Polyarea for noncontinuous shapes

Using a series of points, I would like to calculate the area the shape creates. For example, the following: x=(-.24 -.29 -.19 -.31 -.14 -.15 -.34 -.03 -.31 -.01 -.23 -.19 -.13 -.09) y=(-.01 -.07 -.06 -.05 -.03 0 .05 .07 .11 .15 .19 .21 .26 .27) doesn't graph as a continuous ellipsoid and as such the polyarea function doesn't work appropriately. I tried converting the points from cart2pol and back using pol2cart but that only creates a continual ellipsoid for shapes where the point (0,0) lies inside. For shapes where (0,0) does not lie inside (such as the example with the points given) this does not work. Can anyone suggest a way to correctly calculate the area of these? Thank you!

[Sean de Wolski]

It's not clear what you're after. Perhaps you could post a picture of the expectations (points/shapes etc.)?

In the mean time, I might recommend reading Steven Lord's reply in this old newsreader thread:

http://www.mathworks.com/matlabcentral/newsreader/view_thread/256591

[Laura Kloepper]

Ah, thank you for that Sean. I'm now able to reconstruct the curve but my problem of finding the area enclosed by the curve still exists. The final output for the curve according to the tutorial (xb and yb) are both 2xn and (as far as I understand it) polyarea only works with 1xn inputs. Is there a way around this?

[Sean de Wolski]

I don't follow on xb/yb being 2xn? They're lists of x/y coordinates right? So why shouldn't they be 1xn or nx1? I think this is a place where picture=='1000words';

Answer 1

[Laura Kloepper]

When the original points listed are plotted, it looks like this: http://i40.tinypic.com/swz22p.jpg which has x and y values of 1x53 each.

When the curve is calculated with Delaunay triangulation it looks like this: http://i40.tinypic.com/2e5pikw.jpg This is ultimately what I'd like to calculate the area of.

But the xb and yb values are each 2x53, hence why the polyarea function won't work. Ideas?

[Sean de Wolski]

Are the rows of xb and yb identical? How were they generated from your above points?

[Laura Kloepper]

Yes. They are identical and were generated from the delaunay curve fitting tutorial you suggested. Also, when I run the exact script from the tutorial (#7) it generates 2x192 for both xb and yb.

Answer 2

[Sean de Wolski]

So you do want the convex hull! That simplifies it a lot.

x=[-.24 -.29 -.19 -.31 -.14 -.15 -.34 -.03 -.31 -.01 -.23 -.19 -.13 -.09]; 
y=[-.01 -.07 -.06 -.05 -.03 0 .05 .07 .11 .15 .19 .21 .26 .27];

tri  = DelaunayTri(x',y');
[junk, the_area] = convexHull(tri);

Or you can skip the Delaunay triangulation all together and use the second output of convhull:

[junk, the_area] = convhull(x',y');

[Laura Kloepper]

Awesome! Thanks so much Sean. You have no idea how much this helps!