## 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 |
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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 |
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### Conference

Conference | 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, IEEEI 2000 |
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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