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I have a space with obstacles I wish to find a path through. What I can do is discretize the space into a grid and use A* (or D* or whatever) to find a path through it. I wish to now add orientation to the algorithm. So the node location now becomes a 3d vector (x, y, phi). You can go from one node to another one only if they belong to an arc (both positions are on a circle and are oriented along the tangent lines). How do I discretize the space so that angles don't explode in a sense that by traversing the graph, the set of possible angles becomes finite?

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