The purpose of this example is to mesh a 2d rectangle by triangles and to partitionize the nodes whose coordinates verify f(x,y,z)<=0 from the other nodes.

The graph is composed by

nodes with coordinates & state in {0,1}
ports with no state.

Nodes are the summit of the triangles & the ports are placed on its edges.

We want to select all the node whose coordinates verify f(x,y,z)=x-y<=0.

For each triangle whose one summit' state is different from the 2 each others, a new triangle is added with its summits are in the middle of the edges of the pattern triangle.

The f(x,y,z) is computed for each new nodes & the state is sate to 1 if the functon is positive and 0 otherwise.

The initial, pattern & transform graphs are as follow:


initial graph	pattern graph	transform graph

The rule of the graph consists in

removing the edges between 2 ports of the pattern triangle
adding connections between the freed pattern graph ports and the freed transform graph ports
update the coodinates & states of the new nodes
the mapping rules are to
- disable the mapping of triangles by permutation of its summits (isUpToAutomorhism=true)
- valid the mapping by testing if one of state of pattern node is different from the 2 others.

the rule is written as follow:

 #list of ids of vertices of pattern graph to remove
 0 
 #list of ids of edges of pattern graph to remove
 3
 1
 4
 7
 #list of edges between Pattern graph & Transform graph to add in the form source,target
 6
 3,10
 4,9
 5,12
 6,11
 7,14
 8,13
 #group node ids rules
 groupNodeIds=
 #group port ids rules
 groupPortIds=
 
 #mapping rules for pattern vertex
 2
 IsUpToAutomorphism=true
 ((state_P_0<>state_P_1) || (state_P_0<>state_P_2) || (state_P_1<>state_P_2) )
 
 #state nodes update
 6
 T_0=0.5*(P_0+P_1)
 T_1=0.5*(P_1+P_2)
 T_2=0.5*(P_2+P_0)
 state_T_0=((T_0.x-T_0.y)<=0)
 state_T_1=((T_1.x-T_1.y)<=0)
 state_T_2=((T_2.x-T_2.y)<=0)

To compute the 3 first rewriting graph, execute the command:

1 gpm_model.exe --path=./data --output=./output --prefix=mesh --init=mesh-init.txt --nRules=1 --rule=mesh-rule.txt --pattern=mesh-pattern.txt --transform=mesh-transform.txt --iterationsNumber=4 --verbose=./output/mesh.log --verbose-mode=debug make run

The results of the rewriting graphs are as follow:


rewriting graph at iteration 1	rewriting graph at iteration 2

rewriting graph at iteration 3	rewriting graph at iteration 4