Difference between revisions of "Reparametrisation"

Revision as of 20:57, 29 March 2015 (view source) Alec (Talk | contribs) (Created page with "This page requires knowledge of a parametrisation of a curve ==Definition== A function {{M|\tilde{\gamma}:(\tilde{a},\tilde{b})\rightarrow\mathb...")		Latest revision as of 16:30, 23 August 2015 (view source) Alec (Talk | contribs) m (Reverted edits by JessicaBelinda133 (talk) to last revision by Alec)
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	* <math>\tilde{\gamma}(\phi^{-1}(t))=\gamma(t)</math> for all <math>t\in(a,b)</math>		* <math>\tilde{\gamma}(\phi^{-1}(t))=\gamma(t)</math> for all <math>t\in(a,b)</math>
−	{{Definition|Differential Geometry|Geometry of Curves and Surface}}	+	{{Definition|Differential Geometry|Geometry of Curves and Surfaces}}

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Latest revision as of 16:30, 23 August 2015

This page requires knowledge of a parametrisation of a curve

Definition

A function $\tilde{\gamma}:(\tilde{a},\tilde{b})\rightarrow\mathbb{R}^n$ is a reparametrisation of the parametrisation

$$\gamma:(a,b)\rightarrow\mathbb{R}^n$$ if there exists:

$$\phi:(\tilde{a},\tilde{b})\rightarrow(a,b)$$ which is smooth and a bijection, and $\phi^{-1}$ is also smooth where:

• $$\tilde{\gamma}(\tilde{t})=\gamma(\phi(\tilde{t}))$$ for all $$\tilde{t}\in(\tilde{a},\tilde{b})$$
• $$\tilde{\gamma}(\phi^{-1}(t))=\gamma(t)$$ for all $$t\in(a,b)$$