How can I make a missile home to an enemy in arc fashion? (Unity 4.3 2D)

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I am building a 2D game and i've managed to make homing missiles with the following code:

Vector2 destination = player.transform.position - transform.position; lastPos = destination; float angle = Mathf.Atan2(destination.y, destination.x) * Mathf.Rad2Deg; transform.rotation = Quaternion.AngleAxis(angle, Vector3.forward);

destination.Normalize (); transform.position += new Vector3 (destination.x, destination.y, 0) speed Time.deltaTime;

I've made it so that the rocket simply travels in a straight line towards the player. Can anyone guide me in the right direction to make the rocket travel in an arc towards the player instead of a straight line.

Answer 1

Best Answer

Answer by Hamdullahshah · Feb 26, 2014 at 04:34 PM

Use a bezier curve of two point

     private Vector3 CalculateBezierPoint (float t, Vector3 startPosition, Vector3 endPosition, Vector3 controlPoint) {
         float u = 1 - t;
         float uu = u * u;
 
         Vector3 point = uu * startPosition;
         point += 2 * u * t * controlPoint;
         point += t * t * endPosition;
 
         return point;
     }

Call it from update something like

 this.transform.position = CalculateBezierPoint(currentDuration/duration,startPos,endPos,cp);
 
 currentDuration += Time.deltaTime;

where "duration" is total time.

More info on wikipedia for bezier curves: http://en.wikipedia.org/wiki/File:Bezier_2_big.gif

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Li0nSword · Feb 26, 2014 at 06:56 PM 0

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This worked very well. Thanks!

kendyb · Jan 08, 2015 at 03:10 PM 0

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another clear explanation of bezier curves: http://devmag.org.za/2011/04/05/bzier-curves-a-tutorial/

Answer 2

I suggest, using iTween, where you set your waypoints, the easiest way to define this waypoints instead of using a formula, just add 4, the first, your origin, second and third, at 1 third between origin and destiny but with the y above them depending on how your desired arc is, and the fourth your destiny, itween WILL interpolate the movements, after defining that you could play a little with the type of movement, as linear, cuadratic, spring, etc, the code for i tween is something like this

 public Transform[] waypoints;
 public float m_speed = 1.0f;
 public GameObject player1;
 private int i = 0;
 private bool moving = false;
  
 public void Update() {
 if (!moving && i < waypoints.Length - 1) {
 i++;
 moving = true;
 iTween.MoveTo(player1,iTween.Hash("position",waypoints[i],"speed",m_speed,"easetype","linear", "oncompletetarget",gameObject, "oncomplete", "Done"));
 }
  
 }
  
 public void Done() {
 moving = false;
 }

Answer 3

Answer by robertbu · Feb 26, 2014 at 05:02 PM

And another solution to add to the mix. Use the Sin() function to calculate a loft for the missile over the distance traveled. Take the script below and attach to a sphere in the scene. Click the mouse to shoot the sphere to that position:

 #pragma strict
  
 var traveling = false;
 
 function Update() {
     if (!traveling && Input.GetMouseButtonDown(0)) {
         var pos = Input.mousePosition;
         pos.z = 10.0;
         pos = Camera.main.ScreenToWorldPoint(pos);
         ArcToTarget(pos, 0.35, 1.0);
     }
  } 
  
 function ArcToTarget(targetPos : Vector3, arcFraction : float, time : float) {
     traveling = true;
     var startPos = transform.position;
     var timer = 0.0;
     var arcDist = (targetPos - startPos).magnitude * arcFraction;
     
     while (timer < time) {
         var pos = Vector3.Lerp(startPos, targetPos, timer / time);
         pos.y += Mathf.Sin(Mathf.PI * timer / time) * arcDist;
         transform.position =  pos;
         timer += Time.deltaTime;
         yield;
     }
     transform.position = targetPos;
     traveling = false;
 }

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Li0nSword · Feb 26, 2014 at 06:58 PM 0

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This is giving me a close effect. I'm sure with a bit more tweaking I can get what i'm looking for.

Answer 4

Answer by Thorizo · Oct 03, 2018 at 09:26 PM

Let's assume we have 3 points: A (start), B (middle) and C (end). We linearly interpolate over time between A and B, as well as B and C. Meanwhile, we interpolate between the result of the two. The code presented below should work perfectly. Simply call QuadraticCurve in the Update() method. Subsequently, increment the time as we want to go from 0 to 1: time += Time.deltaTime;

 private Vector3 LinearInterpolate(Vector3 start, Vector3 end, float time)
 {
     return start + (end - start) * time;
 }
 
 private Vector3 QuadraticCurve(Vector3 start, Vector3 middle, Vector3 end, float time)
 {
     Vector3 line1 = LinearInterpolate(start, middle, time);
     Vector3 line2 = LinearInterpolate(middle, end, time);
     return LinearInterpolate(line1, line2, time);
 }
 private void Update()
 {
     transform.position = QuadraticCurve(startPoint, middlePoint, endPoint, 
     duration);
     durtation += Time.deltaTime;
 }

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Bunny83 · Oct 04, 2018 at 01:26 AM 0

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While this is true it's actually more complicated / complex that way First of all reinventing the wheel for a lerp is pretty pointless. You can use Vector3.Lerp instead of your "LinearInterpolate".

Calling lerp 3 times is rather inefficient. For a quadratic bezier you should just use a bezier implementation like "Hamdullahshah" posted in his answer. So your answer is the same as Hamdullahshah's answer just less efficient. Also you may want to rethink about your variable names. line1 and line2 do not store lines. They are points. Also "duration" is not a duration. It could be called "time", "progress" or "fraction". Duration describes a usually constant amount of time usually in seconds. The "t" / "time" value of a lerp or a bezier curve is just the interpolation value

How can I make a missile home to an enemy in arc fashion? (Unity 4.3 2D)

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