Voronoi Diagrams
applied
So many applications, explore your own.
Introduction
Be creative with applications of Voronoi diagrams. Identify a landmark in a city e.g. hospitals, coffee shops, emergency services and determine the best location for another of those landmarks. Use the city boundaries as your convex hull and model it properly on Desmos or GeoGebra. Extension: Distance to your landmark may be optimised, but what about journey time? Are there other methods to determine the best location, perhaps using statistics or trial and error? Discuss.
Guiding Questions
- What mathematical models apply to this situation?
- What data do you need to collect and how will you analyze it?
- What assumptions are you making in your mathematical model?
- How can you validate your mathematical conclusions?
- What are the limitations of your approach?
Key Mathematical Concepts
Algorithms
Computational Geometry
Spatial Analysis
Voronoi Diagrams