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Question by Velcer · Dec 27, 2021 at 05:27 AM · game development

Bezier curve click movement?

Greetings,

I'm struggling to understand the mathematics behind what I'm trying to achieve. Here's an image to represent my question.

I'm clicking above my player, to the right side and I want my player to move and angle itself along the green path. I do not want to move straight to the position. alt text

I want my player to be aware of it's current speed, rotation, and velocity, and that green path is a prediction path that my player will move on, represented by a line renderer.

So there's some variables here. StartPosition (Player). End Position (Mouse click). A line renderer draws the prediction, and then the player moves in that same path, accelerating to a Maximum Speed, and decelerating once it reaches the 3/4 position.

Here's my code:

 public class PlayerController : MonoBehaviour
 {
     public Vector2 MoveStartPosition { get; set; }
     public Vector2 MoveEndPosition { get; set; }
  
     private bool _inputActive { get; set; }
     private Rigidbody2D _rb {get;set;}
     private LineRenderer _lr { get; set; }
     private Transform _transform { get; set; }
     public float Power = 5f;
     public float moveForce = 2f;
     public float turnSpeed = 4;
  
     void Start()
     {
         _transform = transform;
         _rb = GetComponent<Rigidbody2D>();
         _lr = GetComponent<LineRenderer>();
     }
  
     // Update is called once per frame
     void Update()
     {
         CheckForInput();
  
         if (_inputActive)
         {
             DrawPath();
         }
  
         Move();
     }
  
     void CheckForInput()
     {
         if (Input.GetKey(KeyCode.Mouse0))
         {
             MoveStartPosition = _transform.position;
             MoveEndPosition = Camera.main.ScreenToWorldPoint(Input.mousePosition);
             _inputActive = true;
         }
         else _inputActive = false;
     }
  
     void Move()
     {
         Vector2 velocity = (MoveEndPosition - MoveStartPosition) * Power;
         _rb.velocity = velocity;
  
         _transform.rotation = Quaternion.LookRotation(_rb.velocity);
     }
  
     void DrawPath()
     {
         Vector2 velocity = (MoveEndPosition - MoveStartPosition) * Power;
  
         Vector2[] trajectory = Plot(_rb, (Vector2)_transform.position, velocity, 500);
         _lr.positionCount = trajectory.Length;
  
         Vector3[] positions = new Vector3[trajectory.Length];
         for (int i = 0; i < positions.Length; i++)
         {
             positions[i] = trajectory[i];
         }
  
         _lr.SetPositions(positions);
     }
  
     Vector2[] Plot(Rigidbody2D rigidbody, Vector2 pos, Vector2 velocity, int steps = 500)
     {
         Vector2[] results = new Vector2[steps];
         float timestep = Time.fixedDeltaTime / Physics2D.velocityIterations;
  
         var angle = Vector2.Angle(MoveStartPosition, MoveEndPosition);
         angle = (float)ConvertToRadians(angle);
  
         Vector2 angleVelocity = new Vector2(Mathf.Cos(angle), Mathf.Sin(angle));
  
         Vector2 accel = (angleVelocity * velocity) * timestep * timestep * turnSpeed;
         float drag = 1f - timestep * rigidbody.drag;
         Vector2 moveStep = velocity * timestep;
  
         for (int i = 0; i < steps; i++)
         {
             moveStep += accel;
             moveStep *= drag;
             pos += moveStep;
  
             results[i] = pos;
         }
  
         return results;
     }
  
     public double ConvertToRadians(double angle)
     {
         return (Mathf.PI / 180) * angle;
     }
 }
  

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