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I have been curious about how this kind of seamless transition from space to planet can be implemented. It would be nice if someone could explain this as I can't really wrap my head around the solution.

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What part of it specifically? It would be similar to any other continuous world implementation. Only loading the content near the player and using a level of detail system to keep resource use low. – Byte56 Nov 29 '12 at 15:36
Perhaps this post from the Infinity developers might help. – Ilmari Karonen Nov 29 '12 at 19:06
Ahh, Infinity. Such a beautiful project. – Djentleman Jan 5 '13 at 6:24
up vote 3 down vote accepted

Over time, move the camera from far away from the planet to close to the planet surface. This is analogous to the way that you can seamlessly transition from one side of a Quake level to the other side, merely by moving the camera from one side to the other.

There really is no fundamental difference between the two.

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I'm adding "completely seamless transitions from one side of a level to the other" to my engine's feature list. ;) – Nathan Reed Nov 30 '12 at 1:52
One thing I notice in the video that you don't mention in your answer is a fairly obvious LOD technique. – Stephan van den Heuvel Nov 30 '12 at 3:03
I haven't watched the video. But honestly, there's nothing magic about going from space to a planet surface. It's all just triangles. :) – Trevor Powell Nov 30 '12 at 4:26
Ah, so easy. I was overthinking it. This would require translating the point of orbit entry into what "level" should be loaded in front of the player. But that's another question I guess. – Phil Nov 30 '12 at 15:07
@TrevorPowell Nothing magic, but if you try to render all the triangles present on the planet's surface (watch the video) when you are very far away, you are going to have a fractional frame rate. You must use a level of detail technique to do this. It is not simply transforming the camera closer to the planet. – Stephan van den Heuvel Nov 30 '12 at 16:08

Write a Function that describes your Surface, and then do low sampling on far distances and tight sampling on near distances. And then add some shiny visual effects.

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This guy did exactly what your looking to do, his site goes into tons of details.

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