December 30th, 2007, 08:08 AM  #1 
Newbie Joined: Dec 2007 Posts: 1 Thanks: 0  Curve fitting.
Hoping someone can help me here. I've been fumbling around for ages with no success. I don't know how to post a picture which would probably help things a lot. I have 5 points and each point has different constraints. I need to find an equation (or equations) that will link the consecutive points with one smooth curve. The curve can only change curvature(inflect form +ve curvature to ve curvatre) at points 2 and 4. Points 1 & 5 (2 constraints each) X,Y known Gradient = 0 Point 2 & 4 (2 constraints each) X known Curvature = 0 Point 3 (2 constraints) Y known Gradient = 0 That's 10 constraints. From what I believe I need a 10 variable equation to achieve it in a single equation or something like one 4th order polynomial and 2 cubic splines to find a solution. Is this right? Hope this is somewhat understandable. If someone can help me I will email excel files to show the track I was on. 
January 12th, 2008, 10:12 AM  #2 
Newbie Joined: Jan 2008 Posts: 22 Thanks: 0 
At first glance, I was going to say that you are seeking a spline; however, most spline routines I know about use just the (x,y) data pairs, and don't allow you to specify curvature or gradient at specific points. Incidentally, I am not clear about your terminology: I assume when you say Gradient=0 you mean the first derivative of the line is zero (i.e.  a horizontal line). However, when you say Curvature=0, what do you mean? Second derivative is horizontal? Are you looking for a theoretical solution? Or do you have real data pairs? You only have five data pairs, why not post them, so we can see what you are working with. As a guess, it sounds like a cosine curve: horizontal at 0, inflection point at 90 degrees, horizontal at 180 degrees, inflection point at 270 degrees, horizontal at 360 degrees. Tom 

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