Getting Started: The Pisces Logo
In this section we describe how to compute the zero set of the default
Pisces model. If you have never run Pisces, you may
wish to read the section of documentation that describes how to launch Pisces.)
Upon beginning a new Pisces session, the main panel appears. Note that the default
model is the Pisces Function,
which means that this is the function for which Pisces will attempt to
compute a level set.
Computing a Level Set
- Open the control panel for the
Adaptive Grid Algorithm
by selecting the first entry on the
- Press the Go button on the algorithm's control panel
in order to request that Pisces use the adaptive grid algorithm
(with the default parameters)
to compute the level set of the current model.
- Open a View Window
by selecting the first entry on the
Output menu. The window should contain the
Pisces logo, which is actually the level set of an 11th degree polynomial
in two variables.
Manually Changing the Viewport
Edit the bounds of the view window's viewport to [-5,5]x[-5,5]
in order to change the
way that the Pisces logo appears on your screen. (Hint: After changing
the minimum value of the x variable to read -5,
<TAB> to the next field. When you have changed the entire viewport, press
<RETURN> to submit the changes.)
Zooming with the Mouse
To zoom in on the Pisces logo, position the cursor of your mouse at
the upper left corner of the logo (just above the tail of the "upper"
fish). Hold down the rightmost mouse button while you drag out a
rectangle that contains the lower right corner of the logo. The
"rubber-band box" should encompass most or all of the Pisces logo.
Release the right mouse button and select Actions->Zoom
in in order to scale everything that was inside the
rubber-band box until it fills the viewport.
Restoring the Default Viewport
Select the menu item Actions->BBox->Viewport
in order to restore the viewport to the domain [-2.2, 2.2]x[-1.2,1.2].
Modifying Model Parameters
Under the Settings menu on the main panel, choose the
first item labeled Model. This action will create a
new panel called the Model Panel. This panel
enables the user to control each model's parameters, domain, and
range. To see how this works, change the value of the parameter
labeled eyerad to read 0.3. Compute the
level set for this new function by pressing the Go
button on the control panel for the Adaptive Grid Algorithm. The View
Window should display a new image of two fish with big eyes. Because
the fish eyes are almost touching the fish's "forehead," this function
is nearly singular, and so the level set in the vicinity of the
forehead will look as if the fish have been attacked by some kind of
Modifying Algorithm Parameters
To cure the Pisces logo of its "scale rot," change the parameter
Max_Depth in the Adaptive Grid Control Panel so that
the parameter has the value 15. Recompute the level set by
pressing the Go button. After a few seconds, the fish
will look much improved.
To print the big-eyed Pisces logo, open the Postscript Panel
located on the Output menu of the Main Panel. On
this panel, press the Print button to create a
postscript file (called
pisces.ps, by default). The file
will appear in the directory from which you invoked Pisces, and may be
sent to any postscript-compatible printer. On UNIX workstations, this
is accomplished with the
Ending the Session
If desired, change other parameters in the
Model Panel and compute the related level set to get a feel for how
the level set changes with the parameters. Similarly, change
parameters that control the Adaptive Grid algorithm to see how each parameter
affects the computation of the level set.
When you are finished, end this Pisces session by selecting
Quit from the File menu on the Main
Next: A Family of Circles
The Pisces Home Page
Comments to: email@example.com
Last modified: Mon Nov 20 17:13:41 1995
Copyright © 1995 by
The Geometry Center,
all rights reserved.