| GRAPH GRAMMAR OPERATION ‘BISECT AN EDGE’ | GRAPH GRAMMAR OPERATION ‘ADD NODE TO A NODE’ |
| Applicable to: any edge of the graph | Applicable to: any node of the graph |
| Update of the graph structure: for a given edge {A,B}, connecting nodes A and B, remove {A,B} from the graph, add a new node C, and introduce two new edges {A,C} and {C,B}. | Update of the graph structure: for a given node A, add a new node C, and introduce a new edge {A,C} |
| Update of the elasticity matrix: the elasticity of edges {A,C} and {C,B} equals elasticity of {A,B}. |
Update of the elasticity matrix: if A is a leaf node (not a star center) then the elasticity of the edge {A,C} equals to the edge connecting A and its neighbor, the elasticity of the new star with the center in A equals to the elasticity of the star centered in the neighbor of A. If the graph contains only one edge then a predefined values is assigned. else the elasticity of the edge {A,C} is the mean elasticity of all edges in the star with the center in A, the elasticity of a star with the center in A does not change. |
| Update of the graph injection map: C is placed in the mean position between the positions of A and B. | Update of the graph injection map: if A is a leaf node (not a star center) then C is placed at the same distance and the same direction as the edge connecting A and its neighbor, else C is placed in the mean point of all data points for which A is the closest node |