4
Treatment of 2D
Meshes

• DESCRIPTION OF A RECTANGULAR MESH
• DESCRIPTION OF A QUADRANGULAR MESH
• DESCRIPTION OF A POLAR MESH
• DESCRIPTION OF A SECTOR MESH
• DESCRIPTION OF A TRIANGULAR MESH
• DESCRIPTION OF A NON-STRUCTURED TRIANGULAR MESH
• DESCRIPTION OF A NON-STRUCTURED QUADRANGULAR MESH
• DESCRIPTION OF A HETEROGENEOUS NON-STRUCTURED MESH
• ALLOCATION OF 2D MATRIX OF FLOATS
• ALLOCATION OF 2D MATRIX OF VECTORS
• FREE A 2D MATRIX OF FLOATS
• FREE A 2D MATRIX OF VECTORS
• 2D MESH CHECKER
• GENERATION OF MESH LIMIT CONTOURS
• GENERATION OF 2D MESH LINES
• GENERATION IN 3D OF 2D MESH LINES
• MESH LINE COLOURING BASED ON AVERAGE VALUE
• MESH LINE COLOURING BASED ON ISOVALUES
• CONSTANT COLOURING OF A 2D MESH SURFACE
• COLOUR 2D MESH POLYGONS
• 2D MESH SURFACE COLOURING BASED ON AVERAGE VALUE
• 2D MESH REPRESENTED BY A 3D SURFACE COLOURED BY ISOVALUE
• REPRESENTATION OF THE SIDES OF A 2D MESH
• ANNOTATED SOLID AND LINE CONTOURING ON A 2D MESH
• SOLID CONTOURING ON A 2D MESH
• ANNOTATED CONTOUR LINES ON A 2D MESH
• ANNOTATED AND COLORED CONTOUR LINES ON A 2D MESH
• 3D COLORED CONTOUR LINES ON A 2D MESH
• 2D CONTOUR LINES PARAMETERS
• TRIANGLE COORDINATE TO TRIANGLES-VERTEX
• TRIANGLE-VERTEX TO TRIANGULAR MESH
• VECTORS FIELD ON A 2D MESH

This chapter introduces PHIGURE functions to deal with 2D meshes of the following type:

- rectangular mesh

- quadrangular mesh

- polar mesh

- sector mesh

- triangular mesh

- non-structured triangular mesh

- non-structured quadrangular mesh

- heterogeneous polygonal mesh

Each of these meshes is described giving its geometry (C structure Tmesh2D), its 2D scalar values (C structure Tscalar2D_data) and its 2D vector values (C structure Tvec2D_data). A PHIGURE function for 2D mesh representation has the following pattern:

txxxxx (struct_id, &mesh, &scal_data1, &scal_data2, ...)

where

txxxxx is the name of the PHIGURE function

struct_id : is the PHIGS structure identifier (to be included in the scene calling tscene function if to be visualized)

&mesh pointer to the structure describing mesh geometry

&scal_data1 pointer to the first set of data

&scal_data2 pointer to the second set of data ...

Description of the C structure mesh:

typedef struct {

	Tmesh2D_type	type;

	union {

		struct {
			Pint		num_x;
			Pint		num_y;
			Pfloat	*x;
			Pfloat	*y;
		} rectangular;
		struct {
			Pint		num_x;
			Pint		num_y;
			Pfloat	**x;
			Pfloat	**y;
		} quadrangular;


		struct {
			Pint		num_r;
			Pint		num_t;
			Pfloat	*r;
			Pfloat	*t;
		} polar;

		struct {
			Pint		num_r;
			Pint		num_t;
			Pfloat	*r;
			Pfloat	*t
		} sector;

		struct {
			Pint		num_triangles;
			Pint		num_edges;
			Pint		num_vertices;
			Pint		*triangle_edge[3];
			Pint		*edge_owner[2
			Pint		*edge_vertex[2];
			Ppoint	*vertex;
		} triangular;

		struct {
			Pint				num_triangles;
			Pint				num_nodes;
			Ttriangle_ind	*triangle_nodes;
			Ppoint			*nodes;
		} ns_triangles;

		struct {
			Pint				num_ quadrangles;
			Pint				num_nodes;
			Ttriangle_ind	*quadrangle_nodes;
			Ppoint			*nodes;
		} ns_quadrangles;

		struct {
			Pint			num_ elems;
			Pint			num_nodes;
			Pint_list	*elem_nodes;
			Ppoint		*nodes;
		} ns_non_homo_2D;
	}geometry;
}Tmesh2D

type stands for the geometry type of the mesh :
typedef enum {
	TRECTANGULAR_MESH,
	TQUADRANGULAR_MESH,
	TPOLAR_MESH,
	TTRIANGULAR_MESH,
	TSECTOR_MESH,
	TNS_OF_TRIANGLES,
	TNS_OF_QUADRANGLES,
	TNS_MESH_NON_HOMO_2D
} Tmesh2D_type;

vertex and nodes stand for mesh nodes :
typedef struct {
	Pfloat	x;
	Pfloat	y;
} Ppoint;

typedef Pint Triangle_ind[3];

Tquadrangle_ind is a four integers array describing the four quadrangle node indices:

typedef Pint Tquadrangle_ind[4];

Description of the C structure scal_data:

typedef union {

	struct {
		Pfloat	**s;
	} rectangular;

	struct {
		Pfloat	**s;
	} quadrangular;

	struct {
		Pfloat	**s;
		Pfloat	so;
	} polar;

	struct {
		Ppoint	*s;
	} triangular;

	struct {
		Pfloat	**s;
	} sector;

	struct {
		Pfloat	*s;
	} ns_triangles;

	struct {
		Pfloat	*s;
	} ns_quadrangles;

	struct {
		Pfloat	*s;
	} ns_non_homo_2D;

} Tscalar2D_data;

typedef union {
	struct {
		Pvec	**v;
	} rectangular;

	struct {
		Pvec	**v;
	} quadrangular;

	struct {
		Pvec	**v;
		Pvec	vo;
	} polar;

	struct {
		Pvec	*v;
	} triangular;

	struct {
		Pvec	**v;
	} sector;

	struct {
		Pvec	*v;
	} ns_triangles;

	struct {
		Pvec	*v;
	} ns_quadrangles;

	struct {
		Pvec	*v;
	} ns_non_homo_2D;

} Tvec2D_data

where Pvec type is PHIGURE vector type:
typedef struct {
	Pfloat	delta_x;
	Pfloat	delta_y;
} Pvec;