# How to create an interpolation surface for a wing ?

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Ionut on 9 Dec 2012
So I got this assignment that says I have to build an interpolation surface for a wing that has the profile in the xOy plane with the coordinates:
x=b*[0 1.25 2.5 5 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100.35]/100;
ye=a*[0 2.06 2.96 4.3 5.42 6.31 7.78 8.88 9.65 10.13 10.35 9.81 8.78 7.28 5.34 2.95 1.57 0.09 -0.1]/125;
yi=a*[0 -0.88 -1.11 -1.18 -1.08 -0.88 -0.36 0.17 0.69 1.12 1.65 1.86 1.92 1.76 1.36 0.74 0.35 -0.09 -0.1]/125;
in wich:
ye- coordinate for the upper surface(extrados)
yi- coordinate for the lower surface.(intrados)
Also the projection in the xOz plane of the wing profile is a trapezoid with the base angle equal to 70° and height c
the thickness profile after axis "oy" is considered to be constant.
a,b,c are constants given.
Does anyone has any idea how to solve this?? I tried using Bezier surface algorithm but cant make it work :(

Jonathan Epperl on 10 Dec 2012
Hi, if you have the Curve Fitting Toolbox, then it's pretty easy, call the GUI
cftool
If you don't have it, on the other hand, I can tell you that it looks like a 3rd-order polynome interpolates your ye nicely, while for the yi part you need a few sin and cos terms.
Once you have nice interpolants you can probably easily put that together as a parametrized surface, but that's something I don't know much about.