## Graphics in QMG |

The numbers *r, g, b* stand for red, green and blue and are the
amount of that color present in the face.
For instance,
*r*=1, *g*=0,
*b*=0 is pure red, whereas *r*=1, *g*=
1, *b*=0 is yellow.

The parameter *a* is sometimes called **alpha**
and is the degree
of opacity. Thus, *a*=1 means the face is completely opaque and
*a*=0 means the face is completely transparent. Somewhere in between
0 and 1 means the face is partially transparent.

Not all the graphics engines support transparency, so you may
find that modifying this parameter strictly between
0 and 1 does not yield the desired result.
It is guaranteed, however, that *a*=0 will yield a completely
transparent (invisible) face for any graphics engine and *a*=1
will yield a completely opaque face.
Making an exterior face invisible is useful for revealing
internal boundaries or completely
interior holes.

The graphics routines are as follows.

Matlab:This routine produces a new brep that is the same as the old brep, except that all faces of dimensionTcl/Tk:newbrep=gmrndcolor(brep {, dim});

gmsetnewbrep[gmrndcolorbrep {dim}]

The *dim* argument is optional;
It defaults to the embedded dimension
of the brep minus 1, or the intrinsic dimension, whichever is smaller.
The function does not alter the color of
a face that is already has a **color** property assigned
to it.

The `gmshowcolor`

routine is useful for displaying the colors assigned by
`gmrndcolor`

.

Matlab:This routine displays a brep or simplicial complex. The display is controlled bygmviz(Tcl/Tk:obj {, colorspec {, dim}});

gmvizobj {colorspec {dim}}

`gmvizgui`

.
The arguments determine which dimension or dimensions of object to
display. For instance, a third argument of 1 indicates that
1-dimensional faces (the edges) of the brep or simplicial
complex should be displayed.
The third argument can also be a vector (a list in Tcl/Tk)
containing several dimensions of the object to plot at
once. The default for the third argument is
min(*d*−1,*k*)
where *d* is the embedded dimension and
*k* is the intrinsic dimension.

The second argument is the color to use. There must be one color
per dimension; in other words,
the second and third arguments to `gmviz`

are in correspondence.
For example, in Matlab, the call

```
``````
gmviz(b, 'rw', [1, 2])
```

will render the 1- and 2-dimensional faces of b (edges and facets).
The edges will be colored red and the facets will
be colored white. The equivalent in Tcl/Tk is:
```
``````
gmviz $b {red white} {1 2}
```

As mentioned above, the second argument is one or more colors,
in correspondence with the dimensions. For a brep, the color specified
in the gmviz call is overridden by the property-value pair color
assigned to the faces. (No such option exists for simplicial complexes
since individual simplices do not
have property-value pairs.)
The default color
is obtained from the `gmvizgui`

control panel.

In Matlab, there are two ways to specify color to the gmviz
command. A color can
either be a one-character string **y**, **m**,
**c**, **r**, **g**,
**b**, **w**, **k** or
**i** standing
for yellow, magenta, cyan, red, green, blue, white, black and invisible.
Several such colors (one for each dimension) are concatenated together
into a string as in the above example.

A color in matlab can also be specified as a matrix with four entries
per row; each row is an *r, g, b, a* encoding as described
above. The number of rows is in correspondence
to the number of dimensions specified in the third argument.
In Tcl/Tk, a color can be any valid X11 color name such as "green".
It can also be a four-tuple of numbers.

An alternative calling format for these routines is:

Matlab:where pair is a mesh-brep pair (2-element cell-array in Matlab, 2-element list in Tcl/Tk). In this calling format, the mesh is displayed using colors inherited from the color values of the faces of the brep. The mesh should belong to the brep.gmviz(Tcl/Tk:pair {, colorspec {, dim}});

gmvizpair {colorspec {dim}}

QMG 2.0 supports two different graphics engine types, internal and external. For Matlab, “internal” means a usual Matlab graphics window. For Tcl/Tk, “internal” means a Tk canvas object. The Matlab internal engine can plot in both two and three dimensions. The Tcl/Tk internal engine is for 2-dimensional objects only.

QMG 2.0 supports one external rendering format, VRML 1.0.
When external rendering is requested, `gmviz`

will
write the objected to be rendered to a file in VRML format.
For information about
VRML, see the VRML repository.
The software supports automatic notification of
Netscape
Communicator (or Netscape Navigator)
in both Unix and Windows.
“Automatic notification” means that `gmviz`

or `gmplot`

will cause the Netscape browser
to load the VRML image as soon as the
data has written to the file in VRML format.
To use notification, the Netscape browser must running on your
workstation (as a separate process)
at the time the `gmviz`

or `gmplot`

statement is executed.
The browser must have a VRML plug-in viewer installed.
You control automatic notification with buttons in
in the GUI created by `gmvizgui`

.

You can also select the file
name to hold the VRML file with the `gmvizgui`

control panel.
The default is `test.wrl`

.
Always choose a file whose suffix is `.wrl`

.
You can also select whether that file is opened in replace-mode
or append-mode. Opening the file in append mode means that each successive
`gmviz`

statement will each its VRML at the end of the file, so
that several different objects can appear at once in the browser.

For Windows only, the software also supports automatic notification of Microsoft Internet Explorer.

The notification is accomplished internally via
`gm_url`

in
Tcl/Tk or the built-in command `web`

in Matlab.
This routine notifies Netscape or IE to load the file using
the DDE protocol under Windows. Under Unix, `gm_url`

uses Netscape
Navigator's remote control feature for automatic notification.

The rendering engines (both external and internal) support "thickening" options. Thickening a vertex means displaying it as a disk or sphere instead of a point. Thickening an edge means displaying it as a fat line or pipe instead of a segment. Thickening a vertex makes it a disk or ball.

Setting the thickness in a VRML plot of either vertices or lines to anything greater than zero increases both the size of the VRML file and the time required ton render the object. This is because vertices of width greater than 0 are plotted as individual spheres, whereas 0-width vertices are plotted as a point cloud. Similarly, edges of width 0 are rendered all together as an indexed line set in VRML, whereas edges of positive width are rendered individually as cylinders.

When `gmviz`

in Matlab displays a 2D object, it provides
six control buttons as follows.
**Zoom In** and **Zoom Out**
zoom in or out on the current center of
the object. **Up**,
**Down**,
**Left**, and
**Right** move your viewpoint
on the object.

When `gmviz`

in Matlab displays a 3D object,
the buttons **Up**,
**Down**, **Left** and
**Right** change your
viewpoint as if you are sitting on the surface of a
circumscribing sphere around the object.

`gmvizgui`

on your screen.
Changes made to a setting in this GUI do not affect
the current plot; instead, changes take effect for the next plot. After the
GUI is closed, its last settings stay in
force. Do not start two different
gmvizgui windows because they will get out of sync.
This panel controls default colors, choice of renderer, file names (in the case of VRML rendering), and thickness of segments and points.

It also controls the number of bezier subdivisions. When plotting a brep with curved boundaries, the rendering routine first converts the curve into a sequence of straight edges or flat triangles. You can control how many subdivisions are made for this purpose. More subdivisions gives a more accurate rendering but at the cost of greater computation time during rendering.

To try these features out, you can use the interactive script
testviz by typing `testviz`

in matlab or
`source $qmg_library2/testviz.tcl`

in Tcl/Tk.

`gm_vizp`

. This routine takes as arguments a brep or
simplicial complex and several other parameters and returns a
list of points, edges, or triangles ready to be plotted.
where mesh is the simplicial complex used for the finite element method, and u is the solution vector. The simplicial complex must have intrinsic dimension 2, and can have embedded dimension of either 2 or 3. The argumentgmplot(mesh, u {, solnrange {, cmap}});

In the case of 3D FEM solutions, you first have to restrict the
mesh to the boundary elements with the
`gmboundary`

function. Then you have to restrict the
FEM solution *u* to the subset of nodes in the new simplicial complex
by subscripting the full FEM solution with the index-source
vector returned by `gmboundary`

. There are examples
of this technique in the test cases.

The routine defaults to the **jet** colormap.
The third
argument is an optional 2-vector with lower and upper bounds on *u*.
These bounds default to the min and max values of the vector *u*.
Specifying the third argument explicitly
is useful
when you are making several
different plots for which you want the same absolute color scale.

Routine `gmplot`

uses
interpolated colors on each triangle in the simplicial complex.
However, it does not use the interpolated-color feature that is built in
to Matlab (I found that earlier versions of interpolated
colors did not work on my color printer. I don't know if this has
been fixed in the more recent Matlab releases). Instead, it divides
each triangle into nine smaller triangles and uses flat colors (that
are linearly interpolated by the `gmplot`

program) on each of the
subtriangles.
Thus, the triangles you see with `gmplot`

are subtriangles of
the actual triangles used in the finite element solver.

The matlab command `colorbar`

is useful in conjunction
with the `gmplot`

routine.

This documentation is written by Stephen A. Vavasis and is copyright ©1999 by Cornell University. Permission to reproduce this documentation is granted provided this notice remains attached. There is no warranty of any kind on this software or its documentation. See the accompanying file 'copyright' for a full statement of the copyright.

Stephen A. Vavasis, Computer Science Department, Cornell University, Ithaca, NY 14853, vavasis@cs.cornell.edu