Parametric Geometry

Was browsing through the threejs cookbook and came across a chapter on parametric geometry and I had remembered a few years ago when working on a prototype for a games workshop warhammer game that we had a bit of trouble with one part. We had created a 3D landscape using random perlin noise and displacement, basic stuff. But when we wanted to start creating forest areas, we didnt want to place just tree after tree as that would have been an expensive polycount. But we did come up with the idea of using a programmatically generated geometry of a sort of forest canopy, something that could render the sides of a densely populated forest and also merge it into a tree top canopy.

For example you can see from the image below, that patterns can be found in how a large area of forest could be represented in 3D from the top.....

 
We completed it last time by sticking parts of these models together but wanted to really do it using good old math. So started to look into it again seeing as I had found this section on parametric geometry and whilst searching online I just found it a very interesting topic as parametric geometry and tessellation methods are creeping into more than just games but art, nature, design, architecture and more including the use of 3D printing....

 

I also found a university study someone had done on the actual process of dynamically generating tree's etc which shed's some light on the topic of mathematical 3d model generation.... 

 Parametric Generation of Polygonal Tree Models for Rendering on Tessellation-Enabled Hardware - Jørgen Nystad

The fact that threejs has enabled this sort geometry creation is definitely something I will be exploring again soon. 

In a game I have been working for a while I generate a dynamic city scape, but this city very much works on the grid based system found in New York. Parametric Geometry could be a key tool to generating more organic looking cities such as London's winding roads and alleys.