Surface Fitting using gridfit

Model 2-d surfaces from scattered data

Description

Those wishing to model a surface from data in the  
form of z(x,y) from scattered or semi-scattered  
data have had few options in matlab - mainly  
griddata.  
 
Griddata is a valuable tool for interpolation of  
scattered data. However it fails when there are  
replicates or when the data has many collinear  
points. Griddata is also unable to extrapolate  
beyond the convex hull of the data unless the 'v4'  
option is used, which is slow.  
 
Gridfit solves all of these problems, although it  
is not an interpolant. It builds a surface over a  
complete lattice, extrapolating smoothly into the  
corners. You have control of the amount of  
smoothing done, as well as interpolation methods,  
which solver to use, etc.  
 
This release allows the user to solve much larger problems using a new tiling option. There is essentially no limit on the size of the suface one builds now, as long as you have dense enough data and enough memory to store the final gridded surface.  
 
Example uses are found in the file gridfit_demo.m,  
as well as comparisons to griddata on the same  
surfaces.

• Acknowledgements: This submission has inspired the following:; HOW TO PLOT A COLOURED SURFACE FROM 3D SCATTER
• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: Gridfit should be accessible to older versions of matlab, as long as symamd and colamd are available. Older releases could use one of the iterative solvers, such as symmlq.
• Published M Files: gridfit_demo

Other Files

gridfitdir/.DS_Store,
gridfitdir/bluff_data.mat,
gridfitdir/gridfit.m,
gridfitdir/ravine.jpg,
gridfitdir/demo/.DS_Store,
gridfitdir/demo/gridfit_demo.m,
gridfitdir/doc/Understanding_gridfit.rtf,
gridfitdir/test/.DS_Store,
gridfitdir/test/test_main.m,
gridfitdir/demo/html/gridfit_demo_10.png,
gridfitdir/demo/html/gridfit_demo_09.png,
gridfitdir/demo/html/gridfit_demo_01.png,
gridfitdir/demo/html/gridfit_demo_02.png,
gridfitdir/demo/html/gridfit_demo_03.png,
gridfitdir/demo/html/gridfit_demo_04.png,
gridfitdir/demo/html/gridfit_demo_05.png,
gridfitdir/demo/html/gridfit_demo_06.png,
gridfitdir/demo/html/gridfit_demo_07.png,
gridfitdir/demo/html/gridfit_demo_08.png,
gridfitdir/demo/html/gridfit_demo.png

[Michael Robbins]

Neat picture!

[Urs (us) Schwarz]

simply said: just another extremely useful member of the d'erriconian-draconian family of must-haves if you're professionally serious about nd-data investigation / reconstruction / interpolation / visualization, which smoothly unites with its now-famous siblings (consolidator, inpaint-nans) into a very nice toolbox for those everyday cheating-with-data endeavors...  
the code is very clean and the profiler reveals no unnecessary hot-spot...  
HOWEVER, in contrast, the help bit is just unbelievably clumsy and almost indigestible without sever anxiolytic medication - JOHN, JOHN! this part requires some serious overhaul and sprucin'-up...  
altogether, very well done - and thank you for this snippet  
us

[Chaowen Liang]

This is exactly what I am looking for... Thanks you!!! Save me a lot of time to write one...

[Alberto Baraldi]

I was struggling against griddata since days, beacause of its problems when extrapolating...this is absolutely great!  
Thank you for your great help to the Matlab community. We love you

[Kong Zuor]

Well done John, I have been looking for this while ago and I think it is a must have code. Thank you very much for being so helpful to mathlab community

[CASTRY Alen]

Thank you...

[Julio Oliveira]

Great ! Thank you!

[David Barker]

This is an excellent program. It makes it easy to fit surfaces to 3D data.

[Kevin Denis]

 

[T O]

Excellent Work!

[Wen Soong]

Does a great job!

[Aslak Grinsted]

Should be included into the default distribution of matlab! perhaps somehow integrated into griddata?

[thank you]

Marvelous!

[Andy Lulham]

 

[Håvard Torpe]

Works like a charm right from the moment you start using it.  
 
However: I'd like gridfit() NOT to extrapolate values for gridnodes that has no datapoint in the vicinity. Any ideas?

[John D'Errico]

I'll invite Håvard Torpe to contact me via e-mail to discuss this idea. But while I COULD allow the user to turn off extrapolation in gridfit, this will likely cause singularities - serious numerical problems, for most users who might do so.

[Christopher Schwalm]

Excellent program and documentation.  
 
A question: the help states "Gridfit is not an interpolant." Why is that? It seems to be perfectly able to be used as such, given the outputs and how they were generated. One use I see in my work is to use this function to interpolate where repeated values are present. I've yet to find another Matlab solution that works as well as this does.

[Wolfgang Schwanghart]

Excellent! This is exactly what I was searching for. Thank you very much for this great contribution.

[Phani Ivatury]

Excellent!!!

[Thomas Clark]

Excellent function, John - this has been extremely useful to me.  
 
The ability to turn off extrapolation beyond the bounds of the data would be very useful, though.  
 
A note for the inexperienced user:  
If you have repetitions (multiple points with the same (x,y) but different (z)), this algorithm will handle where griddata might fall. In such a case, think hard about why you have these repetitions; it may be that volumetric plotting is more appropriate than surfaces. If so, you could get a good-looking surface out of this algorithm; which isn't totally meaningful.  
 
 
That's not a fault with this algorithm; it just means that you have to think hard about why you are getting repeated points in Z: If it's acceptable to average these out to a surface, this algorithm is for you!

[Carlos Adrián Vargas Aguilera]

Very very good John! Take good care of Amy!

[E Farhi]

This is simply great, with all we can expect for a replacement to griddata (which fails too often).

[Zhijun Wang]

This is very very good work!

[Ken Lin]

Thanks for your programs. It solves my problem now:)  
by the way, would you like to work out some way to interpolate the data just like the surfer does

[David Sprinkle]

Great tool and insightful docs! Gridfit succeeds where griddata fails; that is, with noisy & ill-spaced data such as exist in the real world. Thanks!

[gabriele flauti]

 

[Juan Perez]

 

[Hendawi Mohamed]

I just write to say..."Thank you"!  
 
PS. but I add: It would be perfect if there was a way to sidestep the extrapolation of the the gridnodes beyond the datapoint boundary. It should be added in matlab next release!

[Darren Paget]

Thanks heaps for the function, it saved me a lot of work. Surface fitting has come a long way! absolutely awesome fit to my data. and really easy to use.

[Henrique Mendes]

It is not working! Matlab says:  
"??? Input argument "x" is undefined.  
Error in ==> gridfit at 325  
x=x(:);"  
I tried to change x(:) to x(:,1), but the problem kepps the same. My Matlab is version 7. It had to be more recent?

[John D'Errico]

Henrique - My guess is that you have called gridfit with no arguments. This code is not a gui or command. See the demos for examples of the use of this code. It truly does work, at least when called with data. John

[Gassilloud rémy]

How to use gridfit with polar coordinates ?  
[th,r] = meshgrid((0:5:360)*pi/180,0:5:300);  
[X,Y] = pol2cart(th,r);  
Z=griddata(x,y,z,X,Y);  
 
Thank you,  
Rémy

[Tim Marvin]

 

[V P]

What is wrong with calling GRIDFIT? Needs improvement.  
 
Z=rand(100);  
a=1:100;  
[X,Y]=meshgrid(a,a);  
good=(X-50).^2+(Y-50).^2>100;  
x=X(good);  
y=Y(good);  
z=Z(good);  
bad=~good;  
xi=X(bad);  
yi=Y(bad);  
zi=gridfit(x,y,z,xi,yi);  
??? Error using ==> gridfit at 404  
xnodes and ynodes must be monotone increasing  

[John D'Errico]

The problem that VP has is he failed to read the help, or apparently bother to understand what gridfit does. I'd recommend reading the help, and perhaps looking at the examples when you don't understand what you are using. I do understand that real men don't need no steenkin help. Perhaps this is the approach that VP has followed.  
 
Gridfit does not interpolate a surface at some random scattered list of points, as would griddata.  
 
Gridfit generates a surface from scattered data on a complete, regular lattice of points. The node arguments are what he might have passed into meshgrid. Again, READ THE HELP.  

[V P]

1. In strict accordance with the help, xi and yi WERE x-nodes and y-nodes of interest, generated by MESHGRID. If this kind of input is not accepted by GRIDFIT, this means that GRIDFIT must be improved.  
2. This is also necessary for comparison with GRIDDATA, which has no problems with my example.  
3. If these arguments are still insufficient, and you insist that I am incorrect, then you have to improve the description of xi and yi in your help and define them as VALID INPUT arguments for MESHGRID. However, this will again mean an improvement.  
4. If this is not convincing for you, look at the example below. If it is not a strong indication of necessary improvements, then I have to follow the principle of "haende khokh" - this is much better than the cold war around an empty egg.  
 
Z=rand(100);  
a=(1:100)';  
[X,Y]=meshgrid(a,a);  
z=gridfit(X(:),Y(:),Z(:),a,a);  
norm(z(:)-Z(:))  
ans =  
    4.9225

[Alex Gardner]

 

[Carlos Adrián Vargas Aguilera]

Hi John:  
    
I've been using your incredible program for some years and in a wide range of applications. My question is, do you have written any kind of documentation in a scientific journal, for example, for any citation and also to know a little bit more about this super "surface fitting". Any reference can help too.  
    
BTW: VP uses the more silly test to "compare" GRIDDATA and GRIDFIT, and, as John says, he doesn't bother to read that by default the former is 'linear' and the latter uses 'smooth' to 1. But, any way...

[Anmol Agrawal]

Excellent utility!! A default setting did everything I needed with minimal error.

[gai cs]

it is very good toolbox ?thanks

[Andrey Matseevskiy]

You wrote "For example, my computer took 1020 seconds to solve a 500x500 problem." What an old comp do you use? I need 5 second to solve 500x500 problem. Download my prog from http://www.smartfills.com/Html/2D.zip . Compare with your own method. My own is in fact interpolation, but could be modified for approximation without much problems.  
Andrey, Kamchatka

[John D'Errico]

The review by Andrey is a bit of self serving braggadocio, since he does not actually offer Matlab code on the file exchange that replicates in any form what gridfit does. By the way, the link he gives is for a .exe file - BEWARE.  
 
His time comparisons are also meaningless of course, since the times referred to are for a now wildly obsolete computer, and comparing an interpolation code to this class of modeling code makes no sense anyway.  
 
Finally, converting an interpolation code to a noise reducing surface modeling code is not at all trivial. I welcome Andrey to do so and provide MATLAB code for the purpose, if that is truly so easy.

[Cedric Testaz]

 

[Pauline Wong]

Versatile smoothing function.

[Cristina Velasco]

 

[Alexis]

Good job John, beautiful tool! Very parameterizable and helps a lot in giving you a feel of how your data is behaving.  
 
Does anyone know how I can anchor the surface to any given point? I'd like to force the surface to pass through a given set of (x,y,z) anchor points, something like establishing an "infinite" weight to these keypoints, while not altering the weight of the other "normal" points...

[Jveer]

wow! looks awesome! was wondering if there was any way to fit a surface around a 3D scatter? maybe this could be used on the data of for e.g x,y data corresponding to max(z) and then repeating for max(x) and max(y)?

[Michael Jordan]

 

[J Ú]

 

[Bryan Raines]

 

[Michael Dupin]

 

[Karl]

This is spectacular. I hope the Mathworks is paying you some sort of royalty for your efforts!

[Chris Sherwood]

This routine is almost magic...it is the only routine I have found that finds surfaces I know are there amidst very noisy elevation data. Thanks for contributing it.

[Angel Atanasov]

Thank you mr. D'Errico, for making my life easier.You piece of code is really good.