# How to plot a 3D surface plot in Python?

In this tutorial, we’ll try to understand how to plot a 3D surface plot in python.

## What is a surface plot?

A surface plot shows a functional relationship between a designated dependent variable (Y), and two independent variables (X and Z). The plot is a companion plot to the contour plot. A surface plot is like a wireframe plot, but each face of the wireframe is a filled polygon.

We can plot a 3D surface plot using the matplotlib `Axes.plot_surface()` method.

## Using the `matpltolib.Axes.plot_surface()` method

We can plot a 3D surface plot using the `matplotlib.Axes.plot_surface()` method. Note that to create (any) 3d plot in matplotlib, you need to pass `projection='3d'` when creating the plot’s axes object. This way matplotlib knows that we’re creating a 3D plot. Once you have the axes object, use the `plot_surface()` method to get the relevant 3d surface plot.

Basic Syntax:

`Axes.plot_surface(X, Y, Z, *, norm=None, vmin=None, vmax=None,lightsource=None, **kwargs)`

Parameters:

• X, Y, Z: Data values
• rcount, ccount: Maximum number of samples used in each direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Defaults to 50.

For more details about the parameters refer this.

Now let us understand the usage of the above method with some examples.

### Example 1

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
x = np.outer(np.linspace(-2, 2, 30), np.ones(30))
y = x.copy().T
z = np.cos(x ** 2 + y ** 2)

#generating a figure and a 3D axes
fig = plt.figure()
ax = plt.axes(projection='3d')

#plotting the 3D surface plot
ax.plot_surface(x, y, z)
plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using `axes.plot_surface` method.

### Example 2

You can customize the surface plot with additional parameters to the `Axes.surface_plot()` function. For example, use a different color map, change the edge color, etc.

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
x = np.outer(np.linspace(-2, 2, 30), np.ones(30))
y = x.copy().T
z = np.cos(x ** 2 + y ** 2)

#generating a figure and a 3D axes
fig = plt.figure()
ax = plt.axes(projection='3d')

#plotting the 3D surface plot
ax.plot_surface(x, y, z,cmap='viridis', edgecolor='none')
plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using `axes.plot_surface` method with customizations.

### Example 3

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
r = np.linspace(0, 6, 20)
theta = np.linspace(-0.9 * np.pi, 0.8 * np.pi, 40)
r, theta = np.meshgrid(r, theta)

x= r * np.sin(theta)
y = r * np.cos(theta)

def f(x, y):
return np.sin(np.sqrt(x ** 2 + y ** 2))

z = f(x, y)

#generating a figure and a 3D axes
fig = plt.figure()
ax = plt.axes(projection='3d')

#plotting the 3D surface plot
ax.plot_surface(x, y, z,cmap='viridis',rstride=1, cstride=1, edgecolor='none')
plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using the `axes.plot_surface` method with customizations.

### Example 4

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
x = np.outer(np.linspace(-3, 3, 32), np.ones(32))
y = x.copy().T # transpose
z = (np.sin(x **2) + np.cos(y **2) )

#generating a figure and a 3D axes
fig = plt.figure(figsize =(14, 9))
ax = plt.axes(projection ='3d')

#plotting the 3D surface plot
ax.plot_surface(x, y, z)
plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using `axes.plot_surface` method with customizations.

### Example 5

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
x = np.outer(np.linspace(-3, 3, 32), np.ones(32))
y = x.copy().T # transpose
z = (np.sin(x **2) + np.cos(y **2) )

#generating a figure and a 3D axes
fig = plt.figure(figsize =(14, 9))
ax = plt.axes(projection ='3d')

#plotting the 3D surface plot
surf = ax.plot_surface(x, y, z,
cmap = 'hot',
edgecolor ='none')

fig.colorbar(surf, ax = ax,
shrink = 0.5, aspect = 5)
plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using `axes.plot_surface`.
• Add colorbar to the figure using `figure.colorbar` (Refer this).

### Example 6 – 3D surface plot having 2D contour projections

```import numpy as np
import matplotlib.pyplot as plt

#defining the variables
x = np.outer(np.linspace(-3, 3, 32), np.ones(32))
y = x.copy().T # transpose
z = (np.sin(x **2) + np.cos(y **2) )

#generating a figure and a 3D axes
fig = plt.figure(figsize =(14, 9))
ax = plt.axes(projection ='3d')

#plotting the 3D surface plot
my_cmap = plt.get_cmap('hot')

# Creating plot
surf = ax.plot_surface(x, y, z,
rstride = 8,
cstride = 8,
alpha = 0.8,
cmap = my_cmap)
cset = ax.contourf(x, y, z,
zdir ='z',
offset = np.min(z),
cmap = my_cmap)
cset = ax.contourf(x, y, z,
zdir ='x',
offset =-5,
cmap = my_cmap)
cset = ax.contourf(x, y, z,
zdir ='y',
offset = 5,
cmap = my_cmap)
fig.colorbar(surf, ax = ax,
shrink = 0.5,
aspect = 5)

ax.set_xlabel('X-axis')
ax.set_xlim(-5, 5)
ax.set_ylabel('Y-axis')
ax.set_ylim(-5, 5)
ax.set_zlabel('Z-axis')
ax.set_zlim(np.min(z), np.max(z))
ax.set_title('3D surface having 2D contour plot projections')

plt.show()```

Output:

The steps followed in the above example are:

• Import required modules
• Define the variables to plot
• Generate the figure and a 3D axes
• Plot the surface plot using `axes.plot_surface`.
• Add contour projections using `Axes.contourf` method.

To understand more about Contour plots, refer this.

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