Quaternion.Slerp

Description

Spherically interpolates between a and b by t. The parameter t is clamped to the range [0, 1].

Use this to create a rotation which smoothly interpolates between the first quaternion (a) to the second quaternion (a), based on the value of the parameter (a). If the value of the parameter is close to 0, the output will be close to a, if it is close to 1, the output will be close to b.

// Interpolates rotation between the rotations "from" and "to"
// (Choose from and to not to be the same as
// the object you attach this script to)

using UnityEngine;
using System.Collections;

public class ExampleClass : MonoBehaviour
{
    public Transform from;
    public Transform to;

    private float timeCount = 0.0f;

    void Update()
    {
        transform.rotation = Quaternion.Slerp(from.rotation, to.rotation, timeCount);
        timeCount = timeCount + Time.deltaTime;
    }
}

See Also: Lerp, SlerpUnclamped.