Proximity Playground

Learning Objectives

By exploring this demo, you'll understand that:

• Delaunay Triangulation (DT) is the "full" mesh used for surfaces and terrain modeling
• Gabriel Graph (GG) and Urquhart Graph (UG) are "pruned" versions optimized for efficient networking
• Voronoi Diagram is the "dual" map showing territory and influence regions

The Hierarchy

These graphs form a nesting relationship:

Every Urquhart edge is also a Gabriel edge, and every Gabriel edge is a Delaunay edge.

How It Works

• DT: Maximizes minimum angles - no point falls inside any triangle's circumcircle
• GG: An edge exists only if its diameter disk contains no other points
• UG: Created by removing the longest edge from each Delaunay triangle
• Voronoi: The dual of Delaunay - each cell contains all points closest to one seed

Interactions

• Click canvas to add points
• Drag points to move them in real-time
• Hover over edges to see the "X-Ray" visualization
• Use keyboard shortcuts (1-4, R, C, M, N) for quick actions