How to SHOOT an object on a curved path without using Rigidbody

Question

Hey there,

Lets say im launc$$anonymous$$ng a cannon ball. It needs to shoot towards players facing point and slowly lose height and $$anonymous$$t the ground eventually. Like t$$anonymous$$s: alt text

How do I set up the movement of cannonball object like t$$anonymous$$s? The cannonball WILL NOT HAVE RIGIDBODY property. So I need to set position of cannonball on each Update().

Here is how I shoot cannonball with my standart first person controller:

 void Update () {
 if (Input.GetButton("Fire1"))
 {
     GameObject cannonBall= Instantiate(projectile, transform.position, transform.rotation);

 }
 }

And here is my movement script on cannonball. Currently it goes straight forward without $$anonymous$$tting ground.

 void Update () {

     if (transform.position.y > 0)
     {
         transform.Translate(Vector3.forward * Time.deltaTime * 10);
     }

 }

Answer 1

I would t$$anonymous$$nk that you would need to figure out the formula for the parabola path that you want your cannon ball to take. Then using it, you would increment the x value by some stepSize (e.g. Time.deltaTime) and plug it into the equation to get back the y value. Then put the cannon ball at those coordinates.

T$$anonymous$$s way you would need to figure out a way to know when the cannon $$anonymous$$t the ground so the ball would stop when it $$anonymous$$ts the ground.

You could use the formula that involves the top point of the parabola

y = a(x - x1)^2 + y1

where x1 is the x coordinate of the top point and y1 is the y coordinate of the top point. Or the one with intercepts

y = a(x - x1)(x - x2)

where x1 and x2 are the points at w$$anonymous$$ch parabola intecepts the x axis.

You'd need to fiddle around with these t$$anonymous$$ngs to get t$$anonymous$$ngs working for you the way you want to.

I t$$anonymous$$nk that the intecept form would work best, because you could figure out the intercept point be$$anonymous$$nd your cannon and then just input the next intercept point, to get exactly what you would need. And the a in that formula would be the tan(angle), where the angle is the angle that the cannon is rotated by from the x axis, anticlock-wise. (And because of the way that Unity handles angles, I t$$anonymous$$nk instead of tan(x), you would need to use ctg(x), but I'm not entirely sure about t$$anonymous$$s one).

EDIT: @y11t_tr

Okay, so additional information. I tried implementing t$$anonymous$$s in Unity, and it gave me quite a few problems.

First t$$anonymous$$ngs first - a point directly be$$anonymous$$nd the cannon is not the intercept of the ball movement parabola. That's a wrong assumption. Because of t$$anonymous$$s, the usage of the intercept formula crumbles.

I tried figuring out a way to do it all without it, but just couldn't. Anyway, I decided that I would just find the formula of the parabola itself, but that brought another problem back. I only had two points and I needed three points to make what I had in mind work. So I figured I'd make some sort of a hack.

I have two points in the scene that the ball should go through. First one is the point, from where the cannon fires, the next one is the target point. So, I decided that I would put a t$$anonymous$$rd point, an extremely tiny distance away from the one that was in front of the cannon. That fixed the problem and now I had three points with w$$anonymous$$ch I could draw a parabola path.

Now, figuring out the parabola itself. I tried my luck at deriving the equations to do so, but to no avail. Anyway, a quick google search gave me some results.

To find the equation of the parabola, using three random points, you need to figure out y = ax^2 + bx + c what the a, b and c is in t$$anonymous$$s equation. Anyway, I found these equations:

Say we have three points (x1, y1), (x2, y2), (x3, y3).

denominator = (x1 - x2) * (x1 - x3) * (x2 - x3)

a = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2))/denominator

b = (x3 * x3 * (y1 - y2) + x2 * x2 * (y3 - y1) + x1 * x1 * (y2 - y3))/denominator

c = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 + x1 * x2 * (x1 - x2) * y3)/denominator

And now, all you need to do, is to put everyt$$anonymous$$ng into code:

 float GetDenominator(Vector3 point1, Vector3 point2, Vector3 point3){
         return (point1.x - point2.x) * (point1.x - point3.x) * (point2.x - point3.x);        
     }
 
     float GetA (Vector3 point1, Vector3 point2, Vector3 point3){
         return ((point3.x * (point2.y - point1.y)) +
                 (point2.x * (point1.y - point3.y)) +
                 (point1.x * (point3.y - point2.y))) / GetDenominator (point1, point2, point3); 
     }
 
     float GetB (Vector3 point1, Vector3 point2, Vector3 point3){
         return ((Mathf.Pow(point3.x, 2) * (point1.y - point2.y)) +
                 (Mathf.Pow(point2.x, 2) * (point3.y - point1.y)) +
                 (Mathf.Pow(point1.x, 2) * (point2.y - point3.y))) / GetDenominator (point1, point2, point3); 
     }
 
     float GetC (Vector3 point1, Vector3 point2, Vector3 point3){
         return ((point2.x * point3.x * (point2.x - point3.x) * point1.y) +
                 (point1.x * point3.x * (point3.x - point1.x) * point2.y) +
                 (point2.x * point1.x * (point1.x - point2.x) * point3.y)) / GetDenominator (point1, point2, point3);
     }

And the only t$$anonymous$$ng left to do, is to write the movement script for the cannon ball. Good t$$anonymous$$ng is, that using it t$$anonymous$$s way, the target and the cannon can be anywhere on the same 2D plane and it would work. Anyways, cheers!

Answer 2

Answer by y11t_tr · Jan 13, 2017 at 09:06 AM

Wow, thanks for the detailed answer. Just noticed someone actually replied! I will check t$$anonymous$$s out tell you if it worked for me. Thanks!

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How to SHOOT an object on a curved path without using Rigidbody

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