Chamfers and Quarter-Rounds

So, we finally got our boards perfectly flat and square and they made us disfigure them by using them for another exercise.  We practiced making chamfers (an angled surface connecting to flat surfaces, in this case and typically 45 degrees) and quarter-rounds (a quarter circle connecting the 2 flat surfaces.)  On the ends we did this with our hand plane and on the edges we used chisels.

Chamfers

Quarter-Rounds

The process for making quarter-rounds was especially interesting to me because I am a math geek.  First you mark off how much you want to round over.  The amount doesn't matter.  You take that amount and imagine it to be made from 12 parts.  For example, dividing it in half would put a line at 6 parts.  For this you want to divide it into a 5:7 ratio, with the 5 being toward the inside.  Do that on both the face and edge.  Cut a chamfer that connects the 2 lines.  Now you have created a flat 45 degree surface that is  about 10 parts (Yea pythagorean theorem!).  Dividing that surface in half gives you a line that is on the outer surface of the quarter round, which if this were a full circle would be 1/8 of the way around the circle from starting lines.  It also leaves you with 4 5 part surfaces.  Divide them in half, cut chamfers to connect the lines on surface 1 and 2 and on surface 3 and 4.  Clean up a few edges and you have fairly accurate quarter rounds.  Anyone follow?  Diagrams would help.  They would be fairly easy to do, but I don't have any photo editing software. :(

Here is a quick sketch of the quarter-round concept that I took a picture of with the camera built into my computer.  I never realized that using that camera is like looking in a mirror.  Makes sense for video chatting, but now my numbers are mirrored, which makes this hard to read.  You can start to see how it is becoming round  after only 3 cuts though.

I added 4 more cuts to this sketch and it is now really round.