Spline Toolbox Release Notes 
New Features
This section summarizes the new features and enhancements introduced in the Spline Toolbox 3.1 since Version 3.0 (Release 12.1), and included in Version 3.1.1.
If you are upgrading from the Spline Toolbox 2.0, then you should also see New Features in the Spline Toolbox 3.0 Release Notes.
Smoothing Splines for Scattered Bivariate Data
The new command tpaps
enables you to create thinplate spline approximations f that satisfy, approximately or exactly, the equation for given data values z at given scattered data sites (x,y) in the plane. The associated collocation matrix is provided by stcol
. You can also create the firstorder derivatives of a thinplate spline.
The spline created by tpaps
is in stform, as are its firstorder derivatives. You can create an stform directly from its centers and coefficients using stmak
. As with all forms, you can evaluate the splines in stform with fnval
, plot them with fnplt
, etc.
See Fitting Values at Scattered 2D Sites and The stform in the Spline Toolbox documentation for more information.
splinetool Command History MFile
In the Spline Tool GUI (splinetool
), you can now generate a function Mfile that you can use to generate, from the original data, any or all graphs currently in the GUI. Select File > Save MFile to save the Mfile.
This Mfile also provides you with a written record of the Spline Toolbox commands used to generate the current graph(s), and can be edited, or executed in a loop over different data sets.
SplineSpecific Zero Finder
A new command fnzeros
enables you to find an ordered list of the zeros of a univariate, scalarvalued spline, in its basic interval or in a specified interval.
SplineSpecific Minimum Finder
A new command fnmin
enables you to obtain the minimum or maximum value of a univariate, scalarvalued spline as well as its location, in its basic interval or in a specified interval.
Function Summary
Version 3.1 of the Spline Toolbox provides the following:
New Functions
Function 
Purpose 

Minimum of a function in a given interval 

Find zeros of a function in a given interval 

Scattered translates collocation matrix 

Put together a function in stform 

Thinplate smoothing spline 
Spline Functions with New or Changed Capabilities
Function 
Purpose 

A new value of the part argument, 'variables' , causes fnbrk to return the number of variables of the specified function. 

As a new default, fnrfn now refines the partition (breaks or knots) of the given form by adding to it every midpoint. fnrfn previously had no default. 

splinetool now permits the entry of a vector whose elements replace that many entries in the weights display, starting with the marked entry. 

These functions now treat an empty optional argument the same as not having that optional argument. 
Spline Toolbox Release Notes  Major Bug Fixes 