From a67c084891500d049a36a72af121342bad378a59 Mon Sep 17 00:00:00 2001
From: Thomas A Caswell <tcaswell@gmail.com>
Date: Wed, 22 Sep 2021 18:40:25 -0400
Subject: [PATCH] Backport PR #21153: Improve curve_error_band example.

---
 .../curve_error_band.py                       | 60 +++++++++++--------
 1 file changed, 34 insertions(+), 26 deletions(-)

diff --git a/examples/lines_bars_and_markers/curve_error_band.py b/examples/lines_bars_and_markers/curve_error_band.py
index 56d95977a54c..e55b467849a8 100644
--- a/examples/lines_bars_and_markers/curve_error_band.py
+++ b/examples/lines_bars_and_markers/curve_error_band.py
@@ -10,7 +10,6 @@
 # sphinx_gallery_thumbnail_number = 2
 
 import numpy as np
-from scipy.interpolate import splprep, splev
 
 import matplotlib.pyplot as plt
 from matplotlib.path import Path
@@ -22,8 +21,8 @@
 x, y = r * np.cos(t), r * np.sin(t)
 
 fig, ax = plt.subplots()
-ax.plot(x, y)
-plt.show()
+ax.plot(x, y, "k")
+ax.set(aspect=1)
 
 #############################################################################
 # An error band can be used to indicate the uncertainty of the curve.
@@ -39,34 +38,43 @@
 # `~.Axes.fill_between` method (see also
 # :doc:`/gallery/lines_bars_and_markers/fill_between_demo`).
 
-# Error amplitudes depending on the curve parameter *t*
-# (actual values are arbitrary and only for illustrative purposes):
-err = 0.05 * np.sin(2 * t) ** 2 + 0.04 + 0.02 * np.cos(9 * t + 2)
 
-# calculate normals via derivatives of splines
-tck, u = splprep([x, y], s=0)
-dx, dy = splev(u, tck, der=1)
-l = np.hypot(dx, dy)
-nx = dy / l
-ny = -dx / l
+def draw_error_band(ax, x, y, err, **kwargs):
+    # Calculate normals via centered finite differences (except the first point
+    # which uses a forward difference and the last point which uses a backward
+    # difference).
+    dx = np.concatenate([[x[1] - x[0]], x[2:] - x[:-2], [x[-1] - x[-2]]])
+    dy = np.concatenate([[y[1] - y[0]], y[2:] - y[:-2], [y[-1] - y[-2]]])
+    l = np.hypot(dx, dy)
+    nx = dy / l
+    ny = -dx / l
 
-# end points of errors
-xp = x + nx * err
-yp = y + ny * err
-xn = x - nx * err
-yn = y - ny * err
+    # end points of errors
+    xp = x + nx * err
+    yp = y + ny * err
+    xn = x - nx * err
+    yn = y - ny * err
 
-vertices = np.block([[xp, xn[::-1]],
-                     [yp, yn[::-1]]]).T
-codes = Path.LINETO * np.ones(len(vertices), dtype=Path.code_type)
-codes[0] = codes[len(xp)] = Path.MOVETO
-path = Path(vertices, codes)
+    vertices = np.block([[xp, xn[::-1]],
+                         [yp, yn[::-1]]]).T
+    codes = np.full(len(vertices), Path.LINETO)
+    codes[0] = codes[len(xp)] = Path.MOVETO
+    path = Path(vertices, codes)
+    ax.add_patch(PathPatch(path, **kwargs))
 
-patch = PathPatch(path, facecolor='C0', edgecolor='none', alpha=0.3)
 
-fig, ax = plt.subplots()
-ax.plot(x, y)
-ax.add_patch(patch)
+axs = (plt.figure(constrained_layout=True)
+       .subplots(1, 2, sharex=True, sharey=True))
+errs = [
+    (axs[0], "constant error", 0.05),
+    (axs[1], "variable error", 0.05 * np.sin(2 * t) ** 2 + 0.04),
+]
+for i, (ax, title, err) in enumerate(errs):
+    ax.set(title=title, aspect=1, xticks=[], yticks=[])
+    ax.plot(x, y, "k")
+    draw_error_band(ax, x, y, err=err,
+                    facecolor=f"C{i}", edgecolor="none", alpha=.3)
+
 plt.show()
 
 #############################################################################