Posted on Sept 25, 2014
by Dr. Saeid Nourian

Plotting
implicit equations is made incredibly easy in the new version of Graphing
Calculator 3D. You can plot equations of any complexity without the
restriction of starting them with z= or y=.

This blog describes how easy it is to plot implicit equations
and isosurface graphs with Graphing Calculator 3D.

## Plotting functions that start with 0=

The quickest way to plot an implicit function is to select 0= from
the drop-down list next to the equation (see image below). After this you
may complete the equation by typing it down.

For example to plot this:

x^2+y^2+z^2-2^2=0

you can type the left side of
the equation as shown here:

##
Plotting
arbitrary implicit equations

For maximum flexibility select "Implicit" from the Graph drop-down as shown on the right. This action will convert the
equation textfield to a form that allow typing arbitrary implicit
equations.

Note that you need to have equal (=) sign somewhere in your
equations. For example when plotting x^2+y^2+z^2=2^2 you should type it in
exactly as is.

## Plotting polar, cylindrical and spherical implicit
equations

Plotting implicit equations in polar coordinates follows exactly the
same steps as described above. Except instead of x, y and z your
equation would contain θ φ z and r. An example is shown below.

Note: In order to type θ, φ and r use Ctrl+1 Ctrl+2 and
Ctrl+3 respectively when in spherical coordinates mode. These short-keys
will insert whichever variable applies to current coordinates.

## Download Implicit Grapher

You can
download implicit grapher and try the above examples in it.