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I will do what I can but it may take a while. Please be patient.
Yeah. I suppose I may have to settle for a half-accurate curve when dealing with graphic representations of 3D surfaces. I appreciate the value of splines, I just preferred a single function. It seemed cleaner.
Okay, but remember, that is why they invented piecewise functions and splines. Because it was often impossible to fit one curve through some set of ordered pairs.
With Maple you can plot a couple of points more along the curve than just the three linear points, as I said, I was trying out the mean values and quarter and three-quarter lengths of the arcs, but the resultant curves were really bad. I figured I could either fit a ton of points or try to figure something else out more logical.
I am a perfectionist. If there was something I could do over and over and get a better fit every time, I wouldn't stop doing it until I had it perfect. By near perfect I meant thousandths of a decimal off.
Okay, extremely closely? How big is the error you can stand?
Exactly. A piecewise made into a single function h(x) or whatever we were calling it.
Thank you in advance.
Correct - h(x), the unknown blue curve, is a piecewise function of f(x) from 0 to 75 and g(x) from 75 to 150. The ultimate goal is to fit a single curve defined by a single function.
Alright, here are some images from Maple I made, color-coded in hopes to communicate effectively. On my monitor they look as though they exported with low detail to quality, but they are still readable.
Seeing as I have already performed an application of it, it should be fairly obvious "what I am trying to accomplish".
My calculus class in junior college just happens to use Maple. It doesn't affect my amateurish status for good or not. Does it matter?
To digress for a bit!
Can I ask what you are trying to accomplish by using Thiele's Interpolation to begin with? If you can answer that you certainly are not ignorant or amateurish at all. Also you use Maple which places you ahead of lots of mathematicians.
Well goody for you Andy! Read Paul Nahins or Doron Zeilberger books to get idea about what I mean, what I am saying...