What is Voronoi Tessellation

Penny de Byl
A free video tutorial from Penny de Byl
International Award Winning Professor & Best Selling Author
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Lecture description

This lecture provides a quick introduction to Voronoi Tessellation and explains how the phenomena can be replicated to create mountainous landscapes.

Learn more from the full course

Procedural Terrain Generation with Unity

Programming realistic environments with C# through the algorithmic manipulation of mesh and vegetation data.

15:00:00 of on-demand video • Updated June 2021

  • Use various algorithmic approaches to create procedurally generated content.
  • Manipulated terrain meshes with code to create realistic looking landscapes.
  • Texture terrain meshes procedurally.
  • Discuss the design principles involved in producing aesthetically pleasing terrains.
  • Manipulate the render settings in Unity to produce better looking camera results.
  • Create custom Unity windows and graphical user interface elements for use inside the Editor.
English What do English landscapes, coral, pineapples, bubbles and dry riverbeds have in common? The patterns formed on their surfaces represent a phenomena called Voronoi Tesselation. Voronoi Tesselation can also be formed by the valleys where mountains meet. As such we are going to investigate it as a method for procedural landscape generation. Mathematically, Voronoi Tesselation represents the division of a 2D space such that the regions are based on the distance to points in a specific subset of a plane. More simply, regions in a Voronoi Tesselation represent a set of all points that are closest to the center of a region. In this diagram there are 20 regions each containing a black dot called their seed. Every point inside the same region is closest to their seed and no other. For example any points inside the bright green region are closest to their seed than they are to any other seed on the map. Voronoi Tesselation or Voronoi Diagrams are often used to divide up maps to show the utilities you are closest to when multiple utilities exist. Take for example this map of the Gold Coast in Australia showing the locations of McDonald's stores. By dividing this map into Voronoi regions, you can map out which neighborhoods are closest to which McDonald's stores. Anybody living on the border of two regions has two local stores to choose from, as they are equidistant from them. In using Voronoi for creating mountains on a terrain, we're less concerned about the true mathematics of the system and more about the patterns that are formed. However mathematics inherently come into play. The process we will follow is to take a mesh and raise up the mountain which in turn will just lift the surrounding terrain with it. Just through this process, each of the neighboring vertices are lifted. In a top view you end up with Voronoi Tessellation. In this quick simulation, you can see the tessellation process in action as each color from the seeds radiates out at the same rate when the colors collide they form straight lines. This same process happens in nature where usually rounded phenomena meet and the pressure from both sides can't help but produce straight lines. Now that you've seen it you're going to find it very hard to unsee and you'll be finding tesselated patterns all around you. This is just another example of the beauty of mathematics and why I love procedural generation and computer graphics.