MATLAB Central Newsreader - Calculating the volume under a non-gridded non-uniform surface

Calculating the volume under a non-gridded non-uniform surface

Brian Roberts — Wed, 12 Aug 2009 18:43:19 -0400

I have a dataset "A" (n by 3) of ordered triplets [x,y,z]. I want to calculate the volume between surface defined by "A" and the xy plane. "A" has only positive values but is not uniformly spaced and not gridded. "A" cannot be described by a simple function. Any help?

Re: Calculating the volume under a non-gridded non-uniform surface

Doug Hull — Wed, 12 Aug 2009 19:13:20 -0400

Brian,

This is an excellent question. Without knowing all of your constraints, I can lay out a general plan. I will try to make this answer into a movie. See my other movies here: (http://blogs.mathworks.com/videos)

1.) Make a function (with interp2) that will give you the value at an arbitrary point See similar video about that:
http://blogs.mathworks.com/videos/2007/11/02/advanced-matlab-surface-plot-of-nonuniform-data/

2.) Use quad2d to do the integration.

I am working on this now, so will post more when finished.

Re: Calculating the volume under a non-gridded non-uniform surface

Doug Hull — Wed, 12 Aug 2009 19:32:18 -0400

"Doug Hull" <hull@mathworks.SPAMPROOFcom> wrote in message
> I am working on this now, so will post more when finished.

I got it figured out:

%%%%%%%%%%%
n = 10;
randOffset = 0.1;
h = 1;

x = rand(n);
x(1:4) = [0 0 1 1]'; %force data points at corners so interpolation is valid in [0 1],[0 1]
y = rand(n);
y(1:4) = [0 1 0 1]';%force data points at corners so interpolation is valid in [0 1],[0 1]
z = h + randOffset*rand(n) - randOffset/2; %make average height

plot3(x,y,z,'.')
axis equal
zlim([0 h + randOffset])

interpZ = @(xi,yi) griddata(x,y,z,xi,yi) %set up interpolation

interpZ(0.5,0.5) %test interpolation
vol = quad2d(interpZ,0,1,0,1) %volume should be close to 1

Re: Calculating the volume under a non-gridded non-uniform surface

Luigi Giaccari — Fri, 14 Aug 2009 17:27:19 -0400

It is even easier:

http://www.mathworks.com/matlabcentral/fileexchange/24593

http://www.mathworks.com/matlabcentral/fileexchange/23447

http://www.mathworks.com/matlabcentral/fileexchange/22185

http://www.advancedmcode.org/