With power and angle, what is the best way to create a parabolic arc?

Question

I'm creating a custom controller for a Launch-type game. My opening sequence is already scripted and produces two variables: Angle, and Power. I do not want to use this with a Rigidbody and physics but create the actual parabolic arc and movement myself - I'm targeting lower-end devices. What kind of formula, or script would be best for this method?

EDIT: My goal is to do this using transform. I've already set up the smoothing in order to handle the movement.

 transform.position = Vector3.Lerp(transform.position, targetPosition, Time.deltaTime * smooth);

Answer 1

I'm not sure if you know this, but if you have a non-kinematic Rigidbody and set its velocity and let gravity influence it, it'll follow a parabolic arc. There are simple, specific equations you can use to calculate a projectile's trajectory.

For a slightly more lightweight solution, could alternatively define a class similar to this (in C#):

 public class MyProjectile : MonoBehaviour {
     public Vector3 gravity = new Vector3(0f,-9.81f,0f); //could instead use Physics.gravity
     private Vector3 velocity;
     
     public void Awake() {
         enabled = false; //start off disabled
     }
     
     public void FixedUpdate() {
         //apply gravity
         velocity += gravity*Time.fixedDeltaTime;
         
         /*if you're wanting to collide with things, here would 
         be a good place to perform physics sweep tests / raycasts
         as needed to know where to stop your object and make it 
         bounce*/
         
         transform.position += velocity*Time.fixedDeltaTime;
     }

     //call this from whatever script / method you want to 
     //initialise a projectile from. Eg, if done in another C# 
     //script, where projectilePrefab is a prefab you've made 
     //with this script attached:
     //GameObject o = (GameObject)Instantiate(projectilePrefab);
     //MyProjectile p = o.GetComponent<MyProjectile>();
     //if (p) {
     //    p.Initialise(somePower,someQuaternionAngle);
     //}
     public void Initialise(float power, Quaternion angle) {
         //here, power is speed (ie the magnitude of velocity)
         velocity = angle * Vector3.forward * power;
         enabled = true; //enable this script's update methods once we've initialised
     }
 }

With power and angle, what is the best way to create a parabolic arc?

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