I have two points and would like a metric that tells me how close those points are to each other. Each point is described by both a 3D position and a 3D orientation.

I can determine the distance between the positions of these points using the euclidean distance, and I can find the angular distance of their orientaions.

Is there a metric that encompasses both the distance and orientation as a single value?

I could combine the rotation and translation into a 4x4 transformation matrix, but I don't see how that that would help me get to a single value metric.