DESCRIPTION OF A NON-STRUCTURED QUADRANGULAR MESH

This mesh is defined giving a list of num_quadrangles quadrangles, num_nodes vertices. Each quadrangle is defined giving 4 vertex numbers. The mesh must be "rebuilt" : Each couple of points of a quadrangle (defining a virtual edge) must be referenced twice in the mesh, this means an edge must belong to two mesh elements. (this is a topological and not geometric reference). An edge which belong to only one mesh element is supposed to be on the border of the mesh (or on the skin of the mesh)

Data structure for non-structured quadrangular mesh is:

• num_quadrangles Number of quadrangles of the mesh.
• num_nodes Number of vertices of the mesh.
• quadrangle_nodes Array of the four indices pointing to nodes array, describing the quadrangle nodes.
• nodes Array of num_nodes coordinates of mesh nodes
• s Array of num_nodes values, one for each mesh node.
• v Array of num_nodes vectors, one for each mesh node.

Remark : The array nodes may include vertices which do not belong to any quadrangle of the mesh. In this case the mesh does not provide a continuous numeration of the vertices and num_nodes is not the total number of vertices of the mesh but the dimension of nodes array.

Sample quadrangular mesh with num_quadrangles = 8, num_nodes = 13:

(num_nodes = 14, vertex 8 does not belong to any quadrangle)

quadrangle 0 1 2 3 4 5 6 7

1st vertex 0 1 0 12 7 12 13 1

2nd vertex 11 4 6 11 4 4 2 4

3rd vertex 2 12 1 2 3 7 5 3

4th vertex 5 11 11 13 10 13 7 9

quadrangle_nodes

0	1	0	12	7	12	13	1
11	4	6	11	4	4	2	4
2	12	1	2	3	7	5	3
5	11	11	13	10	13	7	9

Example : vertex 3 of quadrangle 5 is quadrangle_nodes[5][3] = 13

Remark : edges numbers must be given in the right order. If quadrangle_nodes[i] = A,B,C,D, PHIGURE expects AB, BC, CD and DA to be the four edges of the quadrangle, and then AC and BD to be the two diagonals. In previous example quadrangle[0] cannot be described giving 0,2,11,5 : in this case the quadrangle has crossing edges and is degenerate.