Parallel curve: Difference between revisions

Revision as of 07:07, 30 August 2025

Latest revision as of 07:20, 30 August 2025

(One intermediate revision by the same user not shown)

Line 50:

== 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 are rational curves with rational parallel curves, which can be converted to implicit representations. Another class of implicit rational curves with rational parallel curves is notthe possible[[parabola]]s.{{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)