Finding ways from A to B in 3d objects

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In summary, the conversation discusses finding the total number of ways to go from point A to point B in a 2x2x2 object. The participants consider the possibility of a general formula and the use of a 2D visualization to simplify the problem. There is debate over the number of ways and the understanding of the question itself.
  • #1
coldcell
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Find the total number of ways to go from A to B, if each way is the shortest route.

http://img151.imageshack.us/img151/9875/010hr.jpg [Broken]

This is a rough sketch of 2 by 2 by 2 object.

I have to find the number of ways for x by x by x object and x by y by z object.

I tried doing it for 1 by 1 by 1 and 2 by 2 by 2 based on manual calcualting. However I cannot find a general formula for this.

I'm thinking x + y + z, but that's just a pure guess. I tried it on a paper, but it's too hard to show what I tried in this forum.
 
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  • #2
Well, you can only go down, in, or right (depending on how you orient the figure) if you want to go the quickest way, and conversely, as long as you only go one of these three directions at each step, this is a shortest path. (Do you see why?) It might help you visualize things if you flatten the shape out and turn this into a 2D problem.
 
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  • #3
Ah yes I see it... but is it that simple?

We are assuming if we go to the right, it's 1 way. But we have in fact, crossed 2 boxes.

To be honest, I don't really understand the question myself :S
 
  • #4
What? I don't follow you. There is definitely more than one way.
 

1. How do 3D objects differ from 2D objects when finding ways from A to B?

3D objects have an additional dimension, which can make finding ways from A to B more complex. This means that the path between two points may have to navigate through multiple planes, rather than just a flat surface.

2. What methods can be used to find the shortest path between two points in a 3D object?

There are several algorithms that can be used, such as Dijkstra's algorithm and A* algorithm. These methods use mathematical calculations to determine the shortest path between two points in a 3D object.

3. Can 3D objects with irregular shapes be navigated from A to B?

Yes, it is possible to find a path between two points in an irregularly shaped 3D object. However, the path may not always be the most direct route and may require navigating around obstacles or through multiple layers.

4. How does the complexity of a 3D object affect the difficulty of finding a path from A to B?

The complexity of a 3D object can greatly impact the difficulty of finding a path from A to B. Objects with many intricate details or structures can make it more challenging to determine the most efficient path.

5. Are there any real-world applications for finding ways from A to B in 3D objects?

Yes, there are many real-world applications for this type of problem. For example, in robotics, finding the most efficient path for a robot to navigate through a 3D environment is crucial for optimal performance. This problem can also be applied in fields such as transportation and urban planning.

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