Matplotlib Tricontour Smooth User

Introduction

This lab will guide you through the process of creating high-resolution tricontours on user-defined triangular grids using Matplotlib. You will learn how to create a Triangulation, refine data, and plot the triangulation and high-resolution iso-contours.

VM Tips

After the VM startup is done, click the top left corner to switch to the Notebook tab to access Jupyter Notebook for practice.

Sometimes, you may need to wait a few seconds for Jupyter Notebook to finish loading. The validation of operations cannot be automated because of limitations in Jupyter Notebook.

If you face issues during learning, feel free to ask Labby. Provide feedback after the session, and we will promptly resolve the problem for you.

Skills Graph

Analytical Test Function

In this step, we define an analytical test function that will be used to generate z-values for the triangulation. The function is called function_z and takes two arguments, x and y. It calculates z based on the values of x and y, and returns the normalized z values.

def function_z(x, y):
    r1 = np.sqrt((0.5 - x)**2 + (0.5 - y)**2)
    theta1 = np.arctan2(0.5 - x, 0.5 - y)
    r2 = np.sqrt((-x - 0.2)**2 + (-y - 0.2)**2)
    theta2 = np.arctan2(-x - 0.2, -y - 0.2)
    z = -(2 * (np.exp((r1 / 10)**2) - 1) * 30. * np.cos(7. * theta1) +
          (np.exp((r2 / 10)**2) - 1) * 30. * np.cos(11. * theta2) +
          0.7 * (x**2 + y**2))
    return (np.max(z) - z) / (np.max(z) - np.min(z))

Creating a Triangulation

In this step, we create the x and y coordinates of the points using np.linspace and np.repeat. We then use the function_z defined in Step 1 to calculate the z-values. Finally, we create the Triangulation using tri.Triangulation.

n_angles = 20
n_radii = 10
min_radius = 0.15
radii = np.linspace(min_radius, 0.95, n_radii)

angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
angles[:, 1::2] += np.pi / n_angles

x = (radii * np.cos(angles)).flatten()
y = (radii * np.sin(angles)).flatten()
z = function_z(x, y)

triang = tri.Triangulation(x, y)
triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
                         y[triang.triangles].mean(axis=1))
                < min_radius)

Refine Data

In this step, we use tri.UniformTriRefiner to refine the data. We use the refine_field method to refine the z values and create a new Triangulation with higher resolution.

refiner = tri.UniformTriRefiner(triang)
tri_refi, z_test_refi = refiner.refine_field(z, subdiv=3)

Plot Triangulation and High-resolution Iso-contours

In this step, we plot the Triangulation and high-resolution iso-contours using ax.triplot, ax.tricontourf, and ax.tricontour.

fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.triplot(triang, lw=0.5, color='white')

levels = np.arange(0., 1., 0.025)
ax.tricontourf(tri_refi, z_test_refi, levels=levels, cmap='terrain')
ax.tricontour(tri_refi, z_test_refi, levels=levels,
              colors=['0.25', '0.5', '0.5', '0.5', '0.5'],
              linewidths=[1.0, 0.5, 0.5, 0.5, 0.5])

ax.set_title("High-resolution tricontouring")

plt.show()

Summary

In this lab, you learned how to create high-resolution tricontours on user-defined triangular grids using Matplotlib. You learned how to create a Triangulation, refine data, and plot the triangulation and high-resolution iso-contours.