|Spline Toolbox Release Notes|
This section introduces the new features and enhancements added in the Spline Toolbox 3.0 since the Spline Toolbox 2.0.1 (Release 11.0).
Spline Tool Provides a Visual Interface to the Spline Toolbox
splinetool function invokes a new visual interface that allows you to:
Automatic Knot Choice Simplifies Use of spapi and spap2
Until this release, if you wanted to construct a spline interpolant to given data, you had to specify the spline space from which this spline was to be chosen, by providing an appropriate knot sequence. Starting with this release, if you are not so certain about how to choose knots, you can simply specify the order of the spline to be used instead, and
spapi will provide a suitable knot sequence.
The same difficulty of having to choose a knot sequence occurred in the construction of a least-squares spline approximation to given data, and here, too, you can instead merely specify the number of polynomial pieces of the given order to be used in the approximating spline in
Automatic Smoothing Parameter Choice Simplifies Use of csaps
You can now use
csaps without specifying the smoothing parameter to be used. If none is specified,
csaps will optionally return the one it chose for the given data, for further experimentation.
Use of Rational Splines
The relevant function functions (e.g.,
fn2fm, etc.) can now operate on rational splines (NURBS). Specific examples of a rational spline are provided by
rpmak are available to generate arbitrary rational splines in B-form and ppform, respectively.
B-Spline Visual Interface
Splines in the Spline Toolbox are constructed as a linear combination of B-splines. Run
bspligui to show how such a B-spline varies as you vary its knots. You can:
Other New Functions
The following functions have been added in the Spline Toolbox 3.0:
(x,k)provides a good knot sequence for interpolation by splines of order
kto data at
fndiris available for the construction of directional derivatives, and hence of Jacobians, gradients, and surface normals.
fntlris available for the calculation of derivative values; this is particularly useful for rational splines for which formal differentiation is inefficient.
(knots,k)provides a good data site sequence for interpolation by splines of order
kwith knot sequence
spapscan now work with a nonconstant weight in the roughness measure.
spapscan also now deal better with near-zero error weights.
spapsa smoothing parameter rather than a tolerance.
fnbrkcan now change the basic interval of any form.
fnvaltreat splines as continuous from the left.
fnvalin the form
fnval(x,f)as needed for
fnpltcan now be made not to break the graph of a function at a jump.
newknt(fn,newl)has become optional.
aveknt(x,k)can now handle an
k(of use in
optkntcan now handle much more nonuniformly spaced data sites, particularly by using
optknt(tau,k,maxiter)to increase the maximum number of steps used to iteratively solve for the optimal knots.
|Upgrading from an Earlier Release||Major Bug Fix|