K. Brian Kelley (3/19/2014)
I don't think you're going to find a function with just distance. Maybe with a point. The reason I say this is in 2D space there would be two lines parallel to a give line. In 3D space you'd form a cylinder. So there wouldn't just be a line output in either situation.
That is only the case where the lines are similar as well as parallel otherwise even in 2D there will still be an infinite number of parallel lines - the length of the line does not affect whether or not it is parallel.
Any straight line in 2d can be defined by the equation y=mx+c bounded by its min and max ordinates. By changing the bounds or the value of c you will generate a parallel line.