By Topic

Topology preserving inside-outside functions for simple closed curves

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
L. Ben-Bassat ; Dept. of Math., Haifa Univ., Israel ; D. Keren

We examine a simple closed curve and to develop an “inside/outside function” for it. This function should be able to determine whether a given point belongs to the interior or to the exterior of our curve. In other words, the above mentioned function should provide information about the mutual state of a given point relative to the given curve. The creation of this “inside/outside function” is based on the following fundamentals: a continuous and single-valued function f is found. If f operates on a simple closed curve α, a simple closed curve β will result, in a way that the interior of α will be mapped on the interior of β, and the exterior of α will be mapped on the exterior of β. Therefore, if a transformation f* can be constructed in such a way that it will map the given curve on the unit circle, it can be used in the following way: for a given point ξ (ξ represent the pair (x,y) in the ℜ2 plane) we calculate f*(ξ), and examine the mutual state of f*(ξ) relative to the unit circle: if f* (ξ) is within the interior of the unit circle then we can conclude that the point ξ is located inside the original curve. On the other hand, if f (ξ) is not within the boundaries of the unit circle then it can be concluded that the point ξ is located outside the original curve. This approach enables us to deal with the problem of the mutual state of a given point relative to the unit circle, instead of dealing with the original problem that is highly complex

Published in:

Electrical and electronic engineers in israel, 2000. the 21st ieee convention of the

Date of Conference:

2000