Dachausmittlung -- Complex Geometric Roof Design

This example of Dachausmittlung, Geometric Roof Design, is rather complex geometrically and is extremely complex if we were using trigonometry. After I drew out the geometric roof design I checked the plan angles with my RafterTools apps and to my dismay my RafterTools apps were not able to calculate the plan angles for the eave angles when the eave lines are sloping.

3D View of the Roof Design

Wire Frame sketch of the Roof Design with raking/sloping eave lines.

Ground Plan of Roof Design.

Two different roof pitches with two eave lines raking/sloping.

In this drawing I've labeled the eave angles that my RafterTools apps could not calculate the plan angles for.

Drawing showing the geometric construction of the roof design with some of the construction lines removed for clarity. 

Steps for drawing the geometric roof design.

This is one of those roofs where the hip rafters can only be calculated from the geometric design of the roof. I'm not sure if there are any American CAD programs that could automatically draw out the roof design like the German CAD programs do. I'll have to look into writing a new Android/iPhone app that can be used to check the roof plan angles when the eave lines are sloping.