Hey Joe, awesome stuff as usual.
"You need not do the trig - every angle in a Hip/Valley roof may be developed with nothing more than a compass and straightedge"
That is how I have learned to do this. We just use centerlines of each piece and represent a corner of the roof in plan view. From there with the rise, angle of plates, spacing, backing cut, and hip offset one can calculate everything. By laying certain triangles down in plan view and knowing which points to connect the angles can be found. If you are very precise with this you can then use a bevel to transfer the angles on the plywood or paper to the timber for lay-out, probably some of the most challenging geometry I have attempted, but once it clicks it clicks.
