I recently squashed a few remaining bugs in the differential growth simulation from earlier which means it’s ready for sharing. Here’s a link to the Grasshopper definition (note that it uses the current release of SpatialSlur.dll).

As mentioned in the previous post, the simulation uses a half-edge data structure to handle refinement of the surface mesh as it grows. When an edge exceeds a specified maximum length, it splits (along with the triangles on either side). Edges are also spun to unify vertex valence throughout the mesh, resulting in well-proportioned triangles that are ideal for all sorts of things. The video above shows the effect of different maximum edge lengths on the growth process (from large to small).

The half-edge mesh is particularly well-suited to this process because it allows such local topological modifications to be executed in constant time. In other words, splitting an edge will always take the same amount of time regardless of how many other edges are in the mesh. This property is especially important here since we’re working with an algorithm that tends to dramatically increase its own input size from one iteration to the next. Without constant-time topological operators, things would quickly get out of hand.