Difference between revisions of "Regular curve"
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{{Todo|reparametrisation theorem}} | {{Todo|reparametrisation theorem}} | ||
| − | + | ==See also== | |
| + | * [[Parameterisation]] | ||
| + | * [[Curve]] | ||
{{Definition|Geometry of Curves and Surfaces|Differential Geometry}} | {{Definition|Geometry of Curves and Surfaces|Differential Geometry}} | ||
Revision as of 18:43, 25 March 2015
Contents
Definition
A curve [math]\gamma:\mathbb{R}\rightarrow\mathbb{R}^3[/math] usually (however [math]\gamma:A\subseteq\mathbb{R}\rightarrow\mathbb{R}^n[/math] more generally) is called regular if all points ([math]\in\text{Range}(\gamma)[/math]) are regular
Definition: Regular Point
A point [math]\gamma(t)[/math] is called regular of [math]\dot\gamma\ne 0[/math] otherwise it is a Singular point
Important point
The curve [math]\gamma(t)\mapsto(t,t^2)[/math] is regular however [math]\gamma'(t)\mapsto(t^3,t^6)[/math] is not - it is not technically a reparametrisation
Any reparametrisation of a regular curve is regular
TODO: reparametrisation theorem
