I have been battling with this for some time and my noob brain can't quite work it out. I have a standard tile map and currently use the following code to move my enemy sprite around the map

-(void) movePlayer:(ccTime)deltaTime {

    if (CGPointEqualToPoint(self.position, requestedPosition))
        return;


    float step = kPlayerSpeed * deltaTime;
    float dist = ccpDistance(self.position, requestedPosition);
    CGPoint vectorBetweenAB = ccpSub(self.position, requestedPosition);

    if (dist <= step) {
        self.position = requestedPosition;
        [self popPosition];
    } else {
        CGPoint normVectorBetweenAB = ccpNormalize(vectorBetweenAB);
        CGPoint movementVectorForThisFrame = ccpMult(normVectorBetweenAB, step);

        if (abs(vectorBetweenAB.x) > abs(vectorBetweenAB.y)) {
            if (vectorBetweenAB.x > 0) {
                [self runAnimation:walkLeft];
            } else {
                [self runAnimation:walkRight];
            }
        } else {
            if (vectorBetweenAB.y > 0) {
                [self runAnimation:walkDown];
            } else {
                [self runAnimation:walkUp];
            }
        }

        if (self.position.x > movementVectorForThisFrame.x) {
            movementVectorForThisFrame.x = -movementVectorForThisFrame.x;
        }
        if (self.position.y > movementVectorForThisFrame.y) {
            movementVectorForThisFrame.y = -movementVectorForThisFrame.y;
        }
        self.position = ccpAdd(self.position, movementVectorForThisFrame);
    }

}

movePlayer: is called by the classes updateWithDeltaTime: method. the ivar requestedPosition is set in the updateWithDeltaTime method as well, it basically gets the next point out of a queue to move to. These points can be anywhere on the map, so if they are in a diagonal direction from the enemy the enemy sprite will move directly to that point. But how do I change the above code to restrict the movement to vertical and horizontal movement only so that the enemies movement 'staircases' its way along a diagonal path, taking the manhattan distance (I think its called). As shown by my crude drawing below... S being the start point F being the finish and the numbers being each intermediate point along its path to create a staircase type diagonal movement. Finally I intend to be able to toggle this behaviour on and off, so that I can choose whether or not I want the enemy to move free around the map or be restricted to this horizontal / vertical movement only.

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 | |F| | | | | | | |
 | |5|4| | | | | | |
 | | |3|2| | | | | |
 | | | |1|S| | | | |
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