Augmented Reality Demo

I'm trying to build an Augmented Reality Demonstration, like this iPhone App: http://www.acrossair.com/acrossair_app_augmented_reality_nearesttube_london_for_iPhone_3GS.htm

However my geometry/math is a bit rusty nowadays.

This is what I know:

• If i have my Android phone on the landscape mode (with the home button on the left), my z axis points to the direction I'm looking.

• From the sensors of my phone i know what is the angle my z axis has with the North axis, let's call this angle theta.

• If I have a vector from my current position to the point I want to show in my screen, i can calculate the angle this vector does with my z axis. Let's call this angle alpha.

So, based on the alpha angle I have a perception of where the point is, and I'm able to show it in the screen (like the Nearest Tube App).

This is the basic theory of a simple demonstration (of course it's nothing like the App, but it's the first step).

Can someone give me some lights on this matter?

[Update]

I've found this very interesting example, however I need to have the movement on both xx and yy axis. Any hints?

The basics are easy. You need the angle between your location and your destiny (arctangent), and the heading (from the digital compass in your phone). See this answer: Augmented Reality movement There is some objective-c code down there that you can read if you come from java.

What you want is a 3d-Space-Filling-Curve for example a hilbert-curve. That is a spatial index over 3 ccordinate. It is comparable to a octree. You want to store the object in that octree and do a depth-firat search on the coordinate you have recorded with your iphone as fixed coordinate probably the center of the screen. A octree subdivde the space continously in eigth directions and a 3d-Space-Filling-Curve is an hamiltonian path through the space which is like a fracta but it is clearly distinctable from the region of the octree. I use 2d-hilbert-curve to speed search in geospatial databases. Maybe you want to start with this first?