Parallel curve: Difference between revisions

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== Parallel curves of an implicit curve ==

[[File:Offset-of-implicit-curve-c4.svg|250px|thumb|Parallel curves of the implicit curve (red) with equation <math>x^4+y^4-1=0</math>]]

GenerallyNot theall [[implicit curve]]s have parallel curves with analytic representationrepresentations, ofbut athis parallelis curvepossible ofin ansome special cases. For instance, the [[implicitPythagorean hodograph curve]]s isare notrational possiblecurves with rational parallel curves, which can be converted to implicit representations.{{Citation Neededsfn|Farouki|2008|datepp=August216–217, 2025448}}. Only forFor the simplesimpler cases of lines and circles the parallel curves can be described easily.

For example:

: ''Line'' <math>\; f(x,y)=x+y-1=0\; </math> → distance function: <math>\; h(x,y)=\frac{x+y-1}{\sqrt{2}}=d\; </math> (Hesse normalform)