piecewise smooth

A curve α:[a,b]n is said to be piecewise smooth if each component α1,,αn of α has a bounded derivative αi(i=1,,n) which is continuousMathworldPlanetmath everywhere in [a,b] except (possibly) at a finite number of points at which left- and right-sided derivatives exist.

  • Every piecewise smooth curve is rectifiable.

  • Every rectifiable curve can be approximated by piecewise smooth curves.

Title piecewise smooth
Canonical name PiecewiseSmooth
Date of creation 2013-03-22 12:53:26
Last modified on 2013-03-22 12:53:26
Owner cvalente (11260)
Last modified by cvalente (11260)
Numerical id 7
Author cvalente (11260)
Entry type Definition
Classification msc 51N05
Related topic Rectifiable