I’m now at the stage where I am beginning to work through my algorithms for the actual framing of the roof (ie. rafters, ridges, hips and valleys). I begin by breaking down the edges of the roof so that I can determine which are hips, valleys, rakes, flying hips etc… I also want to actually label each as such so when it comes time to dump all of this into the estimating module there is some order to it.
If you look closely at a roof primitive and the edges that constitute that primitive, immediately a number of things jump out at you:
1.) All of the horizontal edges that are at the same Z height as the top fascia line are roof perimeter edges or “fascia edges”. We do have to make an exception for the half hip though, since its fascia edge will be elevated above the eave height.
2.) All of the edges with vertices below the fascia Z height are irrelevant and we won’t be needing those.
3.) If we look at all the edges coming off of the perimeter vertices (we can find those easily enough by comparing against our perimeter points array) it is apparent that the inside angle between two fascia edges will determine whether the edge is a valley or a hip. If the angle is less than 180 deg. then it is a hip. if the angle is greater than 180 deg. it is a valley. If the edges belong to a gable or half hip roof plane then they will be rake edges, rather than hips or valleys.
4.) Next we grab all of the remaining edges where the height of the start and end vertices are equal. These will form ridges. An exception must be made for dutch gable and the half hip. So it is best that we eliminate those edges first.
5.) Fortunately, there are no such thing as flying valleys, only flying hips. By process of elimination the remaining edges will all be flying hips. Flying hips are interesting because they always begin where a valley and ridge intersect and they end either intersecting another hip/flying hip at a ridge or at a peak with possibly multiple hips coming together at a point.
We basically dump each edge in the primitive into a hash so we have ourselves a quick lookup table for each edge that we can access it for future operations (ie. cutting rafters).
When the roof corner angles are all orthogonal (90 deg. or 270 deg.) the algorithm for the rafter framing should be fairly simple. However when you throw in non-orthogonal angles (ie. octagon roofs) things become more complicated and there needs to be some logic to deal with these scenarios specifically.
Another reason that I need to classify the edges is that the width of the valleys, hips and ridges may not be equal, which will impact the trimming of the rafters as they intersect these members.
And that is all the magic there is to it. I think the key breakthrough I had back in May (when I figured out my straight skeleton algorithm) was that I realized that once I somehow generated the roof primitive the rest would easily fall out. Previously, I was trying to mathematically calculate all of these vertices and edges, which turned out to be incredibly difficult and ultimately a dead end.
I now have a coherent plan of attack.
