orientation

Let $\alpha$ be a rectifiable, Jordan curve in $\mathbb{R}^{2}$ and $z_{0}$ be a point in $\mathbb{R}^{2}-\operatorname{Im}(\alpha)$ 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