Degrees to radians , For the above two functions
• On radians

principle ： At the origin of the coordinate system , Will a Unit vector   from X The positive direction of the axis Rotate up α degree , obtain Unit vector At the intersection of the circle P（x,y）,

Trigonometric functions tell us ,cos (α) = x / 1 = x;sin (α) = y / 1 = y. In turn, x = cos (α) , y = sin(α).

We can get it P Coordinates of （ cos(α) , sin (α) ）

thus , The coordinates of points on the circle can be obtained from the rotation angle .

Specific implementation can refer to UNITY Make circular motion around an object _Black-Coder The blog of -CSDN Blog _unity Circular motion

 

An association  

A simple idea of doing spiral motion ： In circular motion , Just increase the radius at a uniform speed .

Take the first circular motion method for example , Center of circle targetTrans Every frame moves away “ Pellet ” Direction of movement . use transform.Translate（） Method . Direction vector away = Center position - Ball position .