szaross / geometric-algorithms-project

Point Location in Two-Dimensional Space Using Separator Method

Point Location in Two-Dimensional Space Using Separator Method

Description

This project is developed as an educational tool to teach and demonstrate the algorithm for locating a point in a two-dimensional space using the separator method. The algorithm determines in which polygonal subdivision element a given point P on the plane is located.

Technologies

• Programming language: Python 3.9
• Graphics libraries: Environment prepared by BIT
• Development environment: Jupyter Notebook

Features

• Loading a region with a polygonal subdivision from a user interface.
• Entering the point P by the user.
• Graphical presentation of the algorithm's steps:
  • Showing the space division.
  • Highlighting point P and tracking the localization path within the structure.
• Visualization of the result – indicating the element containing point P.

How to Run?

1. Clone the repository
2. Install required dependencies requirements.txt
3. You can either use one of our premade polygon divisions saved in raw.py. Should you want to use your own one, add it to the file, please follow the definition
4. Follow usage examples

Regular Subdivision Definition

Let the set of vertices in the subdivision form an ordered sequence with respect to the y-coordinate (in case of equal values, with respect to the x-coordinate).

A vertex (v_k) is considered regular if there exist edges ( (v_i,v_k) ) and ( (v_k,v_j) ) for (i < k < j). A subdivision is regular if all vertices in the sequence, except for the first and last, are regular.

Usage Examples

You can find usage examples at the end of the Jupyter Notebook (main.ipynb)

Authors

• Szymon Szarek szaross
• Kacper Garus gahson