TrajectoryCalculation.cs

using UnityEngine;
using System.Collections;

public class TrajectoryCalculation : MonoBehaviour 
{
	public Rigidbody projectile;
	public Transform target;
	[Header("CalculateBestThrowSpeed")]
	public float timeToTarget = 1f;
	[Header("CalculateTrajectory")]
	public float speed = 10;
	[Range(0, 1)] public float arc = 0;


	void Update()
	{
		if (Input.GetKeyDown("a"))
		{
			GameObject p = Instantiate(projectile, transform.position, transform.rotation) as GameObject;
			p.GetComponent<Rigidbody>().AddForce(CalculateBestThrowSpeed(transform.position, target.position, timeToTarget), ForceMode.VelocityChange);
			Destroy(p, 10);
		}

		if (Input.GetKeyDown("b"))
		{
			Vector3 velocity;
			if (CalculateTrajectory(transform.position, target.position, speed, out velocity, arc))
			{
				GameObject p = Instantiate(projectile, transform.position, transform.rotation) as GameObject;
				p.GetComponent<Rigidbody>().AddForce(velocity, ForceMode.VelocityChange);
				Destroy(p, 10);
			}
			else
			{
				Debug.Log("Target cannot be reached. Increase speed or reduce distance.");
			}
		}
	}


	// from http://answers.unity3d.com/answers/456066/view.html
	static Vector3 CalculateBestThrowSpeed(Vector3 origin, Vector3 target, float timeToTarget)
	{
		Vector3 toTarget = target - origin;
		Vector3 toTargetXZ = toTarget;
		toTargetXZ.y = 0;
		float y = toTarget.y;
		float xz = toTargetXZ.magnitude;
		float v0y = y / timeToTarget + 0.5f * Physics.gravity.magnitude * timeToTarget;
		float v0xz = xz / timeToTarget;
		Vector3 result = toTargetXZ.normalized;
		result *= v0xz;
		result.y = v0y;
		return result;
	}


	// based on http://gamedev.stackexchange.com/questions/114522/how-can-i-launch-a-gameobject-at-a-target-if-i-am-given-everything-except-for-it/114547
	static bool CalculateTrajectory(Vector3 origin, Vector3 target, float speed, out Vector3 velocity, float arc = 0f)
	{
		Vector3 toTarget = target - origin;
		Vector3 toTargetXZ = toTarget;
		toTargetXZ.y = 0;
		float y = toTarget.y;
		float xz = toTargetXZ.magnitude;
		float gravity = Physics.gravity.magnitude;
		float b = speed*speed - y * gravity;
		float discriminant = b * b - gravity * gravity * (xz * xz + y * y);
		if (discriminant < 0) // out of range, need higher shot speed
		{
			velocity = Vector3.zero;
			return false;
		}
		float discRoot = Mathf.Sqrt(discriminant);
		float minTime = Mathf.Sqrt((b - discRoot) * 2) / Mathf.Abs(gravity); // impact time for the most direct shot that hits
		float maxTime = Mathf.Sqrt((b + discRoot) * 2) / Mathf.Abs(gravity); // impact time for the highest shot that hits
		float time = (maxTime - minTime) * arc + minTime;
		float v0xz = xz / time;
		float v0y = y / time + time * gravity / 2;
		velocity = toTargetXZ.normalized;
		velocity *= v0xz;
		velocity.y = v0y;
		return true;
	}

}