Question: Is it possible to reconstruct a grid of polygones or polylines from the centroids?

I am looking for a arcGIS tool or script that will allow me to reconstruct a grid of polygons or polylines from their centroids.

![From centroids](https://i.stack.imgur.com/NTVLC.png)

![to polygons](https://i.stack.imgur.com/bLcSP.png)

Answer: 
you can use Distance Calculator which located in Tool Manager, but if you are interested professional tool, i advice you MapInfo® Routing J Server. 

For Distance Calculater :

```
Tools > Tool Manager > Distance Calculator

```

Description of tool:

> 
> This program calculates the distance form all the objects in one table
>  to all objects in a second table or itself. It then returns the
>  closest or farthest distance(s).
> 
> 
> 

and you can also try RouteWare RouteFinder for MapInfo tool [here](http://www.routeware.dk/download.php)...

i hope it helps you...
calculating the shortest distance , there is a logic behind it.

When we ask the bing or google service to give a shortest distance betwen point A to point B , it gives us the route which is drivable , if there a one way from B to A which is short , it wont give that route.

So how you have to proceed it 

1. Calculate the route and distance from Point A to B
2. Calculate the route and distance from Point B to A.

take the Route which has shortest distance.