TrackballCamera

using UnityEngine;
 
public class TrackballCamera : MonoBehaviour
{
    public float distance = 15f;
    public float virtualTrackballDistance = 0.25f;
    public GameObject target;
    private Vector3? lastMousePosition;
 
 
    private void Start()
    {
        var startPos = (this.transform.position - target.transform.position).normalized * distance;
        var position = startPos + target.transform.position;
        transform.position = position;
        transform.LookAt(target.transform.position);
    }
 
 
    private void LateUpdate()
    {
        var mousePos = Input.mousePosition;
 
        var mouseBtn = Input.GetMouseButton(0);
        if (mouseBtn)
        {
            if (lastMousePosition.HasValue)
            {
                // We are moving from here.
                var lastPos = this.transform.position;
                var targetPos = target.transform.position;
 
                // we have traced out this distance on a sphere from lastPos
                /*
				var rotation = TrackBall(
										lastMousePosition.Value.x,
										lastMousePosition.Value.y,
										mousePos.x,
										mousePos.y );
				*/
                var rotation = FigureOutAxisAngleRotation(lastMousePosition.Value, mousePos);
 
                var vecPos = (targetPos - lastPos).normalized * -distance;
 
                this.transform.position = rotation * vecPos + targetPos;
                this.transform.LookAt(targetPos);
 
                lastMousePosition = mousePos;
            }
            else
            {
                lastMousePosition = mousePos;
            }
        }
        else
        {
            lastMousePosition = null;
        }
    }
 
 
    private Quaternion FigureOutAxisAngleRotation(Vector3 lastMousePos, Vector3 mousePos)
    {
        if (lastMousePos.x == mousePos.x && lastMousePos.y == mousePos.y)
        {
            return Quaternion.identity;
        }
 
        var near = new Vector3(0, 0, Camera.main.nearClipPlane);
        Vector3 p1 = Camera.main.ScreenToWorldPoint(lastMousePos + near);
        Vector3 p2 = Camera.main.ScreenToWorldPoint(mousePos + near);
 
        //WriteLine("## {0} {1}", p1,p2);
        var axisOfRotation = Vector3.Cross(p2, p1);
        var twist = (p2 - p1).magnitude / (2.0f * virtualTrackballDistance);
 
        if (twist > 1.0f)
        {
            twist = 1.0f;
        }
 
        if (twist < -1.0f)
        {
            twist = -1.0f;
        }
 
        var phi = (2.0f * Mathf.Asin(twist)) * 180 / Mathf.PI;
        //WriteLine("AA: {0} angle: {1}",axisOfRotation, phi);
 
        return Quaternion.AngleAxis(phi, axisOfRotation);
    }
 
 
    private Quaternion TrackBall(float p1x, float p1y, float p2x, float p2y, float radius)
    {
        // if there has been no drag, then return "no rotation"
        if (p1x == p2x && p1y == p2y)
        {
            return Quaternion.identity;
        }
 
        var p1 = ProjectToSphere(radius, p1x, p1y);
        var p2 = ProjectToSphere(radius, p2x, p2y);
        var a = Vector3.Cross(p2, p1); // axis of rotation
                                       // how much to rotate around above axis
        var d = p1 - p2;
        var t = d.magnitude / (2.0f * radius);
 
        // clamp values to stop things going out of control.
        if (t > 1.0f)
        {
            t = 1.0f;
        }
 
        if (t < -1.0f)
        {
            t = -1.0f;
        }
 
        var phi = 2.0f * Mathf.Asin(t);
        phi = phi * 180 / Mathf.PI; // to degrees
 
        return Quaternion.AngleAxis(phi, a);
    }
 
 
    /// <summary>
    /// Projects an x,y pair onto a sphere of radius distance.
    /// OR onto a hyperbolic sheet if we are away from the center
    /// of the sphere
    /// </summary>
    /// <returns>The point on the sphere</returns>
    /// <param name='distance'>Distance</param>
    /// <param name='x'>X</param>
    /// <param name='y'>Y</param>
    private Vector3 ProjectToSphere(float distance, float x, float y)
    {
        float z;
        float d = Mathf.Sqrt(x * x + y * y);
        if (d < distance * 0.707f)
        {
            // inside sphere
            z = Mathf.Sqrt(distance * distance - d * d);
        }
        else
        {
            // on hyperbola
            var t = distance / 1.4142f;
            z = t * t / d;
        }
 
        return new Vector3(x, y, z);
    }
}