Delaunay Triangulation Visualizer

Delaunay triangulation is a way to connect a set of points to form triangles such that no point is inside the circumcircle of any triangle. This creates triangles that are as equilateral as possible, avoiding thin and elongated triangles.

Key Properties:

• Maximizes the minimum angle of all triangles
• Empty circumcircle property: no points lie inside any triangle's circumcircle
• Unique for a given set of points (except in degenerate cases)
• Dual graph of Voronoi diagram

The Bowyer-Watson algorithm is an incremental algorithm for computing Delaunay triangulation:

1. Start with a super-triangle that contains all points
2. For each point:
   • Find all triangles whose circumcircle contains the point
   • Remove these "bad" triangles
   • Find the boundary of the polygonal hole
   • Re-triangulate the hole by connecting the point to all boundary edges
3. Remove triangles connected to the super-triangle vertices

Time Complexity: O(n log n) average case, O(n²) worst case

• Computer Graphics: Mesh generation, terrain modeling
• GIS: Spatial interpolation, surface reconstruction
• Computer Vision: 3D reconstruction, feature matching
• Scientific Computing: Finite element analysis, numerical methods
• Data Analysis: Nearest neighbor searches, clustering

• Click: Add new points to the triangulation
• Random Points: Generate a random set of points
• Toggle Circumcircles: Show/hide the circumcircles of triangles (validates Delaunay property)
• Toggle Voronoi: Show/hide the dual Voronoi diagram
• Show Points/Triangles: Control visibility of different elements