How to get object to follow a curved path to reach a moving destination?

Questions & Answers
1

I am making a board/card game where cards are moving around. For example, cards can go from the deck to the player’s hand. However, because of how the player’s hand adjusts itself for different kinds of cards, it’s possible that the player’s hand will change before the card from the deck reaches its destination.

How to make a card follow a somewhat curved path to its moving destination? I would also like for the card to smoothly speed up and slow down along this path, so preferably the method would maintain a consistent speed and wouldn’t have to speed up/slow down to adapt to a different destination.

2

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(exaggerated rotations are intentional, you can disable them by editing rotation interpolation curve)_
[185726-animate-cards-answer.zip|185726] right click / save link as file
_

using System.Collections;
using UnityEngine;

public class CardsAnim : MonoBehaviour
{

	[SerializeField] Transform _p0, _p1, _p2, _p3;
	[SerializeField] Transform _card;
	[SerializeField] float _duration = 2f;
	[SerializeField] AnimationCurve _translationInterpolation = new AnimationCurve(
		new Keyframe(0,0) , new Keyframe(0.03f,0.03f) , new Keyframe(0.3f,0.03f) , new Keyframe(1,1,4.3f,0)
	);
	[SerializeField] AnimationCurve _rotationInterpolation = new AnimationCurve(
		new Keyframe(0,0) , new Keyframe(0.82f,5.7f,26f,26f) , new Keyframe(1,1)
	);

	void OnEnable ()
	{
		StartCoroutine( AnimateCard() );
	}

	#if UNITY_EDITOR
	void OnDrawGizmos ()
	{
		if( _p1 ) { Gizmos.color = Color.red; Gizmos.DrawCube( _p1.position , Vector3.one*0.5f ); }
		if( _p2 ) { Gizmos.color = Color.blue; Gizmos.DrawCube( _p2.position , Vector3.one*0.5f ); }
		if( _p0 && _p1 && _p2 && _p3 )
		{
			Vector3 a = _p0.position, b = _p1.position, c = _p2.position, d = _p3.position;
			const int numSteps = 20;
			float dt = 1f / (float) numSteps;
			Gizmos.color = Color.white;
			for( int i=0 ; i<numSteps ; i++ )
				Gizmos.DrawLine( SampleBezierCurve( i*dt , a , b , c , d ) , SampleBezierCurve( (i+1)*dt , a , b , c , d ) );
			Gizmos.color = Color.red; 	Gizmos.DrawLine(a,b);
			Gizmos.color = Color.green; Gizmos.DrawLine(b,c);
			Gizmos.color = Color.blue;	Gizmos.DrawLine(c,d);
		}
	}
	#endif

	IEnumerator AnimateCard ()
	{
		float time = 0;
		yield return null;
		while( time<_duration )
		{
			float t = time/_duration;
			_card.position = SampleBezierCurve( _translationInterpolation.Evaluate(t) , _p0.position , _p1.position , _p2.position , _p3.position );
			_card.rotation = Quaternion.SlerpUnclamped( _p0.rotation , _p3.rotation , _rotationInterpolation.Evaluate(t) );
			
			yield return null;
			time += Time.deltaTime;
		}
		_card.position = _p3.position;
		_card.rotation = _p3.rotation;

		StartCoroutine( AnimateCard() );
	}

	static Vector3 SampleBezierCurve ( float t , Vector3 a , Vector3 b , Vector3 c , Vector3 d )
		=> a*Mathf.Pow((1f-t),3) + b*(3f*t*Mathf.Pow((1f-t),2f)) + c*(3f*Mathf.Pow(t,2f)*(1f-t)) + d*Mathf.Pow(t,3f);

}