During the class at Highland Woodworking, Curtis and I were chatting about the trig tables that we use and teach for figuring out the sighting lines and resultant angles. He mentioned that someone had shown him a means for arriving at the solutions by mapping them out, as opposed to going to Drew Langsners book "The Chairmakers Workshop" or some other math route for the charts. This really appealed to me, but Curtis couldn't recall how it was done. So, I set out to figure my own way.
The sight line angle wasn't so tough, it's really just the overhead view of the chair and I've been drawing those for years, but the resultant angle for drilling was a bit trickier. After a bit of thought and doodling, I had one of those lovely eureka moments.
Below is the first step, which picks up where we left off with the diagonal of the rectangle which gives us the sight line angle. Simply draw a line at a right angle to the diagonal and the same "common rise" as used on the front and side views.
Then, complete the triangle to the other side of the diagonal line. And there it is, the resultant angle is opposite the diagonal line.
Hopefully, the drawing below will help clarify what it is that you are seeing. It is the profile of the plane that the leg is in.
Sorry for the crappy images, my scanner is down and photos are my only solution. Even more exciting and useful for me (it's still faster to use the trig tables) is that while doing this, I remembered a technique that I came up with years ago (and then forgot how it worked) for viewing a chair that I am designing from any angle. Once again, I know that computers can spin an object in space with no effort, but to see it emerge on the page still gets me going.
I know that I am not the first person to figure any of this out, but I see this kind of problem solving as skill building for working with the complex geometry in chairs. So with a little more primer on orthographic projection, we'll get to the real fun stuff.