Roof Design using Dachausmittlung

On our Black Mountain job the house has a slopping ridge. However, it also has two valley rafters and two cripple hip rafters intersecting at the same point. I had asked the architect if he had drawn the roof plan in 3D, because the roof plan in this area with the sloping ridge didn't look correct. He said he used math to draw it out and for me to fix it, if it didn't work out correctly.

Joe Bartok might have been able to use math, trigonometry, to calculate the intersection of the  two valley rafters and two cripple hip rafters with the sloping ridge. However, the easiest way for me to find the intersecting point is to use Dachausmittlung (roof slope averaging).

The main profile rafter slope is 4:12 (18.43495°). The intersection of Valley Rafters and Cripple Hip Rafters determines the 22.27275° Roof Slope Angle on the front of this roof in plan view. By using Dachausmittlung (roof slope averaging) you can locate the intersection of the averaging lines and draw in the hip rafter in plan view to intersect the sloping ridge on plan view.