You can use the 3D Graph app to draw 3D graphs in three-dimensional space using $x$-, $y$-, and $z$-coordinates. You can graph lines, planes, spheres, cylinders, and cones using built-in templates, or you can manually enter functions to draw lines, curved surfaces, solids of revolution, and other forms.

1. h > 3D Graph

This displays the Function tab.



2. Press O (or select T > [Enter Equation]) to display the Type menu.^*

This displays the Type menu.



3. On the Type menu, select [Templates] > [Sphere].

This displays a list of sphere templates.



4. Select [].

This displays the template’s numeric value input window.

Since we want to graph “$x^2+y^2+z^2=2^2$”, input a=0, b=0, c=0, and r=2.

0E0E0E2E



5. Press O.

This displays the template name (Sphere) along with the values you input.



6. To draw a 3D graph using a built-in template you stored, press >.

This displays the View Window menu. Change the range specification as required. For more information, see Specifying the Spatial Range and Drawing Accuracy for 3D Graphing (View Window).

7. Highlight and then press O.

This draws the graph on the Graph tab.



8. To return to the Function tab, press > or b.

1. Use d to highlight “2:” on the Function tab.



2. Press O. On the menu that appears, select [Z‎=‎].

Alternatively, you could also perform the operation T > [Enter Equation] > [Z‎=‎].

3. Input $\mathrm{Z}={\mathrm{X}}^2+{\mathrm{Y}}^2-3$.

Xi+P-(Y)i-3E



4. To draw the 3D graph, press >. Next, on the View Window menu that appears, highlight and then press O.

This draws the graphs on the Graph tab.



5. To return to the Function tab, press > or b.

The Out of Drawing Range warning message appears when there is nothing to draw in the window when you try to draw a graph. If this happens, choose the desired operation from the menu that appears.

You can use the Function tab to store templates and functions you want to use for 3D graph drawing. You can store up to a total of three templates and/or functions. The example screen below shows the Function tab when one template and two functions are stored.

1. On the Function tab, highlight the line where you want to store a template.

2. Select T > [Enter Equation] > [Templates].

This displays the Select Template menu.



3. Select the template you want to use.

Use the template menu to select what you want to graph and the graphing method you want to use.

To graph this:	Select this menu item:
Straight line with the equation $\frac{\mathrm{X}-{\mathrm{X}}_0}{\mathrm{a}}$ = $\frac{\mathrm{Y}-{\mathrm{Y}}_0}{\mathrm{b}}$ = $\frac{\mathrm{Z}-{\mathrm{Z}}_0}{\mathrm{c}}$	[Line] > []
Straight line by using a vector equation $\overrightarrow{\mathrm{r}}=\overrightarrow{{\mathrm{r}}_0}+\mathrm{t}\overrightarrow{\mathrm{v}}$ (two vectors)	[Line] > []
Straight line by specifying the coordinates of two points	[Line] > [Line through 2 points]
Straight line by specifying the coordinates of one point and a direction vector	[Line] >[ Through point‎ (X0‎,Y0‎,Z0) Direction vector [a,b,c] ]
Plane by using the equation $\mathrm{a}\mathrm{X}+\mathrm{b}\mathrm{Y}+\mathrm{c}\mathrm{Z}+\mathrm{d}=0$	[Plane] > []
Plane by using a vector equation $\overrightarrow{\mathrm{r}}=\overrightarrow{{\mathrm{r}}_0}+\mathrm{s}\overrightarrow{\mathrm{u}}\mathrm{ }+\mathrm{t}\overrightarrow{\mathrm{v}}$ (three vectors)	[Plane] > []
Plane by specifying the coordinates of three points	[Plane] > [Plane through 3 points]
Sphere by using the equation: ${(\mathrm{X}-\mathrm{a})}^2+{(\mathrm{Y}-\mathrm{b})}^2+{(\mathrm{Z}-\mathrm{c})}^2={\mathrm{r}}^2$	[Sphere] > []
Sphere by using the equation: ${\mathrm{X}}^2+{\mathrm{Y}}^2+{\mathrm{Z}}^2+\mathrm{a}\mathrm{X}+\mathrm{b}\mathrm{Y}+\mathrm{c}\mathrm{Z}+\mathrm{d}=0$	[Sphere] > []
Cylinder	[Cylinder]
Cone	[Cone]

Selecting any one of the above options displays a window for inputting the selected template’s values.

4. Depending on the template you chose, input the required value in each cell (or row) in the window.

5. After inputting all of the values, press O.
   (If you chose [Cylinder] or [Cone] in step 3, highlight and then press O here.)

This returns to the Function tab.

Note

Note that the following input in step 4 results in an error.

For this template:	This type of input results in an error:
[Line] > []	a=0 or b=0 or c=0
[Line] > []	X, Y, Z elements = 0 for $\overrightarrow{v}$
[Line] > [Line through 2 points]	Both points = Identical coordinate values
[Line] >[ Through point‎ (X0‎,Y0‎,Z0) Direction vector [a,b,c] ]	All direction vector elements = 0
[Plane] > []	a=0 and b=0 and c=0
[Plane] > []	X, Y, Z elements of either or both $\overrightarrow{u}$ and $\overrightarrow{v}$ = 0 $\overrightarrow{u}$ and $\overrightarrow{v}$ = Identical orientation
[Plane] > [Plane through 3 points]	Two of three points = Identical coordinate values Three points are on a straight line
[Sphere] > []	r = 0 or less
[Sphere] > []	Input values do not satisfy a2+b2+c2>4d.
[Cylinder]	Radius: 0 or less Same value for Zmin and Zmax
[Cone]

1. Highlight the line where the template you want to edit is located, and then press O.

This displays the template’s numeric input window.

2. Make changes to the existing values as required.

3. After everything is the way you want, press O.
   (If you are editing a [Cylinder] or [Cone] template, highlight and then press O here.)

To delete a stored template, use the same operation as that for deleting a Graph&Table app’s stored function. See To delete a function for details.

1. On the Function tab, highlight the line where you want to store a function.

2. Select T > [Enter Equation].

3. Perform the operations shown in the table below.

To select this function type:	Select this menu item:
Cartesian coordinate type (Z=$f$(X, Y) form)	[Z‎=‎]
Parametric type $\left(\begin{array}{c}\mathrm{Xst}＝f\left(\mathrm{S},\mathrm{T}\right)\\ \mathrm{Yst}＝f\left(\mathrm{S},\mathrm{T}\right)\\ \mathrm{Zst}＝f\left(\mathrm{S},\mathrm{T}\right)\end{array}\mathrm{ }\text{form}\right)$	[Parametric]
Solid of rotation on the X-axis (Y=$f$(X) form)*1	[‎$x$-Axis Rotate]
Solid of rotation on the Y-axis (Y=$f$(X) form)*2	[‎$y$-Axis Rotate]

This draws a three-dimensional graph on the XY plane input using the Y=f(X) format and rotates it 360 degrees around the X axis.

This draws a three-dimensional graph on the XY plane input using the Y=f(X) format and rotates it 360 degrees around the Y axis.

4. Input the function in accordance with the selected type.

Press X to input the variables (X or T) in accordance with the function type you chose.

To input “Y” for a Z= form function, press P-(Y) or press C and then input using the menu that appears.

To input “S” for a parametric type function, press P/(S) or press C and then input using the menu that appears.

Example 1:  To input the Cartesian coordinate type $\mathrm{Z}={\mathrm{X}}^2+{\mathrm{Y}}^2$

T > [Enter Equation] > [Z‎=‎]
Xi+P-(Y)iE



Example 2:  To input the parametric type $\{\begin{array}{c}\mathrm{Xst}＝2\cos \left(\mathrm{T}\right)\\ \mathrm{Yst}＝3\sin \left(\mathrm{T}\right)\\ \mathrm{Zst}＝3\cos \left(\mathrm{T}\right)\end{array}$

T > [Enter Equation] > [Parametric]
2cX)E
3vX)E
3cX)E



Example 3:  To input the solid of rotation on the X-axis type $\mathrm{Y}={\mathrm{X}}^2-2$

T > [Enter Equation] > [‎$x$-Axis Rotate]
Xi-2E



Note

You can input only Absolute Value and Hyperbolic Calc category functions using the menu that appears when you press C in step 4.

To edit or delete a stored function, use the same operation as one in the Graph&Table app. See To edit a function and To delete a function for more information.

On the Function tab, highlight the row that contains the graph drawing settings you want to change and then perform the operations described in the table below.

The line color and area color you specify are shown by the icons to the left of each line of the Function tab as shown below.

1. On the Function tab, highlight a line where a template or function is stored.

2. Press T.

This displays a Tools menu with [Select] highlighted.

3. Change [Select] to (On) to enable or to (Off) to disable graphing for the selected template or function.

4. Press b to close the Tools menu.

The on/off setting of step 3 is indicated by the icons to the left of each line of the Function tab.

… On

… Off

Press > or highlight and then press O. This causes the View Window menu^*1*2 to appear so you can specify the range of the graph window. Change the range specification as required. For more information, see Specifying the Spatial Range and Drawing Accuracy for 3D Graphing (View Window).

To return to the Function tab, press < or b.

Press + to zoom in or - to zoom out.

Use the cursor keys to rotate a 3D graph up, down, left, and right.

You can use the View Window menu to specify the spatial range ($x$-, $y$-, and $z$-axis ranges) and the precision for drawing a 3D graph. This View Window also lets you specify the range of values for drawing a parametric type graphs, and the viewpoint of a 3D graph.

On the Graph tab, select T > [View Window].

Use the View Window to input values for the items below.

‎$x$‎ Minimum, ‎$x$‎ Maximum, ‎$x$‎ Grid ($x$-axis minimum value^*1, maximum value^*1, grid value^*2*3)

‎$y$‎ Minimum, ‎$y$‎ Maximum, ‎$y$‎ Grid ($y$-axis minimum value^*1, maximum value^*1, grid value^*2*3)

‎$z$‎ Minimum, ‎$z$‎ Maximum ($z$-axis minimum value^*1, maximum value^*1)

These settings are applied when drawing parametric graphs. Use the View Window to input values for the items below.

S Minimum, S Maximum, S Grid (parameter S minimum value^*1, maximum value^*1, grid value^*2*3)

T Minimum, T Maximum, T Grid (parameter T minimum value^*1, maximum value^*1, grid value^*2*3)

Use the settings below to adjust the viewpoint of the graph display with respect to the $x$-axis and $z$-axis. Always specify a value in degrees, regardless of the current S > [Angle] angle unit setting.

Angle‎ $\mathrm{\theta }$‎: Specifies the angle of clockwise rotation of the $x$-axis (-180° < $\mathrm{\theta }$ < 180°) viewed from the positive end of the $x$-axis (0°).

Angle‎ $\mathrm{\phi }$‎: Specifies the angle rotation of the $z$-axis towards the back (0° < $\mathrm{\phi }$ < 360°) viewed from the positive end of the $z$-axis forward (0°).

On the View Window menu, select [Pre-set Windows] > [Initialize].

 

You can display the cross section of a 3D graph sliced with any vertical plane relative to the $x$-, $y$-, or $z$-axis. This operation is available for lines, planes, spheres, cylinders, or cones drawn using a template.

On the Graph tab that already shows a 3D graph, perform the operations in the table below.

While a cross section is displayed, perform one of the operations below.

Press U or D to move a cross section on the applicable axis. You can also specify a location on a cross section by directly inputting a coordinate value on the applicable axis.

You can use the operations below to determine the intersect of two lines, the intersect of a line and a plane, or the intersect of two planes. This operation can be performed on lines and/or planes drawn using a template.

You can determine the relationship between two 3D graphs using the combinations below.

This operation can be performed on lines and/or planes drawn using a template.

Trace displays a crosshair pointer () on a graph that you can use to read the coordinate values at a specific location. To enable trace, select T > [Trace].

The operations that can be performed while the trace function is enabled are described in the table below.

You can rotate a 3D graph automatically using Auto Rotate. Auto rotation stops automatically after two rotations.

1. On the Graph tab, select T > [Rotate].

2. On the menu that appears, select a rotation direction.

To stop the auto rotation part way through, press a.

You can use sketch to draw dots and text within the graphing area. The following table shows what you can do with sketch.

The Settings menu items described below are specific to the 3D Graph app.

S > [3D Axes] ... Shows/hides Cartesian coordinate axes in the graph window.

S > [Box] ... Shows/hides boxed axes in the graph window.

S > [3D Label] ... Shows/hides axis labels in the graph window.