A Family of Circles
This section of the tutorial assumes that you have completed the
section on computing level sets of the default model.
In this section we describe how to animate the computation of a
level set for a family of functions.
Launch Pisces and open the
Model Panel, the
Adaptive Grid Control Panel,
Changing Models We want to compute level sets that are
circles, so we first need to choose a model that has such levels.
Select the Cubic 2D model from the
Model menu on the Main Panel.
The Model Panel should update to reflect that you have changed models.
In the Model Panel, set all parameters equal to zero except for
coef_y^2 which should be set to 1.
The current model is now set to be x^2 + y^2. We want to compute the
level set of 1, therefore change the range value to c=1.
Lastly, we want to compute the level set on the domain
[-2,2]x[-2,2], so modify the entries that determine the
bounding box in which
Pisces will compute a level set. (Hint: Use
<TAB> to move
from field to field when inputting data.)
Finally, press the Go button on the Adaptive Grid
Control Panel to compute the unit circle x^2+y^2=1. (If you
don't see anything in the View Window, make sure you have set
c=1 in the Model Panel.) The circle will look elliptical
because the viewport of the View Window is not square. Correct this
by telling Pisces to use the current bounding box as the current
viewport. To do this, select BBox->Viewport from
the Actions menu of the View Window.
Now we will compute a family of level sets as a parameter is varied.
Open the Animation Panel by selecting the Animate
item from the Utilities menu on the Main Panel. On
the Animation Panel, find the menu labeled Parameter to
Animate and select Model.c from that
menu. Set the values of the Starting Value to 0.5,
the Ending Value to 4.0, the Number of
Steps to 7, and then press the Go button on
the Animation Panel. You should see 7 circles appear on the View
Window, each circle replacing the previous circle.
Suppose you wanted to create a contour plot of the function x^2+y^2
or, equivalently, you want to simultaneously look at a family of
level sets for the same model. To do this, open the
Output Panel by
selecting the Settings->Output menu option from the
Main Panel. Toggle the New Geometry option so that it is set to
adds to last. Now clear all of the current Pisces data by
selecting the Output->Erase all Graphics item from the
Main Panel. Once again press Go on the Animation Panel
and see a family of circles superimposed in the same View Window.
Viewing 3D Data
This portion of the tutorial is only valid
for those installations that have hooked up Geomview to interface with
Pisces. To begin, clear all Pisces graphics by selecting the
Output->Erase all Graphics item from the Main
From the Output menu on the Main Panel, select the
Geomview option. After a short wait, a Geomview
session should begin. (This may not happen if you are running Pisces
remotely. For example, if you are running Pisces on an SGI computer
but displaying the results on a Sun.)
Once Geomview has been launched, once again press the
Go button on the Animation Panel. As the level sets
are computed, they will be simultaneously plotted in Geomview. After
the level sets appear, you can use Geomview to zoom out and rotate the
levels, which sweep out an approximation to the graph of
Ending the Session
If desired, use the animation panel to animate other parameters of the
When you are finished, end this Pisces session by selecting
Quit from the File menu on the Main
Panel. If Geomview is running, you will need to quit that application
Next: Conic Sections
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Last modified: Tue Nov 21 09:05:52 1995
Copyright © 1995 by
The Geometry Center,
all rights reserved.