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My camera system has two objects: the isometric camera itself, and an empty object it's attached to which handles both movement and rotation. When the player drags the middle mouse button, the camera (or, rather, the empty object) moves like this:

Vector3 diff = lastFramePosition - currFramePosition;

float xchange = diff.x / 5;
float ychange = diff.y / 5;

//flips the direction of movement if the rotation of the object is a certain way
if (transform.rotation.y == 90 || transform.rotation.y == 180)
                ychange *= -1;

if (transform.rotation.y == 270 || transform.rotation.y == 180)
                xchange *= -1;


Vector3 pos = transform.position;

//moves the camera and restrains it within the limits of the map (core.mapx and core.mapy)
transform.position = new Vector3(Mathf.Clamp(xchange + pos.x, 0, core.mapx), 3, Mathf.Clamp(ychange + pos.z, 0, core.mapy));

It turns out, though, that since it moves the empty object along the X and Y axes, dragging up/down or left/right moves it along those axes instead of actually moving the camera view up/down and left/right. The best way I can describe it is like those old isometric games that do the exact same thing. Is there any way I can get it to move like this?

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You could achieve this affect by rotating the empty parent object 45 degrees in y, and counter-rotate the camera so it still points the original direction. Now, when you move, move the empty object along its transform.right and transform.forward vectors by xchange and ychange.

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