Tutorial

• Introduction

• Environment definition

• Attribute definition

• Rules definition

• Initial Graph definition

• Execution process

• Results visualization

Configuration

• Writing permission

• Project management

• Preferences

Environment managment

• Global constants

• Global functions

• Attribute managment

Graph managment

• Initial graph construction

• Vertex state settings

• Edge state settings

• Graph visualization and options

Rules managment

• Attributes and variables definition

• Match conditions

• Rules window

• Trigger actions on items

• Trigger actions on states

• Math formula Parser

Execution managment

• Run settings

• Visualizaton Window

Graph Managment

The graph is the central concept of GPaR. It is a pregraph such that

• a port is connected to at most one node,
• a port is connected to at most one port.

In this context, encoding classical graph edges between nodes necessitates the use of 2 ports and 3 edges. We will call a classical graph edge a link . A link between two nodes n₁ and n₂ is encoded as two port-node edges (p₁,n₁) and (p₂,n₂) with p₁ and p₂ being ports which are linked via the port-port edge (p₁,p₂). Moreover, nodes, ports and edges can have attributes. By default, nodes have there 3D-positions as attributes. Additional attributes on nodes, on ports and also on edges have to be defined in the state window.

Initial graph construction

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Graph window

graph window tools bar

vertex popup menu

• add edge will add an edge between source vertex and the existing target vertex which is at the pointer of the mouse.
• add edge to node will add an edge between the source vertex and the new node created at the pointer of the mouse if it does not exist.
• add edge to port will add an edge between the source vertex and the new port created at the pointer of the mouse if it does not exist.
• delete vertex will delete the source vertex.
• edit vertex will edit the state of the vertex, the state then can be modified. (see the vertex state settings section )

A shortcut function is included in add edge and add edge to node , it allows to create in one click a link between 2 nodes. This function will create an edge node-port, a port, an edge port-port, a port an edge port-node, and optionally the target node. Moreover, during the construction of the initial graph, the graph conditions must be satisfied. It is not allowed to construct, from a given port, 2 port-port connections. In the same way, it is not allowed to construct, from a given port, 2 port-node connections. In both cases, the second edge is not created and an error message appears.

edge popup menu

Generate grid options

To generate a mesh in the rectangle [X_min,X_max] × [Y_min,Y_max], fill in the boxes x_min, Y_min, width=X_min -X_max and height=Y_min -Y_max. The last boxes you have to fill in correspond to the refinement of the rectangle. More precisely, let us denote nRows and nCols these two integers, (nRows+1)(nCols+1) nodes are created and there coordinates are (X_min+$\frac{\mathrm{width}}{\mathrm{nRows}}$ × i, Y_min+$\frac{\mathrm{height}}{\mathrm{nCols}}$ × j ) for all integer i between 0 and nRows and for all integer j between 0 and nCols. In addition, ports, edges and also nodes are added depending on the type of the mesh you have selected. Four different type of meshes are available :

• Rectilinear grid: The set of nodes of this graph is named N and is composed of the (nRows+1)(nCols+1) nodes previously defined. Moreover two nodes of N with coordinates (x,y) and (x',y') are linked if x=x' ± $\frac{\mathrm{width}}{\mathrm{nRows}}$ xor y=y' ±$\frac{\mathrm{height}}{\mathrm{nCols}}$. Thus, the graph contains 2(nRows+1)(nCols+1) ports and 3(nRows+1)(nCols+1) edges. Finally, it is a planar graph containing nRows × nCols cells. When width=height, the grid is a cartesian grid and it can be viewed as the mesh of a 2 dimensional cellular automaton with a Von Neumann neighborhood.
• Right-angle triangular mesh : it corresponds to the rectilinear grid where the rectangles are cut in half along the diagonal. The set of nodes is again N. Two nodes of coordinates (x,y) and (x',y') are linked if (x=x' ± $\frac{\mathrm{width}}{\mathrm{nRows}}$ xor y=y' ±$\frac{\mathrm{height}}{\mathrm{nCols}}$) or (x=x' + $\frac{\mathrm{width}}{\mathrm{nRows}}$ and y=y' + $\frac{\mathrm{height}}{\mathrm{nCols}}$) or (x=x' - $\frac{\mathrm{width}}{\mathrm{nRows}}$ and y=y' -$\frac{\mathrm{height}}{\mathrm{nCols}}$). Inside the mesh, all the nodes which not belong to a border have degree 6 . It is a grid formed by tiling the plane regularly with right-angled triangles.
• Isosceles triangular mesh : The rectilinear grid is expand by a set N' of nRows ×nCols new nodes. there coordinates are: (x_min+ $\frac{\mathrm{width}}{\mathrm{2\; nRows}}$ + $\frac{\mathrm{width}}{\mathrm{nRows}}$ × i, Y_min+$\frac{\mathrm{height}}{\mathrm{2\; nCols}}$+$\frac{\mathrm{height}}{\mathrm{nCols}}$ × j ) for all integer i between 0 and nRows-1 and for all integer j between 0 and nCols-1. In addition, the nodes of N' are linked to the 4 closest nodes of N. The degree of nodes belonging to N' is 4. The degrees of nodes of N are 8, 3,4 or 5.
• Moore grid : The rectilinear grid is expand by adding links. Two nodes of N with coordinates (x,y) and (x',y') are linked if x=x' ± $\frac{\mathrm{width}}{\mathrm{nRows}}$ or y=y' ±$\frac{\mathrm{height}}{\mathrm{nCols}}$. It can be viewed as the mesh of a 2 dimensional cellular automaton with a Moore neighborhood.

Vertex state settings

Vertex State Window

Edge state settings

Edge State Window

Graph visualization and options

This section deals with the drawing options.

The result graphs can be very different depending on the initial graph and the rewriting system. Some graphs can have a large number of nodes. Some others can be not planar with a lot of crossing edges. The presence of ports can complicate the readability of graphs. In some cases, only nodes are meaningful, in other cases, the visualization is better without the representation of ports and/or nodes. To adapt the visualization to the current graph some options are available in the second tool bar of the graph windows:

• roll up the mouse 's wheel to zoom out or click on the button of the drawing area tools bar
• roll down the mouse 's wheel to zoom in or click on the button of the drawing area tools bar
• click on the left button of the mouse and by maintaining the left button pressed, select the drawing zone to fit
• click on the button of the drawing area tools bar to fit the best drawing zone which contains all the elements of the graph
• to move the drawing zone, click on the button of the drawing area tools bar and move the mouse. The drawing zone becomes read only.

drawing area tools bar

A graph window contains menu and corresponding tool bar.

To save the plotting area in a file select File->save as image. The image formats may be either bmp, png, ppm, xbm, xpm, jpg or .eps.

The zoom may be selected precisely using the zoom setting window by selecting Zoom->Zoom setting

Set the min and max absissa value and the min and max ordinate value and click set to set the zoom rectangle exactly.

The options of the graph window appear by selecting Edit->Options.

The different options are listed below: