Voronoi Diagram: Algorithm and Implementation

A Voronoi diagram is a computational geometry structure that partitions a plane into regions, where each region contains all points closest to a specific generator point. Voronoi diagram code refers to computer programs that implement algorithms to generate these spatial partitions. This implementation typically involves calculating Euclidean distances between seed points and applying geometric algorithms like Fortune's algorithm (sweep-line approach) for O(n log n) efficiency. The code finds applications in numerous domains including cartography for creating service areas, image processing for texture analysis, and computer vision for feature segmentation. The core algorithm works by computing perpendicular bisectors between point pairs and constructing convex polygons through their intersections. Visualization is achieved by rendering these polygonal boundaries with connecting edges to neighboring regions. Voronoi diagram code represents a powerful computational technique with broad interdisciplinary applications in spatial analysis and pattern recognition.