| Spline Toolbox | |
Tensor Product Splines
The toolbox provides (polynomial) spline functions in any number of variables, as tensor products of univariate splines. These multivariate splines come in both standard forms, the B-form and the ppform, and their construction and use parallels entirely that of the univariate splines discussed in previous sections, The ppform and The B-form. The same commands are used for their construction and use.
For simplicity, the following discussion deals just with bivariate splines.
The tensor-product idea is very simple. If 
is a function of 
and 
is a function of 
, then their tensor-product 
is a function of 
and 
, i.e., a bivariate function. More generally, with 
and 
knot sequences and
a corresponding coefficient array, we obtain a bivariate spline as
This section discusses tensor product splines for the standard forms:
| | Use | B-form | |