Valve's Portal: How'd they do that?

I'm a Computer Science major and I enjoy designing games in my free time. When I play other games, I always enjoy breaking them down in my head to understand how the algorithm works behind certain mechanisms. I recently played the game Portal, made by Valve, and I'm racking my brain on how they designed the portal gun and how it works. I played the inspiration of Portal, Narbacular Drop, and still have no clue as to how it works.

Any ideas? Sources would be much appreciated too, thanks!

Update:

Rudjard, before playing the game, I figured it was that simple too. After playing the game, though, I realized how complex and seamless it really is. You can create a portal and see yourself running through it, as well as stick a box so that one half dangles on one side of the portal and rest dangles on the other.

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