A very different approach to tree growth simulations has been developed by Colin Smith and Przemyslaw Prusinkiewicz (Colin Smith 2006). It is quite different from most methods where trees are described as a set of modified cylinders. The authors of this paper made an observation that a tree in the process of its growth changes quite a lot. These changes take place at a cellular level. Therefore, the method that they describe tries to mimic misbehaviors of cells in a tree tissue.
The authors developed vertex-to-vertex (vv) formalism to describe cell-like system behavior. This means that the approach is targeted at dynamic systems, which change through time. Vertex-to-vertex formalism is similar to L-systems in that it uses lineage information and context to identify elements of structure. Vertex-to-vertex formalism relies only on local information in contrast to L-system declarative nature, which describes rules for the whole structure. This method allows associating each vertex of a polygonal mesh with a list of its neighboring vertices. The resulting structure is manipulated using vv algebra, which includes a set of various operators.
The form change in vv formalism is a result of tensions introduced to tissues by growth. Each vertex is affected by a sum of forces from neighboring vertices. Also, external forces can be introduced, such as gravity and the pressure of the internal structure layer to its external layer.
Fig 24. Picture taken from: Colin Smith. 2006. On Vertex-Vertex Systems and Their Use in Geometric and Biological Modeling. Doctor of philosophy diss., The University of Calgary.
The resulting forces are updated until equilibrium is reached.
The simulated objects are directly represented as polygonal meshes. Each vertex of the polygonal mesh is manipulated according to tension energies from its neighboring vertices, as well as other forces. The final shape of the plant is generated by calculating the local stresses resulted by local growth. This method might be not the best to produce full-grown tree models, but it could be very important in modeling small plants or parts of them.
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