Programming Puzzle for you Experts out There

[Joe]

First a little background:

I'm in the process of writing a fatigue and damage tolerance analysis
program using python.  One of the things the math engine can do is
compute the remaining strength of the material after it has sustained
damage.  However, there are two problems:

1)  Redisual strength is influenced by two competing physical
properties of the metal.  So far, nobody has developed a method for
evaluating the transition between these properties so the conventional
wisdom is to "eyeball" a curve between them.

2)  Sometimes, the damage or fatigue involves a "ligament break", this
will suddenly change the stress field and, not surprisingly, cause a
step change in the residual strength curve.

So here is the problem......

I have two vectors that, when plotted against each other are mostly
smooth with occasional inflection points and step changes.  I want to
keep the step changes but inscribe a smooth arc below the inflection
points that will eventually be tangent to the intersecting curves.

Now, here is the hard part......

To get the boundary conditions, I must sample the vectors "as is".
Re-iterating the numbers to get better data will require me to go back
into the math engine which will suck up processor time.

I've tried 4th order polynomial fits and hyperbolic fits but neither
have been robust enough to track all of the fracture scenarios I've
thrown at it without Gibb's overshoots or other issues.  I have not
tried Fourier or other series fits as of yet.  Probably try that next.

Still working on it....but I'm willing to entertain suggestions. 

Joe