MATLAB Function Reference

griddata3 - Data gridding and hypersurface fitting for 3-D data

Syntax

w = griddata3(x,y,z,v,xi,yi,zi)
w = griddata3(x,y,z,v,xi,yi,zi,method)
w = griddata3(x,y,z,v,xi,yi,zi,method,options)

Description

w = griddata3(x,y,z,v,xi,yi,zi) fits a hypersurface of the form to the data in the (usually) nonuniformly spaced vectors (x, y, z, v). griddata3 interpolates this hypersurface at the points specified by (xi,yi,zi) to produce w. w is the same size as xi, yi, and zi.

(xi,yi,zi) is usually a uniform grid (as produced by meshgrid) and is where griddata3 gets its name.

w = griddata3(x,y,z,v,xi,yi,zi,method) defines the type of surface that is fit to the data, where method is either:

If method is [], the default 'linear' method is used.

w = griddata3(x,y,z,v,xi,yi,zi,method,options) specifies a cell array of strings options to be used in Qhull via delaunayn.

If options is [], the default options are used. If options is {''}, no options are used, not even the default.

Examples

Create vectors x, y, and z containing nonuniformly sampled data:

rand('state',0);
x = 2*rand(5000,1)-1;
y = 2*rand(5000,1)-1;
z = 2*rand(5000,1)-1;
v = x.^2 + y.^2 + z.^2;

Define a regular grid, and grid the data to it:

d = -0.8:0.05:0.8;
[xi,yi,zi] = meshgrid(d,d,d);
w = griddata3(x,y,z,v,xi,yi,zi);

Since it is difficult to visualize 4D data sets, use isosurface at 0.8:

p = patch(isosurface(xi,yi,zi,w,0.8));
isonormals(xi,yi,zi,w,p);
set(p,'FaceColor','blue','EdgeColor','none');
view(3), axis equal, axis off, camlight, lighting phong 

Algorithm

The griddata3 methods are based on a Delaunay triangulation of the data that uses Qhull [1]. For information about Qhull, see http://www.qhull.org/. For copyright information, see http://www.qhull.org/COPYING.txt.

See Also

delaunayn, griddata, griddatan, meshgrid

Reference

[1] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469-483. Available in PDF format at http://www.acm.org/pubs/citations/journals/toms/
1996-22-4/p469-barber/.

griddata

griddatan