Learn more about Spline Toolbox

Technical Conventions

• Vectors

• Naming Conventions

• Using Spline Toolbox Functions

Vectors

The Spline Toolbox product can handle vector-valued splines, i.e., splines whose values lie in R^d. Since MATLAB started out with just one variable type, that of a matrix, there is even now some uncertainty about how to deal with vectors, i.e., lists of numbers. MATLAB sometimes stores such a list in a matrix with just one row, and other times in a matrix with just one column. In the first instance, such a 1-row matrix is called a row-vector; in the second instance, such a 1-column matrix is called a column-vector. Either way, these are merely different ways for storing vectors, not different kinds of vectors.

In this toolbox, vectors, i.e., lists of numbers, may also end up stored in a 1-row matrix or in a 1-column matrix, but with the following agreements.

A point in R^d, i.e., a d-vector, is always stored as a column vector. In particular, if you want to supply an n-list of d-vectors to one of the commands, you are expected to provide that list as the n columns of a matrix of size [d,n].

While other lists of numbers (e.g., a knot sequence or a break sequence) may be stored internally as row vectors, you may supply such lists as you please, as a row vector or a column vector.

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Naming Conventions

Most of the Spline Toolbox commands in this toolbox have names that follow one of the following patterns:

cs... commands construct cubic splines (in ppform)

sp... commands construct splines in B-form

fn... commands operate on spline functions

..2.. commands convert something

..api commands construct an approximation by interpolation

..aps commands construct an approximation by smoothing

..ap2 commands construct a least-squares approximation

...knt commands construct (part of) a particular knot sequence

...dem commands are demonstrations now reached via the Demos tag in the MATLAB Help browser.

Some of these naming conventions are the result of a discussion with Jörg Peters, then a graduate student in Computer Sciences at the University of Wisconsin-Madison.

Note   See the "Glossary" for information about notation used in this book.

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Using Spline Toolbox Functions

For ease of use, most Spline Toolbox functions have default arguments. In the reference entry under Syntax, we usually first list the function with all necessary input arguments and then with all possible input arguments. When there is more than one optional argument, then, sometimes, but not always, their exact order is immaterial. When their order does matter, you have to specify every optional argument preceding the one(s) you are interested in. In this situation, you can specify the default value for an optional argument by using [] (the empty matrix) as the input for it. The description in the reference page tells you the default value for each optional input argument.

As in MATLAB, only the output arguments explicitly specified are returned to the user.

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Expected Background

Examples

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