🖌️ Visualization of surfaces and curves¶

With this small project, you can learn how to visualize surfaces and curves in three-dimensions using Python.

Before start¶

Install Python and learn basic skill of it.

Python is a very (probably the most) useful programming language for general purpose programming. You’d better learn it ASAP if you want to keep up-to-date.

Steps¶

Step #1¶

Install numpy, matplotlib packages for your Python using command

$ pip install numpy
$ pip install matplotlib

If these packages are already installed in your computer (which is the case mostly), you can jump to the next step.

Step #2¶

Download the Python scripts to be used by clicking on:

You will see the following functions in these scripts. Study the scripts carefully to learn how to use them to plot curves or surfaces.

Plot a curve in three-dimensions.

curve.curve(x, y, z, t_range)[source]¶

Plot a curve in three-dimensions.

Parameters:

x – the $x(t)$ parametric function.
y – the $y(t)$ parametric function.
z – the $z(t)$ parametric function.
t_range – the range of the parameter $t$ .

Plot a surface in three-dimensions.

surface.surface(z, x_range, y_range)[source]¶

Plot a surface in three-dimensions.

Parameters:

z –
The function that represents the surface.

If you have the equation of the figure in the form

$F(x, y, z) = 0,$

You should first re-write it into the form

$z(x, y) = 0.$
x_range – The range of $x$ -coordinates.
y_range – The range of $y$ -coordinates.

Step #3¶

Once you understand how these scripts work, you can use them to visualize

the surface $F(x, y, z) = \sin (\pi x) + \cos(6\pi y) - z = 0$ in the range of $x\in[0,2]$ and $y\in[0,0.5]$ ,
the curve $\left\lbrace\begin{aligned}x &= \sin(3\pi t)\\y &= \cos(2.5\pi t)\\z &= -0.25 t\end{aligned}\right.$ in the range of $t\in[0,2]$ .