a shader implementation of delaunay triangulation
This repository is about computing Delaunay triangulation in the GPU. Assumption: the Voronoi diagram and Delaunay triangulation are mathematically dual structures in computational geometry, meaning they are closely related and can be derived from one another.
Voronoi Diagram: A Voronoi diagram partitions a plane with n points (seeds, sites) into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other. These polygons are called Voronoi cells.
Delaunay Triangulation: Delaunay triangulation for a set of points in a plane gives a triangulation such that no point is inside the circumcircle of any triangle. Delaunay triangles maximize the minimum angle compared to any other triangulation of the points.
The Relationship:
- If you take the circumcenters of the Delaunay triangles in a Delaunay triangulation, these points will be the vertices of the Voronoi cells in the corresponding Voronoi diagram.
- Conversely, if you connect the points (seeds) of neighboring Voronoi cells, you obtain the edges of the Delaunay triangulation.
- This implies that if you have computed one structure, you can derive the other without additional point location or distance calculation, just by connecting points or calculating circumcenters accordingly.
To use these shaders and the patch, you should have Max/MSP Jitter installed on your computer. Load the shaders into your Jitter projects to apply the Delaunay triangulation and Voronoi algorithms. The Max patch can be opened directly in Max/MSP for an interactive experience with these algorithms.
- Max/MSP Jitter
Contributions to this project are welcome. Please ensure that any enhancements or bug fixes are compatible with the latest version of Max/MSP Jitter.
Many thanks to Matteo Marson for the help!