Das neue Buch vom alten Wissen der Schiftung
The new book on the ancient knowledge Schiftung
The new book on the ancient knowledge Roof Framing
The new book on the ancient knowledge Roof Framing Geometry
by Bernd Küppers
the angle between the hip line and the auxiliary line in the arc, is not necessarily 90 °. The important thing is, that the pitch break holds at least 3 tiles.
the legs of the upper triangle are hip lines and form the transition between curved and straight roof surface.
the third is the valley line in the front view
and the fourth is indeed the inner top edge of the inner valley rafter.
If you want, you can add the pages of the eyebrow dormer to your blog. This should explain the drawing method of the straight valley line.
I'm helping Bernd translate his book to readable English. Billy or Brad take a look at Bernd's current English translation and see if it make sense. I think the biggest difference between his method and what I know on eyebrow dormer roof design, is the concept of designing the eyebrow dormer for tiles, instead of composition shingles.
Here's an image of the eyebrow dormer with the straight throat that Bernd Kuppers shared.
Here's a drawing by Bernd Brueck showing the hip and valley rafter of the eyebrow dormer and ribs with a straight throat.
Here's a link to the 3-D PDF file
Bernd Brueck Fledermausgaube