reparametrization

A monotone bijection φ : I → I. If γ : I → ℝⁿ is a parametrized curve, γ ∘ φ traces the same image in the same direction, possibly at a different pace (and reversed if φ is decreasing). Two parametrized curves are "the same up to reparametrization" when one is γ ∘ φ of the other — the working definition of "the same curve" in differential geometry.