Page: Parametric - Representation

0

Parametric representation of curves overcomes all of the aspects mentioned in the non parametric form.

- It allows close and multiple valued functions to be easily defined and replaces shapes with tangent vectors.
- In case of commonly used curves such as linear and cubic, these equations are polynomial rather than being equations involving roots.
- The parametric representation of geometry involves expressing relationships for the x and y not in terms of each other but of one or more independent variables known as parameters.
- A single parameter, say u, is used to represent curves by expressing x and y in terms of two variables.

For e.g., a point can be represented by:

$p(u)=[x(u) \ \ \ y(u)]$ where $(u_{min}\le u\le u_{max})$

The value of u is taken in general between 0 & 1 in order to normalize the parametric value.