| Spline Toolbox | |
Scattered translates collocation matrix
Syntax
Description
colmat = stcol(centers,x,type) is the matrix whose (i,j)th entry is
with the bivariate functions 
and the number n depending on the centers and the string type, as detailed in the description of stmak.
centers and x must be matrices with the same number of rows.
The default for type is the string 'tp', and for this default, n equals size(centers,2), and the functions 
are given by
with 
the thin-plate spline basis function
and with 
denoting the Euclidean norm of the vector 
.
Note
See stmak for a description of other possible values for type.
|
The matrix colmat is the coefficient matrix in the linear system
that the coefficients 
of the function 
must satisfy in order that 
interpolate the value 
at the site x(:,i), all i.
stcol(...,'tr') returns the transpose of the matrix returned by stcol(...).
Examples
Example 1. The following evaluates and plots the function
on a regular mesh, with 
the above thin-plate basis function, and with c1, c2, c3 three points on the unit circle; see the figure below.
a = [0,2/3*pi,4/3*pi]; centers = [cos(a), 0; sin(a), 0]; [xx,yy] = ndgrid(linspace(-2,2,45)); xy = [xx(:) yy(:)].'; coefs = [1 1 1 -3.5]; zz = reshape( coefs*stcol(centers,xy,'tr') , size(xx)); surf(xx,yy,zz), view([240,15]), axis off
Example 2. The following also evaluates, on the same mesh, and plots the length of the gradient of the function in Example 1.
zz = reshape( sqrt(... ([coefs,0]*stcol(centers,xy,'tp10','tr')).^2 + ... ([coefs,0]*stcol(centers,xy,'tr','tp01')).^2), size(xx)); figure, surf(xx,yy,zz), view([220,-15]), axis off
See Also
| | spmak | stmak | |
