= Piecewise Parameterization =

'''Piecewise parameterization''' is the process of [[Calculus/ParametricEquation|parameterizing]] a curve that is not everywhere differentiable but is piecewise differentiable.

<<TableOfContents>>

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== Description ==

Consider a rectangle formed by ''[a,b] x [c,d]''.

{{attachment:rect.svg}}

The four faces of this rectangle can be defined as four separate curves like:

 * ''C,,1,, : r,,1,,(t) = <t,c>'' for ''a≤t≤b''
 * ''C,,2,, : r,,2,,(t) = <b,t>'' for ''c≤t≤d''
 * ''-C,,3,, : r,,3,,(t) = <t,d>'' for ''a≤t≤b''
 * ''-C,,4,, : r,,4,,(t) = <a,t>'' for ''c≤t≤d''



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CategoryRicottone