Cubic Sline with constraints

[sgrya1]

I finally worked it out. I used 4 parabolic equations (ie 12 variables) and the following equations.

1 Point 1 (Eqn1)
2 Point 2 (Eqn1)=Point 2(Eqn2)
3 Point 3 (Eqn2)
4 Point 3 (Eqn3)
5 Point 4 (Eqn3)=Point 4(Eqn 4)
6 Point 5 (Eqn4)
7 Gradient 1(Eqn1)=0
8 Gradient 2(Eqn1)=Gradient2(Eqn2)
9 Gradient 3(Eqn2)=0
10 Gradient 3(Eqn3)=0
11 Gradient 4(Eqn3)=Gradient4(Eqn4)
12 Gradient 5(Eqn4)=0

Curvature in parabolas never hit's 0 but at least they have single curvature. The curvature is constant apparently which confuses me. It's not perfect but it seems to do the trick. Also, as it's structural, a parabolic fit is what I should have been after in the first place. Turns out to be a considerable difference in the shape of the two.

I realized also though that regression analysis applies if you need to fit a curve given too many constraints.

Thanks again though VBAHack. Happy New Year!