13.1.1 Implicit vs. Parametric Representations

There are two general ways to represent differential constraints:
parametric and implicit. Many parallels can be drawn to the
parametric and implicit ways of specifying functions in general.
Parametric representations are generally easier to understand and are
simpler to use in applications. Implicit representations are more
general but are often more difficult to utilize. The intuitive
difference is that implicit representations express velocities that
are *prohibited*, whereas parametric representations directly
express the velocities that are *allowed*. In this chapter, a
parametric representation is obtained wherever possible; nevertheless,
it is important to understand both.

- 13.1.1.1 Implicit representation

- 13.1.1.2 Parametric constraints
- 13.1.1.3 Conversion from implicit to parametric form

Steven M LaValle 2020-08-14