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Dynamic labyrinth with A*

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I need to connect 3 points "a" on top of the screen to their respectives points "b" at the bottom. this connection I would like to do it via labyrinths that are intertwined. so far so good, the real problem is, I want to make these labyrinths dynamic, I've thought about making pieces like horizontal pipes, vertical pipes, and elbows that can be connected based on a 3d grid and avoid each other via collision detection, using an A* algorithm to "grow" them, but maybe this is not the best way, anyone has another direction I can look in to? maybe an algorithm or an idea about how to work this out? Thanks in advance guys.

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