Modulef
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5.4 Complete description of the module

5.4.1 The different input data possible

Utilization with finite element results:

The admissible data structures for a mesh consisting of triangles are the AM( The name of the author, A. Marrocco.) or NOPO data structures.

The AM data structure is composed of 2 records (binary):

N, NT, ...
NU(3,NT), C(2,N), JND(NT), ...

where N is the number of nodes in the mesh and NT is the number of triangles. NU is the array containing the vertex numbers and C is the array containing the nodal coordinates. JND is an array containing the sub-domain number of each element.

The NOPO data structure must be 2D and composed of P1 triangles only.

Several possibilities are offered as far as the results of the computation defined on the mesh are concerned:

the file (binary) contains a set of records, each record corresponds to the nodal values of a solution (vector of length N);
the file (binary) is composed of a set of records, each record containing the vectors U(N), V(N), C(2,N) and X.
(U and V may represent a solution vector, C is the array containing the nodal coordinates and X is a real scalar)
the file contains a B structure (corresponding to the NOPO structure).

Utilization, visualization of array T(NX,NY):

The (binary) file is composed of a set of records, each of length NX*NY and corresponds to array T(NX,NY).

The program will inquire what the record number is. NX and NY must be the same for the different records and must also be compatible with those defined (further on) with command MAILLE-XY.

Utilization of an external function:

Already seen.

Function F typed on the keyboard:

The interpreted functions (function parser) are used here.

5.4.2 Main commands

The main commands correspond to BORNES-XY, MAILLE-XY and GRAD-ECH-XYZ.

BORNES-XY

This command is used to define a rectangular window in the (X,Y) plane, which serves as the domain in which function F(X,Y) is defined.

The input parameters are: XMIN, XMAX, YMIN and YMAX, the window extremities.

The initial values are, respectively, 0, 1 , 0 and 1.

For the case where the module is used to interpret the finite element results, we choose the domain bounds as XMIN, XMAX, YMIN and YMAX.

MAILLE-XY

To define a grid in the window defined by XMIN, XMAX, YMIN and YMAX.

The input parameters are:

NX, number of points in the x-direction, and NY, number of points in the y-direction.

The initial values are NX = NY = 40.

GRAD-ECH-XYZ

To choose the representation scale, linear or logarithmic, in the z-direction only. The initial choice corresponds to a linear scale.

5.4.3 General display characteristics

Initially, there is an automatic scaling of the three-dimensional object to be represented (this can be prevented!).

The commands available at this level are: OBS, DIM, MODE, AXES, LEGEND and (return).

The "return" key is used to exit from the current subroutine and execute the plot.

The signification of the above commands is now given:

OBS

Positioning of the observer in spherical coordinates and observation angle. The input parameters are:

the angle with respect with the OX axis (in degrees)
the angle with respect to the XOY plane (in degrees) (elevation)
vis the half angle of observation (in degrees) (value < 90).

The initial values of the parameters are: , and vis 2.

The observer always views the center of the box defined by XMIN, XMAX, YMIN, YMAX, ZMIN and ZMAX and his/her distance is calculated automatically such that the entire object is in view.

DIM

To define or modify the size (in cm.) of the plot.

The input parameters are: X1, X2, Y1 and Y2.

The initial values depend on the terminal used and correspond to the maximum size usable.

MODE

The surface display mode. There are several possibilities:

MODE = 1 or 2:
The domain for the function definition is:
X in the interval [ XMIN, XMAX ] and
Y in the interval [ YMIN, YMAX ].

In the present case, this is also the domain displayed.

For MODE = 1 the surface is represented using lines.
For MODE = 2 the surface is represented using a grid.
MODE = 3 or 4:
The domain for the functional definition is:
X in the interval [ XMIN, XMAX ] and
Y in the interval [ YMIN, YMAX ].

In the present case, the displayed domain can be different to the definition domain as supplementary constraints can be imposed by the relations:

The user has the choice of parameters CX, CY, B0, B1, TX and TY, respectively initialized to the values: 0, 0, 0, 1, 1 and 1.

For MODE = 3 the surface is represented using lines.
For MODE = 4 the surface is represented using a grid.
MODE = 5 or 6:
The domain for the functional definition is:
X in the interval [ XMIN, XMAX ] and
Y in the interval [ YMIN, YMAX ].

In the present case, the displayed domain can be different to the definition domain as supplementary constraints can be imposed by the relations:

The user has the choice of parameters C CX, CY, B0, B1, TX, TY, AX and AY, respectively initialized to the values: 0, 0, 0, 1, 1, 1, 1 and 1.

For MODE = 5 the surface is represented using lines.
For MODE = 6 the surface is represented using a grid.
MODE = 7 or 8:
The domain for the functional definition is:
X in the interval [ XMIN, XMAX ] and
Y in the interval [ YMIN, YMAX ].

In the present case, the displayed domain can be different to the definition domain as supplementary constraints can be imposed by the relations:

Linear constraints defining half-planes. The user can have up to 10 relations of this type.

The initial values are 2 linear relations and the parameter values given below:

For MODE = 5 the surface is represented using lines.
For MODE = 6 the surface is represented using a grid.

AXES

This part corresponds to the axes. Plots of graded and referenced axes.

Output in space (3D) is obtained by transformation of a reference axis described on the (0,0),(1,0) segment of the XOY plane. The different parameters defining the axis are modified dynamically via a menu indicating the different options available.

Thus, when using keyword (or command) AXES, the following will appear on the screen:

|-------------------------------------------------------------------|
| ACTUELLEMENT on trace  N axes                                     |
|  aspect , mod_const , leg_axes , nb_axes , edit_contr , (return)  |
|-------------------------------------------------------------------|

N indicates the number of axes that we want to plot (this value is initialized to 0, (no plot)).

The line underneath indicates the different commands available. Only the first character of the command --- UPPERCASE (or lowercase depending on the implementation) --- is taken into account as response; this character can be replaced by the position number of the command: 1 for ASPECT, 2 for MOD_CONST, etc.

LEGEND

A legend (5 lines maximum) can be defined on the plot using this command. The user can also if necessary specify the placement, the character size and the thickness of the plotlines.

5.4.4 Axes

This section once again considers the definition of the axes and gives the different commands mentioned above in detail.

ASPECT

Different manners of generating the "reference-box" (parallelopiped), containing the object to be visualized, are possible.

Figure 5.1: Reference-box 1, 2 and 3

Figure 5.2: Reference-box 4, 5, 6 and 7

The different reference-boxes are shown in figures 5.1 and 5.2 for cases 1 to 7. Reference-box number 0 is the one where we visualize nothing, whereas a reference-box with a negative number corresponds to a complete parallelopiped.

Note that reference-box 2 is the default value.

The user then inputs the color of the reference-box lines (and graduations), i.e. the density of the red R (0,1), the density of the green V (0,1) and the density of the blue B (0,1). It is possible to perform modifications.

Remark:: The data, R, V, B, will be output to program VIS3D, although it does not actually utilizes it.

MOD-CONST

Definition and construction mode for axes (graduations):

MOD-CONST = 1 (default value):
Automatic choice for axes to be plotted (number 0, 3, 4, 5 or 6) in such a way that the graduations are placed on the outside of the box as a function of the position of the observer (actually, the observer is placed in the half-space Z>0).
MOD-CONST = -1:
The positioning choice for the axes is not redone as a function of the observer (the graduations and references are considered as an integral part of the former object (using this mode can consequently result inverse printing, among other things).
MOD-CONST = 2 (manual -- not recommended):
ALL the parameters defining the axes need to be input. Thus, for each axis, the user must first input:
A: the following 15 parameters:
1. the number of the starting point (1, 2, 3, ..., 8). The numbering of the points is the same as that used in figure 5.3;
  
  Figure 5.3: Numbers of the points in the cube
2. the number of the final point (1, 2, 3, ..., 8);
3. the value of the starting point;
4. the value of the final point;
  The values of the extremities are the values to be assigned, for example for axis 1-2: XMIN, XMAX (If we decide to plot axis 1-7, diagonal, the corresponding values must be entered)
5. the type of graduation scale (<0 log, linear);
  By default, the graduation scale is linear. If the log scale is chosen, the object must be defined and described using the same scale. There is thus a risk of encountering compatibity problems.
6. reference indicator on the axis (integer value IGRAD);
  
  0: no values printed at graduations
  
  > 0 : printing parallel to the axis direction
  = 1: beneath the axis (reference axis)
  > 1 : above
  
  < 0 : printing perpendicular to the axis direction
  = -1: below
  < -1 : above.
7. generation mode for graduations;
  
  0 ( 1 or 2): subdivision into NGRAD referenced intervals, each interval being subdivided into NSUB sub-intervals.
  
  1: grading using the elementary interval XINT with references at all the NGRAD intervals. XINT is input in objet units, i.e. in relation to the [0,1] interval.
  
  2: graduation mode analogous to 1, but this time XINT is given in subject units, i.e. in terms of the values on the axis (XMIN, XMAX, ...).
8. print format of the values (NF integer);
  
  NF 0: FORTRAN format F with NF digits after the decimal point
  
  NF = -1: FORTRAN format I
  
  NF < -1: FORTRAN format E to |NF| significant digits.
9. line thickness (graduations, numbers, references);
  Thick plot lines possible (value input in mm.).
10. enlargement factor in X of the characters;
11. enlargement factor in Y of the characters;
12. enlargement factor of the dashes (graduations);
  The default size of the characters with respect to the reference axis is units and the size of the dashes is 0.05.
  Parameters 10, 11 and 12 are used to modify the relative value:
  Value > 1: enlargement, or
  Value < 1: reduction.
13. number of referenced intervals (NGRAD);
14. number of sub-intervals (NSUB);
15. length of elementary interval (XINT);
(13, 14 and 15 are linked to the generation mode of the graduations in 7).
B:

The user must then input the legend corresponding to the axis, specify if he/she would like to frame the legend, as well as specify its position (8 positions are possible, see figure 5.4).

Figure 5.4: Positioning of legends on the axes

Note:
There is an incompatibility risk with regard to the printing of the values and the positioning of the legends, for example when:
IGRAD = -1 and IPL = 1 or 2;
IGRAD < -1 and IPL = 3 or 4;
IGRAD = 1 and IPL = 7;
IGRAD > 1 and IPL = 5 ...).

C:

Finally, the user need to specify the vector which, with the axis, defines the printing plane of the graduations, values and legends of the axes.

LEG-AXES
: To define or modify the references (legends) on the 3 principal axes (in X, in Y, in Z, the 3 first ones). The text is typed on he keyboard.

NB-AXES
: To choose or modify the number of axes actually plotted (in automatic mode, the number of axes is 0, 3, 4, 5 or 6)

EDIT-CONTR
: To control and modify the parameters defining the axes locally. Only the graduation scale of the axis cannot be modified because it is in principle linked to the description of the object that we wish to represent. The parameters occuring here are the same as those described when the axes construction mode is 2.

return
: To exit from the module and continue the processing.

Two examples are shown below:

Figure 5.5: Example VIS3XX: manual definition

Figure 5.6: Example VIS3XX: NOPO and B

Next: 6 Diverse visualizations Up: 5 Visualization of surfaces Prev: 5.3 Utilization of VIS3XX Contents