# orientation

Let $\alpha $ be a rectifiable, Jordan curve in ${\mathbb{R}}^{2}$ and ${z}_{0}$ be a point in ${\mathbb{R}}^{2}-\mathrm{Im}(\alpha )$ and let $\alpha $ have a winding number $W[\alpha :{z}_{0}]$. Then $W[\alpha :{z}_{0}]=\pm 1$; all points inside $\alpha $ will have the same index and we define the orientation of a Jordan curve $\alpha $ by saying that $\alpha $ is positively oriented if the index of every point in $\alpha $ is $+1$ and negatively oriented if it is $-1$.

Title | orientation |
---|---|

Canonical name | Orientation |

Date of creation | 2013-03-22 12:56:09 |

Last modified on | 2013-03-22 12:56:09 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 6 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 30A99 |

Related topic | SensePreservingMapping |