# 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, and the View Window.

## 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_x^2` and `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.

## Animation

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.

## Superimposing Data

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 Panel.

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 x^2+y^2.

## Ending the Session

If desired, use the animation panel to animate other parameters of the current model.

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 separately.

Next: Conic Sections