AutoCAD .NET :: Rotating A Block Into New Orientation In 3D

I am trying to write a tool using the .NET API (C#) that will allow me to select a block that currently exists in the drawing, and then select a line, and the tool would calculate the necessary axis of rotation and the amount of rotation to rotate the block into the same orientation as the line. Both the block and the line might be skewed in 3 dimensions. The use case for a tool like this might be for drawing a tubular space frame. I would first define nodes and center lines for the frame, and then have a block of a standard structural member. I want to insert that member multiple times and "snap" it to a center line. I tried using Alignment Parameters.

However, these don't seem to work in all cases. I need to (or rather, SHOULD be able to) create a tool that allows me to re-align an existing block currently inserted into the drawing into a new orientation in 3D using any arbitrary line as a reference line. Clearly this can be done because it is done all the time in Inventor. A similar feature seems to not exist in Autocad.

In order to do this I believe I need to choose some vector to use as a reference within the block. For example, I might choose the BlockReference.BlockTransform.CoordinateSystem3d.Xaxis, and then rotate this vector so that it is equal to whatever reference line I have chosen. The problem I am encountering (and that I think many have encountered) is in understanding how to use the BlockTransform correctly to arrive at the points I need to do the necessary vector calculations to determine the axis of rotation and the degree of rotation such that I can call the BlockReference.TransformBy() method correctly and reliably. 

Many posts say to "Use BlockTransform" but then don't go into any detail. There seem to me many pitfalls around when one can use the BlockTransform matrix, and on which objects, and what the results are likely to be based on one's current UCS etc.