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Voronoi Diagram with Fortune's Algorithm

(1) Ahmad Hanif Adisetya (2) Ibni Shaquille Syauqi Ibrahim (3) Muhammad Alif Ismady

This project implements Fortune's Algorithm to generate a Voronoi diagram for a set of points on a bounded plane. The bounding box constrains the half-infinite edges, converting them to finite line segments that fit within the specified bounds.

Features

  • Bounding Box: The diagram is limited within a defined bounding box, which can use GUI window boundaries for easy visualization.
  • Largest Empty Circle(s): The program identifies and displays the largest empty circle(s) that pass through three or more Voronoi sites. If multiple such circles exist, all are displayed.
  • Flexible Input Options:
    • Text File: Load input points from a text file.
    • Interactive Mode: Users can add points directly onto the diagram using mouse clicks.
  • Interactive GUI: Includes buttons and menu items for easy navigation and functionality control.

Usage

  • Load Points: Input points can be loaded from a .txt file or added interactively with the mouse.
  • View Voronoi Diagram: The Voronoi diagram, bounded by the specified area, is displayed.
  • Show Largest Empty Circles: Largest circles that pass through three or more points are identified and displayed.

Requirements

  • A GUI environment to support interactive input and diagram visualization.
  • Text files should contain point coordinates in a format specified (e.g., one point per line: x y).

This project is developed to fulfill CSCE604045 Computational Geometry course Universitas Indonesia