On Tue, 24 Aug 2004 13:16:22 -0400, Bill Rogers
wrote:


I won't dwell on it, but you still lose me. A 5th degree polynomial
has [at most] four local max/min; i.e. the plot goes
up/down/up/down/up. That's a strange shape for a leg. :-)

The trick is the "at most". I just wanted flat at both ends and the
curve in between equally distributed. At the risk of dwelling on it:
f(x)=6x^5 - 15x^4 + 10x^3 between x=0 and x=1 is the function I
settled on. I think it'sa fairly standard chair leg shape, actually,
although I don't know the name of it. The up/down/up/down/up
part happens outside the range of interest.

It's not as strange as all that, and I probably could have achieved
the same thing with a set of french splines. This way, I got to tell
myself I was "woodworking" when what I was actually doing was
playing with Matlab. I got to have similar fun when I sat down to
plan the angle I needed to cut a desired cove on my table saw. As
always, the doing was much harder than the math.

I find DeltaCad really helpful. A bit of a learning curve for a
drawing klutz like myself, but I finally got the hang of doing spline
curves.

I did find myself a cheap (free) CAD package, but I found it very hard
to use. My (minimal) CAD training is 15 years old, and at that time,
you typed in the coordinates of the points you wanted and the machine
drew it for you. These days, apparently, it's all about starting with
blank shapes and doing cutting planes or rotations on them. This is
not how my brain works at all.


Bill.