From 5c0bbbc4be4faa1269ef52541f32b7780843d676 Mon Sep 17 00:00:00 2001
From: Sridhar Ramesh <sridhar@3blue1brown.com>
Date: Thu, 15 Feb 2018 15:35:37 -0800
Subject: [PATCH 1/2] Removed range_via_num_steps, which was redundant on top
 of np.linspace

---
 helpers.py | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/helpers.py b/helpers.py
index 43d8a7f9..80ee9e33 100644
--- a/helpers.py
+++ b/helpers.py
@@ -689,10 +689,6 @@ class DictAsObject(object):
 def fdiv(a, b):
     return np.true_divide(a,b)
 
-def range_via_num_steps(start, end, num_steps, include_end = True):
-    num_points = num_steps + (1 if include_end else 0)
-    return [interpolate(start, end, fdiv(i, num_steps)) for i in range(num_points)]
-
 # For debugging purposes
 
 def print_mobject_family(mob, n_tabs = 0):

From 4c6af541c13a13550987f26145a97ee92fbb922d Mon Sep 17 00:00:00 2001
From: Sridhar Ramesh <sridhar@3blue1brown.com>
Date: Thu, 15 Feb 2018 15:37:19 -0800
Subject: [PATCH 2/2] Switched WindingNumber to use np.linspace; also, fixed
 missing colon in extract_scene.py

---
 active_projects/WindingNumber.py | 4 ++--
 extract_scene.py                 | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/active_projects/WindingNumber.py b/active_projects/WindingNumber.py
index b9b2faa4..4035ef8a 100644
--- a/active_projects/WindingNumber.py
+++ b/active_projects/WindingNumber.py
@@ -1041,8 +1041,8 @@ class VectorField(Scene):
         x_min, y_min = num_plane.point_to_coords(SPACE_WIDTH * LEFT + SPACE_HEIGHT * UP)
         x_max, y_max = num_plane.point_to_coords(SPACE_WIDTH * RIGHT + SPACE_HEIGHT * DOWN)
 
-        x_points = range_via_num_steps(x_min, x_max, self.granularity)
-        y_points = range_via_num_steps(y_min, y_max, self.granularity)
+        x_points = np.linspace(x_min, x_max, self.granularity)
+        y_points = np.linspace(y_min, y_max, self.granularity)
         points = it.product(x_points, y_points)
 
         sized_arrows = Group()
diff --git a/extract_scene.py b/extract_scene.py
index 82e7a250..0d21e8a7 100644
--- a/extract_scene.py
+++ b/extract_scene.py
@@ -73,7 +73,7 @@ def get_configuration():
       if args.output_name != None:
          output_name_root, output_name_ext = os.path.splitext(args.output_name)
          expected_ext = '.png' if args.show_last_frame else '.mp4'
-         if not output_name_ext in ['', expected_ext]
+         if not output_name_ext in ['', expected_ext]:
             print "WARNING: The output will be to (doubly-dotted) %s%s"%output_name_root%expected_ext
             output_name = args.output_name
          else: