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

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

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

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.