Figure 30.6: Interpolation from a scattered data to a regular grid
An important use of the Delaunay tessellation is that it can be used to
interpolate from scattered data to an arbitrary set of points. To do
this the N-simplex of the known set of points is calculated with
delaunay, delaunay3 or delaunayn. Then the
simplices in to which the desired points are found are
identified. Finally the vertices of the simplices are used to
interpolate to the desired points. The functions that perform this
interpolation are griddata, griddata3 and
griddatan.
Generate a regular mesh from irregular data using interpolation. The function is defined by z
= f (x,y). Inputs x,y,z are vectors of the same length or x,y are vectors and z is matrix.The interpolation points are all
(xi,yi). If xi, yi are vectors then they are made into a 2-D mesh.The interpolation method can be
"nearest","cubic"or"linear". If method is omitted it defaults to"linear".See also: delaunay.
Generate a regular mesh from irregular data using interpolation. The function is defined by v
= f (x,y,z). The interpolation points are specified by xi, yi, zi.The interpolation method can be
"nearest"or"linear". If method is omitted it defaults to"linear".
Generate a regular mesh from irregular data using interpolation. The function is defined by y
= f (x). The interpolation points are all xi.The interpolation method can be
"nearest"or"linear". If method is omitted it defaults to"linear".
An example of the use of the griddata function is
rand("state",1);
x=2*rand(1000,1)-1;
y=2*rand(size(x))-1;
z=sin(2*(x.^2+y.^2));
[xx,yy]=meshgrid(linspace(-1,1,32));
griddata(x,y,z,xx,yy);
that interpolates from a random scattering of points, to a uniform grid. The output of the above can be seen in fig:griddata.