Centroid of an airfoil

clc;clear all;close all

%I separated the data points of the top and the bottom of the airfoil so I
%can use interp1 separately for both

%Data points of the top part of the airfoil
x=[1 0.8518 0.7040 0.5536 0.3988 0.2454 0.0937 0.0199 0.0015 0];
y=[0 0.0355 0.0819 0.1206 0.1347 0.1200 0.0777 0.0363 0.0162 0];

%Data points of the bottom part of the airfoil
x2=[0 0.0169 0.0812 0.2054 0.3525 0.4979 0.6457 0.7974 0.9497 1];
y2=[0 -0.0197 -0.0428 -0.0645 -0.0749 -0.0701 -0.0506 -0.0249 -0.0026 0];

%Smoothing both the top and bottom part of the airfoil using
%interp1('pchip')
xx=linspace(1,0);
yy=interp1(x,y,xx,'pchip');

xx2=linspace(0,1);
yy2=interp1(x2,y2,xx2,'pchip');

%Plotting both my smoothed top and bottom data points into the same plot
figure
plot(xx,yy,'b',xx2,yy2,'b')
grid on

This is what I have come up with so far. How do I find the centroid of this airfoil

[Walter Roberson]

Programs that have "clear all" in them are almost always wrong.

Answer 1

[Walter Roberson]

If you have the image processing toolbox, you can use the xx, yy, xx2, yy2 coordinates as inputs to poly2mask(). Then you can use regionprops() to find the centroid of the mask.

[Image Analyst]

That's what I was thinking, though I was waiting/thinking/hoping that there was some built in function to do that, like polyarea for the area. I thought there might be polycentroid(). The IPT way requires quantization of the data into an image. I bet Roger has an analytical solution. If not, then regionprops will be reasonably accurate as long as your image matrix has high enough resolution.

[Walter Roberson]

Oh, there are more direct methods ;-)

[Image Analyst]

Looks like Wikipedia has it. Too bad MATLAB doesn't. But it's simple enough to program https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

[Walter Roberson]

I'm pretty sure that a good-enough approximation can be done much much more easily than that. But I'm feeling mean mean tonight I guess.