Difference between revisions of "GUI-in-Scilab/C2/Plotting-3D-parametric-curves-in-GUI/English"

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Learning Objectives

In this tutorial, we will learn:

• To plot the parametric equation of a sphere using GUI.

• Use of surf command.

• Use of mesh command and;

• Use of meshgrid command

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System Requirements

Only Narration

To record this tutorial, I am using:

• Ubuntu 18.04 OS

• Scilab 6.1.0 and;

• GUI Builder Toolbox 4.2.1

The process demonstrated in this tutorial is identical in Windows OS also.

Annotations are added to the tutorial if there are any differences.

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Pre-requisites

https://www.spoken-tutorial.org

To follow this tutorial:

• The learner must have basic knowledge of Scilab and GUI Builder toolbox.

• For pre-requisite Scilab tutorials please visit this website.

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Code Files

• The files used in this tutorial are provided in the Code files link.

• Please download and extract the files.

• Make a copy and then use them while practising.

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What is a Parametric Equation of a Sphere?

The parametric equation of a sphere is:
x = r*cos(θ)*sin(φ) , y = r*sin(θ)*sin(φ) & z = r*cos(φ).

Where,

• x, y, z are the cartesian coordinates of a given point on the sphere.

• r is the radius of the sphere and;

• theta & phi are the spherical coordinates. They lie in the range 0 to 2𝞹.

We will use these three equations to plot the sphere.

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Commands to create 3D surface plots

Scilab offers many ways to create and customize various types of 3D plots.

We will learn to use the surf and mesh commands in this tutorial.

These commands are used to create a 3D surface plot.

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What is the surf command?

Only Narration

The surf command draws a 3D parametric surface plot.

It essentially creates a surface with a solid edge and solid face colors.

Hence, in this tutorial, the surf command will plot a colored 3D sphere.

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What is the mesh command?

Only Narration

The mesh command also draws a 3D parametric surface plot.

In this case, the surface has solid edge colors but no face colors.

So, in this tutorial, the mesh command will plot a 3D sphere with a white surface.

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Scilab Help Documentation

For more information on mesh and surf commands type the following on the Scilab console:

help surf

help mesh

Switch to GUIBuilder Toolbox.

Open the plotting3dcurves.sce file.

Locate the plotting3dcurves.sce file in the saved folder.

Open the file plotting3dcurves.sce using the GUIBuilder Toolbox.

On the Graphic Window Number 1,

hover over the Slider, Text box and an Axes.

It shows the GUI with three objects, namely Slider, Text box and an Axes.

The Slider has Tag ‘sl_radius’ and String ‘Radius’.

Its value can vary from 10 to 20.

On the Graphic Window Number 1,

hover over the Text box.

Next, we have a Text box to display the radius.

It has Tag ‘txt_radius’ and the String ‘Radius’.

On the Graphic Window Number 1,

hover over the Axes.

Lastly, we have the Axes to display the plot of the sphere.

It has Tag ‘ax_plot’ and String ‘Sphere’.

Now let us generate the Scilab code for the same.

On the GUIBuilder Palette Window,

in the menu bar,

click on Generate.

Click on Generate GUI Code .

Go to the GUIBuilder Palette, and click on Generate in the menu bar.

Then click on Generate GUI Code.

On the uiputfile Window,

type parametric-3d.

Click on OK.

I will name this file as parametric-3d.

Click on the OK button.

Cursor on GUI Created Window,

click on OK.

It shows a new dialog box that displays “GUI created successfully!”

Click on OK.

The corresponding Scilab code file opens.

On SciNotes Window,

highlight,

handles.txt_radius.

On SciNotes Window,

highlight,

handles.ax_plot.

On SciNotes Window,

highlight,

handles.sl_radius.

On SciNotes Window,

inside sl_radius_callback function,

highlight,

handles.txt_radius.string = string(handles.sl_radius.value)

r = strtod(handles.txt_radius.string)

Now notice the sl_radius_callback function definition.

It has two lines of code in it.

The code essentially connects the Slider to the Text box.

As a result when the Slider is moved, its exact value is displayed in the Text box.

Then the value of the Text box is stored inside a variable ‘r’.

On the SciNotes Window,

type on new line outside the sl_radius_callback function,

function plot_sphere()

delete(handles.ax_plot.children)

u = 0:0.1:2*%pi;

v = 0:0.1:2*%pi;

[phi, theta]= meshgrid(u,v)

x = r*cos(theta)*sin(phi);

y = r*sin(theta)*sin(phi);

z = r*cos(phi);

surf(x, y, z);

//mesh(x, y, z);

xtitle('Plotting sphere', 'X-axis', 'Y-axis')

xgrid()

endfunction

Now, let us write a user-defined function plot_sphere() to plot the sphere.

Type the code as shown here with the same syntax.

The same code can be found under the Code files section.

You can use it as explained earlier in this tutorial.

Highlight,

delete(handles.ax_sphere.children).

highlight,

u = 0:0.1:2*%pi;

v = 0:0.1:2*%pi;

[phi, theta]= meshgrid(u,v);

Notice the next three lines.

The meshgrid command is used.

It is used to generate u and v matrices for three-dimensional plots.

The range of u and v is defined from 0 to 2𝞹 with a step size of 0.1.

Finally, the matrices u and v are stored into phi and theta respectively.

highlight,

x = r*cos(theta)*sin(phi);

y = r*sin(theta)*sin(phi);

z = r*cos(phi);

highlight,

surf(x, y, z);

highlight,

//mesh(x, y, z);

Then next we will see the mesh command.

For now, I have commented out this line by putting two forward slashes.

Hence the output of only surf command will be plotted.

On the SciNotes Window,

highlight,

xtitle('Plot of sphere', 'X-axis', 'Y-axis')

xgrid()

On the SciNotes Window,

inside sl_radius_callback function,

type,

plot_sphere()

Now let us call the plot_sphere() function inside the callback function.

At the end of sl_radius_callback function definition type plot_sphere().

As a result, varying the radius value on the Slider the sphere will be plotted.

On the SciNotes Window,

Press Ctrl + S on the keyboard.

On the SciNotes Window,

click on the Execute button in the menu bar.

Click on File with echo.

Now, run this simulation by clicking on the Execute button in the menu bar.

Click on File with echo.

The Graphic Window Number 2 will appear.

On the Graphic Window Number 2,

move the Slider indicator towards right slowly.

We can see that as we move the indicator on the Slider, a sphere is being plotted.

The surf command now plots a colored 3D sphere.

Now let us test the output of the mesh command.

Close the Graphic Window Number 2.

On the SciNotes Window,

//surf(x, y, z);

mesh(x, y, z);

Press Ctrl + S.

I'll now add two forward slashes before the surf command to comment it out.

Then I’ll remove the forward slashes added before the mesh command to now see its output.

Save the code by pressing Ctrl + S keys together.

On SciNotes Window,

click on Execute,

click on File with echo.

On Graphic window Number 2.

move the Slider indicator towards the right slowly.

The Graphic window Number 2 will now show the output of the mesh command.

Let us move the Slider indicator and observe the output.

As stated earlier, the mesh command now plots a 3D sphere with a white surface.

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Summary

Let us summarize.

In this tutorial, we have:

• Plotted the parametric equation of a sphere using GUI.

• Used the surf command.

• Used the mesh command and;

• Used the meshgrid command.

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Assignment

As an assignment, please do the following.

• Using surf and mesh, build a GUI to plot a 3D hemisphere.
  Parametric equations: x = r*cos(θ)*sin(φ) , y = r*sin(θ)*sin(φ) & z = r*cos(φ).

• Place the hemisphere on a horizontal plane.

• Change radius ‘r’ from 1 to 10 using a Slider and display it in a Text box.

• Consider that theta & phi vary from 0 to 𝞹.

• Add grid lines to the plot and label the Axes.

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About Spoken Tutorial Project

The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

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Spoken Tutorial Workshops

We conduct workshops using Spoken Tutorials and give certificates.

Please contact us.

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Answers for THIS Spoken Tutorial

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Textbook Companion project

The FOSSEE team coordinates the TBC project.

For more details, please visit this site.

The FOSSEE team coordinates the Lab Migration project.

For more details, please visit this site.

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Acknowledgements

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Thank you

This is Utkarsh Anand, a FOSSEE intern 2021, IIT Bombay signing off.

Thanks for joining.