Spline Toolbox

Technical Conventions

Vectors.   the Spline Toolbox 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, that is, 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, that is, a d-vector, is always stored as a column vector. In particular, if you wish 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.

Naming conventions..   Most of the 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 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 start particular demos

Some of these naming conventions are the result of discussions with J\"org Peters.

Organization of the Document

Typographical Conventions