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Overview
Surface Evolver graphics consists of drawing edges and facets. There
is a single graphics driver routine which produces colored edges and
facets in 3D and sends them to a set of display routines. There are
three main sets of display routines:
- Native screen graphics, built-in
Evolver graphics of various qualities on various platforms,
- Interface to the Geomview 3D viewer, for
Unix/Linux users without OpenGL/GLUT graphics compiled into Evolver,
- PostScript files, for everybody wanting
to make 2D images for publications, web sites, etc.
The Surface Evolver has the ability to produce its own
screen graphics directly. The Windows version has nice
OpenGL/GLUT graphics,
which should also be available on any Unix/Linux/Mac OSX system.
The Mac OS 9 version has some simple graphics, and there is a primitive
X-windows graphics module for Unix/Linux systems that for some reason
can't do OpenGL. Those compiling unix
versions must link in the appropriate graphics
module.
Screen graphics appear in their own window but can be controlled by
typing graphics commands
at the "graphics command: " prompt in the main window.
OpenGL graphics can also be controlled by mouse and keyboard
actions in
the graphics window.
Main prompt commands relevant to screen graphics:
The native screen graphics view is
controlled by a view transformation matrix, which may be specified in
the datafile,
and which is dumped by the d or
list topinfo commands.
The view matrix may be changed with graphics mode
commands.
The view matrix elements may be
read or set at runtime by view_matrix[i][j], where
the indices start at 1. In particular, one can write
command scripts to save and reload particular view matrices;
see saveview.cmd in the distribution package.
The view matrix does not affect geomview.
The display consists entirely of facets and edges. Special edges
(fixed edges,
boundary edges,
constraint edges, triple edges,
bare edges) are
always shown, unless you make their color CLEAR.
The individual
facet edges can be toggled with the graphics mode command
`e'.
When the native graphics display is invoked by the
's' command
or the various `show' commands,
the Evolver enters graphics
mode, with the prompt `Graphics command: '.
A graphics
command is a string of letters followed by RETURN. Each
letter causes an action. Some commands may be preceded by an integer
count of how many repetitions to do. Example command: 15u2z,
which does 'u' 15 times and 'z' twice.
Rotation commands may be preceded by a real number giving the
degrees of rotation; an integer will give a repetition count
with the default angle of 6 degrees. A real number is indicated
by including a decimal point.
Repeatable commands:
- u
- Graphics mode command.
Tip up. Rotates image about horizontal axis,
default 6 degrees.
Example: `15u' does 90 degree rotation,
`15.0u' does 15 degree rotation.
- d
- Graphics mode command.
Tip down. Rotates image other way, default 6 degrees.
Example: `15d' does 90 degree rotation,
`15.0d' does 15 degree rotation.
- r
- Graphics mode command.
Rotate right. Rotates about vertical axis, default 6 degrees.
Example: `15r' does 90 degree rotation,
`15.0r' does 15 degree rotation.
- l
- Graphics mode command.
Rotate left. Rotates about vertical axis, default 6 degrees.
Example: `15l' does 90 degree rotation,
`15.0l' does 15 degree rotation.
- c
- Graphics mode command.
Rotate clockwise about center of screen, default 6 degrees.
Example: `15c' does 90 degree rotation,
`15.0c' does 15 degree rotation.
- C
- Graphics mode command.
Rotate counterclockwise about center of screen, default 6 degrees.
Example: `15C' does 90 degree rotation,
`15.0C' does 15 degree rotation.
- z
- Graphics mode command.
Zoom. Expands image by factor, default 1.2. Examples:
`z' zooms by 1.2, `2z' zooms by 1.44, '2.0z' zooms by 2.
- s
- Graphics mode command.
Shrink. Contracts image by factor, default 1.2.
- arrow keys
- Graphics mode command.
Move image in appropriate direction. May be prefixed by
a real number, which is multiple of thirds of screen width to
move. Default move is 1/12 screen width.
May not work on all terminals.
Non-repeatable commands:
- R
- Graphics mode command.
Reset viewing angles to original defaults and rescale
the image to fit the viewing window.
- m
- Graphics mode command.
Center image in viewing window.
- e
- Graphics mode command.
Toggle showing all the facet edges.
- h
- Graphics mode command.
Toggle hiding hidden surfaces. When ON, takes longer to
display images, but looks better.
-
b
- Graphics mode command.
Toggles display of bounding box. Useful for visualizing
orientation. In the native graphics window, the 'o'
key does the same thing.
- t
- Graphics mode command.
Reset mode of displaying
torus model. Choice of
raw unit cell,
clipped unit cell, or
connected bodies.
- w
- Graphics mode command.
Toggles display of facets entirely on
constraints.
For a one-sided
constraint, applies to facets whose vertices all hit the
constraint.
"w" stands for "wall".
- B
- Graphics mode command.
Toggles display of facets on
boundaries or
equality constraints.
- v
- Graphics mode command.
Toggles showing of convex and concave edges in different
colors. "v" stands for "valleys".
- +
- Graphics mode command.
Increments color number used for facet edges.
- -
- Graphics mode command.
Decrements color number used for facet edges.
- ?
- Graphics mode command.
Prints help screen for graphics commands.
-
q
,x
- Graphics mode command.
Exit from graphics mode, and return to main command mode.
OpenGL graphics
Ideally, you have a version of the Evolver that uses OpenGL/GLUT
for its screen graphics. OpenGL is standard on Mac OSX, most unix systems,
and Microsoft Windows.
Tbe graphics display is invoked with the 's' command, which leaves you
at the graphics prompt, which you should quit 'q' right away since graphics
commands are better given in the graphics window.
There are many mouse and keyboard actions that can be performed in the
graphics window itself. Holding down and dragging the
left mouse button moves the
surface continuously, and the clicking right mouse button
picks vertices, edges, and facets. Picked element
id numbers are printed in the console window.
With the graphics window in the foreground, these keyboard commands are
active:
h | Print a help screen on the console window. |
r | Rotate mode for left mouse button. |
t | Translate mode for left mouse button. |
z | Zoom mode for left mouse button (and use F to focus on particular vertex). |
c | Clockwise/counterclockwise spin mode for left mouse button. |
+ | Widen edges. |
- | Narrow edges. |
b | Decrement edge front bias by .001. |
B | Increment edge front bias by .001 (to show edges more clearly). |
R | Reset the view. |
m | Center the image. |
M | Have the right mouse button bring up a menu instead of picking. |
P | Have the right mouse button do picking instead of menu (default). |
p | Toggle orthogonal/perspective projection. |
s | Toggle cross-eyed stereo. |
e | Toggle showing edges, regardless of "show edge" condition. |
f | Toggle showing facets obeying "show facet" condition or no facets. |
F | Move the rotate/zoom origin to the last picked vertex. |
G | Start another graphics window with independent camera. |
o | Toggle drawing a bounding box. |
g | Toggle Gourard (smooth) shading. |
x | Close the graphics window. |
arrow keys | Translate a bit. |
| And some more advanced commands most users will never use, but are
listed here for completeness: |
H | Print advanced help. |
a | Toggle using OpenGL element arrays. |
i | Toggle interleaved elements in OpenGL arrays. |
I | Toggle indexed OpenGL arrays. |
S | Toggle OpenGL triangle strips. |
Y | Toggle strip coloring (I was curious as to what OpenGL triangle
strips would look like). |
D | Toggle using a display list. |
Q | Toggle printing drawing statistics. |
Excellent screen graphics on Unix systems
can be done through the free 3D viewing program
geomview.
Geomview can be started
with the P command, option 8.
One caution: geomview does
not deal well with object sizes below 1e-5, so displaying micron-size
objects using MKS units is ill-advised.
Main prompt commands relevant to geomview:
- geomview
or P 8 to start geomview
- P 9 to end geomview
- geompipe
to pipe geomview input someplace else
- geomview
string
to send user commands to geomview
- gv_binary
toggle to control interface mode
- view_4D
to toggle sending 3D or 4D info to geomview
- D or
autodisplay for toggling automatic redraw when the surface changes.
Default is automatic redraw when geomview is started.
The View Matrix
The mapping of coordinates from ambient space to the graphics display is done
by a matrix called the view matrix. The matrix uses homogeneous
coordinates, thus is a square matrix whose size is one larger than
the dimension of the ambient space. The view matrix can be
initialized in the top of the datafile,
or its elements may be
read or set at runtime by view_matrix[i][j], where
the indices start at 1. In particular, one can write
command scripts to save and reload particular view matrices;
see saveview.cmd in the distribution package.
The view matrix is saved in dump files.
Multiple view transforms.
Evolver can display multiple transformations of a surface
simultaneously, for all of the possible graphics displays.
Each transform is defined by a matrix in homogeneous coordinates,
which for a 3D surface means 4x4 matrix which has a 3x3 rotation matrix
in the upper left, a translation vector in the last column, and
a row (0,0,0,1) on the bottom. There are two ways to specify the
transform matrices:
- List each matrix individually in the datafile; see
view_transforms.
- List a set of transforms in the datafile (see
view_transform_generators)
and use the transform_expr
command at run time to generate a set of transforms. I much prefer the
second way.
The final list of transforms may be accessed by the matrix
view_transforms[][][].
Because some transformations may reverse the front and back sides of
surfaces, transforms can be made to swap frontcolor and backcolor
attributes of facets; see
view_transforms or
view_transform_generators)
for syntax. The read-only array view_transform_swap_colors[]
has a 1 entry for the transforms that do swap
Picking elements.
One of the big advantages of using geomview or the OpenGL
version is that you
can pick vertices, edges, and facets in the geomview window by
right-mouse-clicking, and the
id numbers of the picked objects will
be printed in the main window. Be careful when picking; it does not
always work as you might hope. It may be necessary to zoom in on the
surface to get a clear shot at the element you want. Be wary when
the element returned is 1; that seems to be a common response when
Evolver is confused as to what element was picked.
Also, Evolver polls geomview for pick results only when at a
prompt awaiting user input.
Picked vertex, edge, and facet numbers are stored in the internal variables
pickvnum, pickenum, and pickfnum, respectively.
The 'F' key command on the graphics window sets the rotation and scaling
center to the pickvnum vertex. Pickvnum is settable with ordinary assignment
commands, so the user can zoom in on any vertex desired.
Note: Since vertices are not drawn individually, Evolver reports a vertex
as picked only when two edges with a common vertex are simultaneously
picked. Therefore a vertex at the end of a single edge cannot be picked.
It is possible to have the graphics display clip the surface
with multiple clipping planes.
A clipping plane is defined by a plane of the form ax + by + cz = d.
The visible volume is ax + by + cz <= d.
Up to 10 clipping planes may be stored in the array clip_coeff[][],
with the first plane coefficientsa,b,c,d stored in clip_coeff[1][1]
through clip_coeff[1][4], etc.
The user does not have to create clip_coeff[][].
To use clip view,
first set the coefficients of however many clip planes you want
and then use the clip_view toggle.
For example, to get a vertical clipping plane parallel to the y and z axes
and a little in front of them:
clip_coeff[1] := 1;
clip_coeff[2] := 0;
clip_coeff[3] := 0;
clip_coeff[4] := .2;
clip_view;
With OpenGL graphics, the first clip plane
plane can be varied interactively by hitting the 'l' key (lower case L)
in the graphics
window and dragging the mouse horizontally.
The 'k' key will make mouse dragging change the orientation of the
clip plane.
Hit 'r' or 'c' or 't' to
get back to another mouse mode. 'L' will turn off clip_view.
Clip view works separately, and after, torus model viewing modes such
as clipped and
connected,
so it is no problem to have them together.
In case clip_view and slice_view
are both in effect, slice_view operates instead of clip_view.
It is possible to plot a cross-sectional slice of a surface.
The slice is defined by a plane of the form ax + by + cz = d.
The coefficients a,b,c,d are stored in the array slice_coeff[]
(which the user does not have to create). To use slice view,
first set the coefficients and then use the slice_view toggle.
For example, to get a vertical slice parallel to the x and y axes
and a little in front of them:
slice_coeff[1] := 1;
slice_coeff[2] := 0;
slice_coeff[3] := 0;
slice_coeff[4] ;= .2;
slice_view;
The cross-section will be in the form of line segments of the same color
as the facets they are sections of. With OpenGL graphics, the slice
plane can be varied interactively by hitting the 'l' key (lower case 'L')
in the graphics
window and dragging the mouse horizontally.
The 'k' key will make mouse dragging change the orientation of the
clip plane.
Hit 'r' or 'c' or 't' to
get back to another mouse mode.
'L' will turn off slice_view.
Slice view works separately, and after, torus model viewing modes such
as clipped and
connected,
so it is no problem to have them together.
In case slice_view and clip_view
are both in effect, slice_view operates instead of clip_view.
The Surface Evolver can generate PostScript files by either the
postscript command
or the
P command option 3, or just "P 3".
The image is the same one shown with
the native screen graphics,
so one should use the s command and
graphics mode commands
to get the image looking as desired. The variable
brightness can be used to set
the median gray level. The
PostScript image is put into an 8 inch square at the lower left
of the page.
With the P command, you will be prompted for options.
- Show grid lines?
- This is asked if you are graphing a 2D surface. If you reply 'y',
all triangle edges will be plotted. If 'n', only special edges will
be plotted (triple junctions, borders, etc.; this can be controlled with the
show edges command).
Default 'n'.
The postscript command
uses the ps_gridflag toggle to control this.
- Do colors?
- If you reply 'y', edges and facets will be plotted with their
color attributes and shading
(if activated). If 'n', then all edges
are plotted as black, and all facets as white with shading.
Default 'n'.
The postscript command
uses the ps_colorflag toggle to control this.
- Do crossings?
- This is asked if the surface is 1-dimensional (the
string model)
and the dimension of space is at least 3. If you reply 'y', a 3D effect
will be created by plotting edges back to front, with each edge plotted
first as a thick white line and then as a thin black line. This creates
a broken back line and continuous foreground line at each crossing.
Default 'n'.
The postscript command
uses the ps_crossingflag toggle to control this.
-
Do labels? (i for ids, o for originals)
- This PostScript P 3 command subprompt
gives you a chance to put numeric labels on vertices, edges,
and facets, which is useful for debugging or modifying a datafile.
Edge labels are slightly displaced toward the head of the edge, and
facet labels are signed according to which side of the facet is visible.
Choose 'i' or 'y' for the current element id,
or 'o' for the original element number.
If you don't want any labels, just hit RETURN.
The postscript command
uses the ps_labelflag
toggle to control this.
The relative size of the labels can be controlled with the
ps_labelsize variable, whose default value is 3.0.
- Enter file name (.ps will be added):
- Give the name of the PostScript output file. A ".ps"
extension will be added if ".ps" or ".eps"
is missing. Not a good idea to just
hit RETURN, since that will produce the file ".ps".
The linewidth of PostScript edges may be controlled by the user. Widths are
relative to the image size, which is 3 units square.
If the real-valued edge extra attribute ps_linewidth is
defined, that value is used as the edge width. Otherwise
some internal read-write variables are consulted for
various types of edges, in order:
ps_stringwidth - edges in the string model, default 0.004
ps_bareedgewidth - "bare" edges, no adjacent facets, default 0.005
ps_fixededgewidth - "fixed" edges, default 0.004
ps_conedgewidth - edges on constraints or boundaries, default 0.004
ps_tripleedgewidth - edges with three or more adjacent facets, default 0.003
ps_gridedgewidth - other edges, default 0.002
The bounding box listed in the PostScript file is normally the actual
extent of the surface in the window (i.e. the bounding box is never bigger
than the window, but may be smaller). The
full_bounding_box toggle will
force the bounding box to be the full window. This is useful in controlling
the image size while making a series of images of different views or
evolution stages of a surface.
Visibility testing. PostScript files of complicated surfaces
may contain a high proportion of facets not visible in the final image.
This takes much extra file space and rendering time. There is an option
to process the list of PostScript facets to eliminate the non-visible
facets, the visibility_test option command. For my own
debugging purposes, there is a visibility_debug toggle,
which causes printing of verbose information; don't use it.
Other graphics related features.
This section has links to other topics you should consult.
Internal Evolver state information relevant to graphics:
Datafile features that are relevant to graphics are:
Main prompt commands that are relevant to all graphics are:
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Index.