Direction Vector around Mesh's Surface - unity3d

Question

How do I best describe the direction vector to move an object left (or right/up/down) from its current position, factoring the current view perspective into the equation?
For example, imagine the box depicted in the following picture, placed at origin (0,0,0). If I wanted to move the point on top of the box to the left, I'd have to make a step in (-1,0,0) direction (i.e. currentPos = currentPos + Vector3.left).
If I looked at the box from behind, I'd have to make a step in (1,0,0) direction to continue moving in the same direction.
i.e. When I'm looking at this box, placed at origin, and press an input button LEFT, I need for the point to move left and continue moving in that direction for as long as I keep pressing the button. It ultimately wraps around the surface, i.e. if I keep pressing just LEFT the point will wrap around the cube and re-appear so to speak.

Answer 1

To indefinitly trace a decal around a cube:
private Transform Cube;
private Transform Decal;
void Update() {
Vector3 moveLocal = Vector3.zero;
// Set moveLocal from User Input
moveLocal += Vector3.left * Input.GetAxis("Left"); // etc
if (moveLocal.sqrMagnitude > 0) {
var decalDirection = (Decal.position - Cube.position).normalized;
var angle = Vector3.SignedAngle(Cube.forward, decalDirection, Cube.up);
// Align decal to correct cube face
if (angle < -135 || angle > 135) { // Rear face
Decal.forward = -Cube.forward;
}
else if (angle < -45) { // Left face
Decal.forward = -Cube.right;
}
else if (angle > 45) { // Right face
Decal.forward = Cube.right;
}
else { // Front Face
Decal.forward = Cube.forward;
}
// Now move decal in it's local space:
Decal.Translate(moveLocal, Space.Self);
}
}
Admittedly, this only rotates Left/Right, but I hope you get the idea =)

Answer 2

As i mentioned you in my opinion you can achieve this with surface normals. I cracked some code which is not an exact solution because i used collision normals and on corners that gives different results. In any case i share it so that it gives you the idea. You can go left and right with this code relative to camera(even though it does not use anything related to camera) because it depends on surface normals.
private Vector3 normal;
private Vector3 contact;
private Vector3 direction;
private GameObject obj;
void Start () {
}
void Update () {
if (obj == null)
return;
if( Input.GetKey(KeyCode.LeftArrow))
{
obj.transform.position += direction * Time.deltaTime;
}
if (Input.GetKey(KeyCode.RightArrow))
{
obj.transform.position -= direction * Time.deltaTime;
}
}
void OnCollisionEnter(Collision collision)
{
Debug.Log("Collided");
Debug.Log("If works");
obj = collision.gameObject;
normal = collision.contacts[0].normal;
contact = collision.contacts[0].point;
//Cross product of normal and up gives direction Right.
//This up can be cube's up as well in cases it is tilted
direction = (-Vector3.Cross(Vector3.up, normal));
}
You can also see how it works from images below: