Creating and manipulating coordinate systems

I'm looking for a generic algorithm for creating a new XYZRxRyRz coordinate system within a larger "World" coordinate system, by finding points on the edges of the new coordinate system. I *think* I could puzzle out the math eventually, but I'm sure there are smarter people who have done this before. The general concept is this: I use a sensor to find three (or more) points on the edges of an object (let's assume it's a flat square, for the sake of simplicity) -- two points on one edge, one point on an adjoining edge. I have 3D data for each point, in terms of the World coordinate system. What I want to generate from that data is a single