Graphing 3D Plots
In this worksheet, you will learn how to create a 3D plot from a function of two variables. You will also learn a little bit about how to format the look of these plots for maximum effect.
Creating
a 3D QuickPlot from a Function
1. Define a two-variable function:
Then, insert a 3D graph region by selecting Graph / Surface Plot from the Insert menu. Enter the name of the function, G, in the placeholder at the bottom of the 3D graph region:
Tip: Any two-variable function of linear terms produces a plane in a surface plot.
2. Define a two-variable function:
Then, insert a 3D graph region by selecting Graph / Surface Plot from the Insert menu, and enter the name of the function in the placeholder.
Tip: Any two-variable function of quadratic terms produces a paraboloid in a surface plot.
Changing
the Appearance of a 3D Graph
1. Double-click the 3D graph below to access the 3D Plot Format dialog box:
Get this:
On the Appearance page, select "Fill Surface" and "Colormap" and click OK.
Get this:
Click
on the plot itself, hold down the mouse button, and move the mouse around. Notice
that this changes the view you have of the plot.
Double-click on the plot again. On the General page, set the Rotation, Tilt, and Twist as follows:
Rotation: 0
Tilt: 35
Twist: -10
This should make the graph appear as it does to the right
As you can see from the array of options available in the 3D Plot Format dialog box, there are many more ways to customize the look of your graphs.
Using the plot below, follow these steps to rotate the plot interactively with the mouse.
1. Click in the plot, and hold the mouse button down.
2. Drag the mouse in the direction you want the plot to turn.
3. Release the mouse button when the plot is in the desired position.
The original orientation of the plot:
Rotation = 9 deg
Tilt = 34 deg
Twist = 0 deg
You can also rotate the plot by specifying the rotation, tilt, and twist directly in the 3D Plot Format dialog box. Try resetting the previous plot to these View options:
Rotation = 221
Tilt = 50
Twist = 233
Note: If you have manipulated the orientation interactively, new settings for Rotation, Tilt, and Twist will appear in the View options.
You can set a plot in motion so that it spins continuously about an arbitrary axis of rotation. Using the graph below, follow these steps to spin the plots in it:
1. Click in the plot to activate it.
2. Holding the [Shift] key, click the left mouse button and drag the mouse in the direction you want the plot to spin.
3. Release the mouse button to set the plot in motion. The plot spins continuously until you click again inside the plot.
4. The faster you move the mouse while you are holding down the button, the faster the plot will spin.
Fog has been enabled in this plot to lend depth to the graph. Go to the Advanced page in the 3D Plot Format dialog box to control fog.
Note: If you make changes to equations that affect a plot, the plot recomputes even when it is spinning!
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Top
The CreateMesh function lets you specify the name of the function you want to plot, the range for both x and y, and the number of grids in x and y. For example:
Enter a function f(x,y) that you want to plot:
Enter x and y ranges:
Enter the number of grids in x:
3D scatter plot:
Interpolated surface:
