Types of Curves: Parametric vs. Implicit Representations
- Implicit
Curve defined in terms of cartesian coordinates:
f (x, y, z) = 0
- Parametric
Parametrically defined curve in three dimensions is given by three univariate functions:
Q(u,) = (X(u), Y(u), Z(u)),
where u varies from 0 to 1.
To see why the parametric form is more useful, let’s look at a circle: