Abstract
The purpose of this article is to 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 abovementioned function should provide us the information about the mutual state of a given point relative to the given curve. The creation of this " inside/outside function " will be based on the following fundamentals: A continuous and single-valued function f will be found. If f operates on a simple closed curve a , a simple closed curve β will result, in a way that the interior of a will be mapped on the interior of p , and the exterior of a will be mapped on the exterior of p . 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 plane) we will 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 5 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 6 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.
Original language | English |
---|---|
Title of host publication | 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, Proceedings |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 110-113 |
Number of pages | 4 |
ISBN (Electronic) | 0780358422, 9780780358423 |
DOIs | |
State | Published - 2000 |
Event | 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, IEEEI 2000 - Tel-Aviv, Israel Duration: 11 Apr 2000 → 12 Apr 2000 |
Publication series
Name | 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, Proceedings |
---|
Conference
Conference | 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, IEEEI 2000 |
---|---|
Country/Territory | Israel |
City | Tel-Aviv |
Period | 11/04/00 → 12/04/00 |
Bibliographical note
Publisher Copyright:©2000 IEEE.
ASJC Scopus subject areas
- Electrical and Electronic Engineering