Drawing a surface plot in Matlab similar to one obtained using Gnuplot?

Question

Update:

Link to my test dataset

I have some data like this:

10.0 11.0 0.5
10.0 12.0 0.5
10.0 14.5 0.5
10.0 16.0 0.5
10.0 18.5 0.5
10.0 19.0 0.5
10.0 19.5 0.5
10.0 20.0 0.5

Using Gnuplot, I could plot the following picture:

using the following script I wrote:

set data style lines
set surface
set dgrid3d 30,30
set hidden3d
set ticslevel 0.8
set isosample 40,40

set view 60, 30, 1, 1
set contour base

splot "dataset" using 2:1:($3) notitle

I am trying to do some analysis on this graph so wanted to get this into Matlab but am not sure how to draw this. I tried importing the dataset into Matlab and this is how far I could get. I am loading the file and plotting using the following Matlab statements:

load data
rangeY = floor(min(data(:,2))):.5:ceil(max(data(:,2)))
rangeX = floor(min(data(:,1))):.5:ceil(max(data(:,1)))
[X,Y] = meshgrid(rangeX,rangeY)
Z = griddata(data(:,1),data(:,2),data(:,3),X,Y, 'cubic')
surf(X,Y,Z)

The picture looks quite different to me (axis range, shape etc.) Can someone tell me how to get a plot similar to the one I obtained through Gnuplot?

Answer 1

The reason surf won't work right away is that the data are quite noisy, as you'll see if you call

plot3(data(:,1),data(:,2),data(:,3),'.')

Thus, you first need to smoothen the data (which is, I guess, what the gnuplot function does as well). Below is one approach to smoothen the data

%# set bin edges (maybe you want to do 5:10:205)
xEdge = 10:10:200;
yEdge = xEdge;

%# bin the data
xId = sum(bsxfun(@ge,data(:,1),xEdge(2:end-1)),2)+1;
yId = sum(bsxfun(@ge,data(:,2),yEdge(2:end-1)),2)+1;

%# average z within every bin
smoothData = accumarray([xId,yId],data(:,3),[length(xCenter),length(yCenter)],@mean);

%# remove bins with no data
smoothData(smoothData==0) = NaN;

%# bin centers
xCenter = (xEdge(1:end-1)+xEdge(2:end))/2;
yCenter = xCenter;

%# plot
meshc(xCenter,yCenter,smoothData)

Answer 2

I am surprised that your code does not work. I tried it on one of my dataset and it worked ok. As a first answer, I would suggest that your post a link to your dataset (if not sensitive), and that you try other methods of interpolation (starting with the default one, linear).

However, I noticed that griddata produced quite a few NaN at the boundaries of the X-Y domain even though my dataset is quite dense and well distributed in that domain. I checked the doc and it is mentioned that:

Occasionally, griddata might return points on or very near the convex hull of the data as NaNs. This is because roundoff in the computations sometimes makes it difficult to determine if a point near the boundary is in the convex hull.

I don't think this is the cause of your problem, but I still suspect this function not to perform very well with very sparse datasets. You should try TriScatteredInterp instead, which is anyway faster.