Difference between revisions of "Regular curve"
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{{Todo|reparametrisation theorem}} | {{Todo|reparametrisation theorem}} | ||
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| + | * [[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
[hide]Definition
A curve γ:R→R3 usually (however γ:A⊆R→Rn more generally) is called regular if all points (∈Range(γ)) are regular
Definition: Regular Point
A point γ(t) is called regular of ˙γ≠0 otherwise it is a Singular point
Important point
The curve γ(t)↦(t,t2) is regular however γ′(t)↦(t3,t6) is not - it is not technically a reparametrisation
Any reparametrisation of a regular curve is regular
TODO: reparametrisation theorem
