Spline Toolbox | ![]() ![]() |
Put together a function in stform
Syntax
Description
stmak(centers,coefs)
returns the stform of the function given by
the thin-plate spline basis function, and with denoting the Euclidean norm of the vector
.
centers
and coefs
must be matrices with the same number of columns.
st = stmak(centers,x,type)
stores in st
the stform of the function given by
with the as indicated by the string
type
, which can be one of the following:
'tp00'
, for the thin-plate spline;
'tp10
', for the first derivative of a thin-plate spline wrto its first argument;
'tp01'
, for the first derivative of a thin-plate spline wrto its second argument;
'tp',
the default.
st = stmak(centers,coefs,type,interv)
also specifies the basic interval for the stform, with interv{j}
specifying, in the form [a,b]
, the range of the j
th variable. The default for interv
is the smallest such box that contains all the given centers.
Examples
Example 1. The following generates the figure below, of the thin-plate spline basis function, , but suitably restricted to show that this function is negative near the origin. For this, the extra lines are there to indicate the zero level.
inx = [-1.5 1.5]; iny = [0 1.2];
fnplt(stmak([0;0],1),{inx,iny})
hold on, plot(inx,repmat(linspace(iny(1),iny(2),11),2,1),'r')
view([25,20]),axis off, hold off
Example 2. We now also generate and plot, on the very same domain, the first partial derivative of the thin-plate spline basis function, with respect to its second argument.
inx = [-1.5 1.5]; iny = [0 1.2];
fnplt(stmak([0;0],[1 0],'tp01',{inx,iny}))
view([13,10]),shading flat,axis off
Note that, this time, we have explicitly set the basic interval for the stform.
The resulting figure, below, shows a very strong variation near the origin. This reflects the fact that the second derivatives of have a logarithmic singularity there.
See Also
![]() | stcol | tpaps | ![]() |