Ellipse with Units

Introduction

In this lab, you will learn how to compare the ellipse generated with arcs versus a polygonal approximation using Python Matplotlib.

VM Tips

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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.

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Import Libraries

To begin, we will import the necessary libraries.

import matplotlib.pyplot as plt
import numpy as np
from matplotlib import patches

Set Ellipse Parameters

In this step, we will set the parameters for the ellipse.

xcenter, ycenter = 0.38, 0.52
width, height = 0.1, 0.3
angle = -30

Generate Ellipse using Arcs

In this step, we will generate the ellipse using arcs.

theta = np.deg2rad(np.arange(0.0, 360.0, 1.0))
x = 0.5 * width * np.cos(theta)
y = 0.5 * height * np.sin(theta)

rtheta = np.radians(angle)
R = np.array([
    [np.cos(rtheta), -np.sin(rtheta)],
    [np.sin(rtheta),  np.cos(rtheta)],
    ])

x, y = np.dot(R, [x, y])
x += xcenter
y += ycenter

Generate Ellipse using Polygonal Approximation

In this step, we will generate the ellipse using a polygonal approximation.

theta = np.deg2rad(np.arange(0.0, 360.0, 1.0))
x = 0.5 * width * np.cos(theta)
y = 0.5 * height * np.sin(theta)

rtheta = np.radians(angle)
R = np.array([
    [np.cos(rtheta), -np.sin(rtheta)],
    [np.sin(rtheta),  np.cos(rtheta)],
    ])

x, y = np.dot(R, [x, y])
x += xcenter
y += ycenter

Plot Ellipse using Arcs

In this step, we will plot the ellipse using arcs.

fig = plt.figure()
ax = fig.add_subplot(211, aspect='auto')
ax.fill(x, y, alpha=0.2, facecolor='yellow',
        edgecolor='yellow', linewidth=1, zorder=1)

e1 = patches.Arc((xcenter, ycenter), width, height,
                 angle=angle, linewidth=2, fill=False, zorder=2)

ax.add_patch(e1)

Plot Ellipse using Polygonal Approximation

In this step, we will plot the ellipse using a polygonal approximation.

ax = fig.add_subplot(212, aspect='equal')
ax.fill(x, y, alpha=0.2, facecolor='green', edgecolor='green', zorder=1)
e2 = patches.Arc((xcenter, ycenter), width, height,
                 angle=angle, linewidth=2, fill=False, zorder=2)

ax.add_patch(e2)
fig.savefig('arc_compare')

plt.show()

Summary

In this lab, you learned how to compare the ellipse generated with arcs versus a polygonal approximation using Python Matplotlib. You learned how to set ellipse parameters, generate ellipses using arcs and a polygonal approximation, and plot them using Matplotlib.