Definition:Regular Curve/3-Dimensional Real Vector Space

Definition
Let $\alpha : I \to \R^3$ be a smooth curve.

$\alpha$ is said to be regular :
 * $\forall t \in I : \map {\alpha '} t \ne \bszero_{\R^3}$

where:
 * $\alpha '$ denotes the derivative of $\alpha$
 * $\bszero_{\R^3}$ denotes the zero vector in $\R^3$

Also see

 * Definition:Regular Curve: A more general definition for smooth manifolds