Plotting a parametric surface with Python

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Toby Wood 1 year, 6 months ago

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Toby Wood 1 year, 6 months ago

Created this as a copy of Toby's copy of Make a plot with matplotlib.

Name	Status	Author	Last Modified
Make a plot	draft	George Stagg	13/09/2024 11:05
Make a plot with matplotlib	draft	Christian Lawson-Perfect	10/05/2023 13:31
Make a plot with matplotlib	Ready to use	Christian Lawson-Perfect	23/11/2023 11:37
Make a plot	Ready to use	Christian Lawson-Perfect	24/07/2024 10:28
Plotting a parametric surface with Python	draft	Toby Wood	03/04/2024 14:59

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			Name	Type	Generated Value

python_preamble

string

import matplotlib.pyplot as pl

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import matplotlib.pyplot as plt
fig = plt.figure()

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import matplotlib.pyplot as plt fig = plt.figure()

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A figure, called fig, has already been created as follows:

{code_block(python_preamble,"python")}

Now we'll plot a parametric surface in this figure.

The code below is designed to plot the particular surface

$(u,v) \longmapsto (\sin(u)\cos(v),\ \sin(u)\sin(v),\ \cos(u)), \; 0 \leqslant u \leqslant \pi, \; 0 \leqslant v \leqslant 2\pi\,.$

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# To do maths stuff, the numpy package is essential
import numpy as np
​
# We first define linear arrays for our two surface parameters
points = 21
u_lin = np.linspace(0,np.pi,points) # A linear array from 0 to pi
v_lin = np.linspace(0,2*np.pi,points) # A linear array from 0 to 2*pi
# We now convert the linear arrays into a pair of 2D arrays called u and v
u,v = np.meshgrid(u_lin,v_lin,indexing='ij')
​
# Now we can define x, y and z as functions of the parameters u and v
x = np.sin(u)*np.cos(v)
y = np.sin(u)*np.sin(v)
z = np.cos(u)
​
# Finally, we create some 3D axes and plot the surface
ax = plt.axes(projection='3d')
ax.plot_surface(x, y, z, cmap='binary', edgecolor='red')

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Preamble

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import sys
import matplotlib
​
matplotlib.use('Agg')
import matplotlib.pyplot as plt
fig = plt.figure()
fig.savefig(sys.stdout, format='svg')

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fig.savefig(sys.stdout, format='svg')

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Advice

Now you can try plotting other parametric surfaces. Remember, as well as changing the definitions of $x(u,v)$, $y(u,v)$ and $z(u,v)$, you'll also need to set the correct ranges for $u$ and $v$.

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Taxonomy: mathcentre

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Toby Wood 1 year, 6 months ago

Toby Wood 1 year, 6 months ago

Error in variable testing condition

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Plotting a parametric surface with Python

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Toby Wood 1 year, 6 months ago

Toby Wood 1 year, 6 months ago

Error in variable testing condition

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Warning

Generated value: string

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Code

Generated value: `string`