Spline Toolbox™ 3.3.4

Product Description

• Introduction and Key Features
• Working with the Spline Toolbox
• Selecting Knots and Representing Splines

Selecting Knots

Several of the spline-creation commands in the toolbox require you to select an appropriate knot sequence that will identify the kind of spline to be used. Default knot sequences are provided for use when it is difficult to choose a knot sequence for your data. The toolbox also includes a command for improving a given knot sequence.

Representing Splines

The Spline Toolbox enables you to represent a polynomial spline in ppform and B-form. The ppform provides a description in terms of breakpoints and local polynomial coefficients, and is useful when the spline will be evaluated extensively. The B-form describes a spline as a linear combination of B-splines, specifically, the knot sequence and B-spline coefficients. The B-form is particularly useful during the construction of a spline.

All polynomial splines can be represented in ppform and B-form for both univariate and multivariate functions (using the tensor-product construct). This means that the toolbox commands for constructing spline approximations can accommodate gridded data in any number of dimensions. The data being fitted can be vector-valued, enabling you to create curves and surfaces in any number of dimensions.

The toolbox also provides thin-plate splines to enable the smooth approximation of scattered bivariate data.

Two-thirds of a sphere, as described by a nonuniform rational B-spline (NURBS).