Movement Issues: jumping to another GameObject

Question

My code can make a GameObject jump while simulating gravity. Now I want my GameObject to jump. The purpose of this is to always have a nice "touchdown".

Instead of the parabola, I want to use my jump script but I want it to jump using this relation with the other GameObject. I also need it to work while the target point is moving.

Could anyone solve this problem? An answer would be greatly appreciated. If you've got any questions, do not hesitate to reply (I understand that it's hard to understand...).

Answer 1

This ended up being simpler than I expected. Here is the process I followed so you can follow a similar process in the future:

I started writing the basic physics 101 equations with some values in 2d space because it's easier to think about:

a = (0, -9.8) // this is just gravity down
v = v0 + a*t  // velocity is starting velocity + acceleration times time
p = p0 + v0*t + (1/2)*a*t^2 // the position

and then, I assumed the target position would be relative to the start position, so p0 drops out. Rearraging to find v0, I got:

v0 = p - .5*a*t^2 / t

At this point, there are two things to solve for, v0, and t. This makes sense, you can throw a baseball right at your friend or way up high and still have it land at your friends location, even though it will take longer.

So, I took this and created the following two classes that have the desired effect.

public class Jumper : MonoBehaviour
{
    private Vector3 _velocity = Vector3.zero;
    public Vector3 _gravity = 9.8f * Vector3.down;

    public void Update()
    {
        _velocity += Time.deltaTime * _gravity;
        transform.position += Time.deltaTime * _velocity;
    }

    public void SetVelocityToJump(GameObject goToJumpTo, float timeToJump)
    {
        var toTarget = goToJumpTo.transform.position - this.transform.position;
        _velocity = (toTarget - (Mathf.Pow(timeToJump, 2) * 0.5f * _gravity)) / timeToJump;
    }
}

public class JumpTarget : MonoBehaviour
{
    public Jumper Jumper;
    public float TimeToJump;

    public void Start()
    {
        if (Jumper != null) Jumper.SetVelocityToJump(gameObject, TimeToJump);
    }
}

Edit to address comment If you want to keep the same position in the jump as the target moves, then you are no longer talking about a step-wise physics solution, at least not while the jump is happening. It is easily achieved, however, with a coroutine to handle the jump.

using UnityEngine;
using System.Collections;

public class Jumper : MonoBehaviour
{
    public Vector3 _gravity = 9.8f * Vector3.down;

    public void SetVelocityToJump(GameObject goToJumpTo, float timeToJump)
    {
        StartCoroutine(jumpAndFollow(goToJumpTo, timeToJump));
    }

    private IEnumerator jumpAndFollow(GameObject goToJumpTo, float timeToJump)
    {
        var startPosition = transform.position;
        var targetTransform = goToJumpTo.transform;
        var lastTargetPosition = targetTransform.position;
        var initialVelocity = getInitialVelocity(lastTargetPosition - startPosition, timeToJump);

        var progress = 0f;
        while (progress < timeToJump)
        {
            progress += Time.deltaTime;
            if (targetTransform.position != lastTargetPosition)
            {
                lastTargetPosition = targetTransform.position;
                initialVelocity = getInitialVelocity(lastTargetPosition - startPosition, timeToJump);
            }

            transform.position = startPosition + (progress * initialVelocity) + (0.5f * Mathf.Pow(progress, 2) * _gravity);
            yield return null;
        }
    }

    private Vector3 getInitialVelocity(Vector3 toTarget, float timeToJump)
    {
        return (toTarget - (0.5f * Mathf.Pow(timeToJump, 2) * _gravity)) / timeToJump;
    }
}