CAGD-banner.gif
On-Line Geometric Modeling Notes
SUPPORT OF A FUNCTION


Definition of Support

The support of a function $ f(x)$ is the set of points $ x$ in the domain of $ f$ where the function is nonzero.


Example - the Cubic Uniform Blending Function

Consider the cubic uniform blending function

$\displaystyle N_3(t) \: = \: \left\{
\begin{array}{ll}
\frac{1}{2} t^2 \: \: &
...
... \: &
{\rm if} \: 2 \leq t \leq 3 \\
0 & {\rm otherwise}
\end{array}\right.
$

This function, as is displayed below, is continuous and has support in the interval $ [0.3]$.

\includegraphics {figures/uniform-blending-order-3}

We frequently construct the blending functions of our spline curves to have support only in a limited interval about the origin. In this way these functions will have a effect only upon a limited portion of the curve.


Bibliography

1
BARTELS, R., BEATTY, J., AND BARSKY, B.
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling.
Morgan Kaufmann Publishers, Palo Alto, CA, 1987.


\begin{singlespace}
\noindent
\footnotesize\bfseries All contents copyright (c) ...
...ment, University of California, Davis \\
All rights reserved.
\end{singlespace}


Ken Joy
2000-11-28