How to tell which face of a cube is most visible to the camera?

Question

Imagine a camera that shows a randomly rotated cube at an arbitrary position: The cube's pivot is in the center of the cube. This way its six faces could be referred as positive/negative X, Y or Z.

How can you tell which of the faces is most visible to the camera? What's the math to calculate this? Your help is very much appreciated.

Thank you!

Answer 1

public enum CubeFace {
    Left,
    Bottom,
    Back,
    Right,
    Top,
    Front
}

public static GetFaceToward(Transform cube, Vector3 observerPosition) {
    var toObserver = cube.InverseTransformPoint(observerPosition);

    var absolute = new Vector3(
                      Mathf.Abs(toObserver.x),
                      Mathf.Abs(toObserver.y),
                      Mathf.Abs(toObserver.z),
                   );

    if (absolute.x >= absolute.y) {
        if (absolute.x >= absolute.z) {
            return toObserver.x > 0 ? CubeFace.Right : CubeFace.Left;
        } else {
            return toObserver.z > 0 ? CubeFace.Front : CubeFace.Back;
        }
    } else if (absolute.y >= absolute.z) {
        return toObserver.y > 0 ? CubeFace.Top : CubeFace.Bottom;
    } else {
        return toObserver.z > 0 ? CubeFace.Front : CubeFace.Back;
    }
}