From 461584098bd252301452eb3e6e0bfcd2d3c6f0c8 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Tue, 30 Jun 2020 15:05:16 +0530
Subject: last-1 review
---
.../file1_simple_visualization.gif | Bin 686712 -> 675451 bytes
.../file1_simple_visualization.py | 12 ++++----
.../file4_different_curvature_single_curve.py | 18 ++++++++++--
.../file1_parametric_circle.py | 13 +++++----
.../file1_prescribed_plane.gif | Bin 163202 -> 0 bytes
.../file1_tnb_basic.gif | Bin 0 -> 1990818 bytes
.../file1_tnb_basic.py | 31 +++++++++++++++++++++
.../file2_tnb_frame.gif | Bin 150050 -> 0 bytes
.../file2_tnb_frame_manim.py | 23 +++++++--------
9 files changed, 73 insertions(+), 24 deletions(-)
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif
index 858a8de..3f7ecd1 100644
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
index 7ab8908..45058d7 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
@@ -32,6 +32,8 @@ class randomcurve(GraphScene):
dot6 = Dot(tgt6.get_start(), color = RED)
dot7 = Dot(tgt7.get_start(), color = RED)
+ arc = ArcBetweenPoints(dot1.get_center(), dot2.get_center(), color = GREEN_SCREEN, angle = 10*DEGREES).rotate(180*DEGREES)
+
dots = VGroup(*[dot1, dot2, dot3, dot4, dot5, dot6, dot7])
ds = CurvedArrow((-4, 2, 0), (tgt1.get_start() + tgt2.get_start()) / 2, color = YELLOW)
@@ -43,15 +45,13 @@ class randomcurve(GraphScene):
self.wait(2)
self.play(FadeOut(intro))
self.setup_axes(hideaxes=False)
- self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text))
+ self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text), FadeIn(arc))
self.wait(1)
- self.play(FadeOut(self.axes), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text))
- self.wait(2)
+ self.play(FadeOut(self.axes), FadeOut(arc), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text))
+ self.wait(3)
self.play(FadeOut(mid))
self.play(FadeIn(self.axes), FadeIn(graphobj), FadeIn(dots))
-
-
tangents = [tgt1, tgt2, tgt3, tgt4, tgt5, tgt6, tgt7]
for tangent in tangents:
self.play(ShowCreation(tangent), run_time = 0.2)
@@ -60,7 +60,7 @@ class randomcurve(GraphScene):
self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents), FadeOut(dots))
self.wait(1)
self.play(FadeIn(outro))
- self.wait(2)
+ self.wait(3)
self.play(FadeOut(outro))
self.wait(1)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
index d71adda..3ecd57c 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
@@ -47,10 +47,24 @@ class GR(GraphScene):
line.move_to(p0)
return line
+ circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
+ tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
+
+ curvature1 = VGroup(*[circle1, tgt1])
+
+ circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT)
+ tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP)
+
+ curvature2 = VGroup(*[circle2, tgt2])
+
line = always_redraw(get_tangent_line)
self.add(graph,line, dots, text)
self.wait(1.2)
- self.play(tracker.set_value, 6, rate_func=smooth, run_time=13)
- self.play(FadeOut(VGroup(*[graph, self.axes, line, dots, text])))
+ self.play(tracker.set_value, 0, rate_func=smooth, run_time=5)
+ self.play(FadeIn(curvature1))
+ self.play(tracker.set_value, 4, rate_func=smooth, run_time=5)
+ self.play(FadeIn(curvature2))
+ self.play(tracker.set_value, 6, rate_func=smooth, run_time=3)
+ self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text])))
self.wait()
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
index 40b5150..37d079e 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
@@ -11,12 +11,15 @@ class parametricCircle(ThreeDScene, GraphScene):
self.y_axis_label = ""
self.x_axis_width = 10
self.y_axis_height = 10
+ self.y_tick_frequency = 1.9
+ self.x_tick_frequency = 1.4
axes = []
- self.setup_axes()
- self.axes.scale(0.5).shift(3*LEFT)
- axes.append(self.axes)
+ # self.setup_axes()
+ ax = Axes(y_tick_frequency = 1, x_axis_width = 10, y_axis_height = 10, y_min = -5, x_max = 5, y_max = 5, x_tick_frequency = 1, x_axis_label = "", y_axis_label = "", x_min = -5, )
+ ax.scale(0.5).shift(3*LEFT)
+ axes.append(ax)
self.setup_axes()
self.axes.scale(0.3).shift(3*RIGHT + 2*UP)
axes.append(self.axes)
@@ -38,7 +41,7 @@ class parametricCircle(ThreeDScene, GraphScene):
asint = ParametricFunction(
lambda t: np.array([
t,
- np.sin(t),
+ 2*np.sin(t),
0
]), t_min = -np.pi, t_max = np.pi, color = GREEN_E
).shift(3*RIGHT + 2*UP).scale(0.4)
@@ -50,7 +53,7 @@ class parametricCircle(ThreeDScene, GraphScene):
acost = ParametricFunction(
lambda t: np.array([
t,
- np.cos(t),
+ 2*np.cos(t),
0
]), t_min = -np.pi, t_max = np.pi, color = BLUE
).shift(3*RIGHT + 2*DOWN).scale(0.4)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif
deleted file mode 100644
index c8668e3..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif
new file mode 100644
index 0000000..c028db4
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
new file mode 100644
index 0000000..5c68f69
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+ def construct(self):
+ t = TextMobject(r'T', color = YELLOW)
+ n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
+ b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
+ frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
+
+ text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
+ curve = ParametricFunction(
+ lambda t: np.array([
+ np.sin(TAU*t),
+ np.cos(TAU*t),
+ 0
+ ])
+ ).scale(2.5)
+ dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT)
+ tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT)
+ normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN)
+ binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN)
+ square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2)
+ group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0]))
+
+ self.add_fixed_in_frame_mobjects(text)
+ self.add(curve, group)
+ self.wait(1)
+ self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2)
+ self.begin_ambient_camera_rotation(rate = 0.5)
+ self.wait(5)
+ self.play(FadeOut(VGroup(*[text, curve, dot, tgt, normal, square, binormal])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
deleted file mode 100644
index 097652f..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
index ee5e717..176cac5 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
@@ -79,15 +79,16 @@ class tnb(ThreeDScene):
self.play(FadeIn(helix), FadeIn(text))
self.play(ApplyMethod(helix.scale, 4))
self.add_fixed_in_frame_mobjects(bnm0)
- self.play(FadeIn(point0), MoveAlongPath(helix_dot, helix1, run_time=5))
+ self.play(FadeIn(point0))
+ self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5))
self.add_fixed_in_frame_mobjects(bnm1)
- self.play(ApplyMethod(point0.set_color, GRAY), FadeIn(point1))
- self.play(MoveAlongPath(helix_dot, helix2, run_time = 5))
+ self.play(FadeIn(point1))
+ self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5))
self.add_fixed_in_frame_mobjects(bnm2)
- self.play(ApplyMethod(point1.set_color, GRAY), ApplyMethod(bnm1.set_color, GRAY), FadeIn(point2))
- self.play(MoveAlongPath(helix_dot, helix3, run_time=5))
+ self.play(FadeIn(point2))
+ self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5))
dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED)
tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0]))
@@ -111,15 +112,15 @@ class tnb(ThreeDScene):
point5 = VGroup(*[tgt5, nm5, bnm5, plane5])
self.add_fixed_in_frame_mobjects(bnm3)
- self.play(ApplyMethod(point2.set_color, GRAY), FadeIn(point3))
- self.play(MoveAlongPath(helix_dot, helix4, run_time=5))
+ self.play(FadeIn(point3))
+ self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5))
self.add_fixed_in_frame_mobjects(bnm4)
- self.play(ApplyMethod(point3.set_color, GRAY), FadeIn(point4))
- self.play(MoveAlongPath(helix_dot, helix5, run_time=5))
+ self.play(FadeIn(point4))
+ self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5))
self.add_fixed_in_frame_mobjects(bnm5)
- self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5))
+ self.play(FadeIn(point5))
self.wait(2)
- self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
+ self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
--
cgit
From 507d858af69003404b696c522689e3f79d9480f1 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Tue, 30 Jun 2020 15:08:44 +0530
Subject: Update README.md
---
.../tnb-frame-and-serret-frenet-formulae/README.md | 4 ++++
1 file changed, 4 insertions(+)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
index 34885b2..766c91f 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
@@ -1,2 +1,6 @@
+**file1_tnb_basic.py**
+
+
+
**file2_tnb_frame_manim.py**
--
cgit
From 05fb7a8be916f7bb8a0681668a55a2fe0201b1e1 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Tue, 30 Jun 2020 15:10:52 +0530
Subject: new gif
---
.../file2_tnb_frame_manim.gif | Bin 837251 -> 886891 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
index 784b6a6..78e3aa3 100644
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif differ
--
cgit
From 25569ab09dc79cb9d4e1b424ec7dd1a0a7c90edc Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 1 Jul 2020 13:00:25 +0530
Subject: last day
---
.../file3_curvature_interpretation.gif | Bin 0 -> 702280 bytes
.../file3_curvature_interpretation.py | 42 +++++++
.../file3_curvature_intuition.gif | Bin 271189 -> 0 bytes
.../file4_different_curvature_single_curve.py | 16 ++-
.../general-parametric-curves/file2_cycloid.gif | Bin 13674 -> 0 bytes
.../file1_tnb_basic.gif | Bin 1990818 -> 0 bytes
.../file1_tnb_basic.py | 31 -----
.../file1_tnb_creation.gif | Bin 0 -> 1708693 bytes
.../file1_tnb_creation.py | 66 +++++++++++
.../file2_tnb_basic.gif | Bin 0 -> 2002004 bytes
.../file2_tnb_basic.py | 36 ++++++
.../file2_tnb_frame_manim.gif | Bin 886891 -> 0 bytes
.../file2_tnb_frame_manim.py | 126 ---------------------
.../file3_tnb_frame_manim.gif | Bin 0 -> 886891 bytes
.../file3_tnb_frame_manim.py | 126 +++++++++++++++++++++
.../file4_fs1.gif | Bin 0 -> 551048 bytes
.../file4_fs1.py | 23 ++++
.../file5_fs2.gif | Bin 0 -> 629437 bytes
.../file5_fs2.py | 28 +++++
19 files changed, 333 insertions(+), 161 deletions(-)
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
new file mode 100644
index 0000000..39489b7
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
new file mode 100644
index 0000000..cf6b032
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *
+
+class interpretation(Scene):
+ def construct(self):
+ tgt = Vector((1, 2, 0), color = YELLOW)
+ tgtText = TextMobject(r'$r\prime (t)$').next_to(tgt, UP, buff = 0).scale(0.7)
+ tgt2 = DashedLine((0,0,0),(1, 2, 0), color = GRAY).shift(DOWN + 2*RIGHT)
+
+ nm = Vector((2, -1, 0), color = BLUE)
+ nmText = TextMobject(r'$r\prime\prime (t)$').next_to(nm, DOWN+RIGHT, buff = 0).scale(0.7)
+ nm2 = DashedLine((0,0,0),(2, -1, 0), color = GRAY).shift(2*UP + RIGHT)
+ square = Square(fill_color = WHITE, fill_opacity = 0.2).rotate(63*DEGREES).shift(0.5*UP +1.5*RIGHT).scale(1.1)
+ square.set_stroke(width = 0.1)
+ arrow = CurvedArrow(square.get_center() + np.array([2,1,0]), square.get_center() + np.array([0.5,0,0]))
+ arrowText = TextMobject(r'$r\prime (t)\times r\prime\prime (t)$').next_to(arrow.get_start(), DOWN+1*RIGHT, buff = 0).scale(0.7)
+
+ text1 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\left|\frac{dT}{dt}\right|}{\left|\frac{ds}{dt}\right|}$').shift(UP+3*LEFT)
+ text2 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}\times\frac{r\prime (t)}{\left| r\prime (t)\right|}}{\left|r\prime (t)\right|}$').next_to(text1, DOWN, buff = 0.1)
+ unit = VGroup(*[tgt, tgt2, nm, nm2])
+
+ # self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText])))
+ tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES )
+ nm2text = TextMobject(r'$\frac{dT}{dt} = \frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.6).shift(0.5*RIGHT+0.6*DOWN).rotate(-25*DEGREES)
+ unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN)
+
+ self.play(FadeIn(VGroup(*[tgt, tgtText])))
+ self.wait(1)
+ self.play(FadeIn(VGroup(*[nm, nmText])))
+ self.wait(1)
+ self.play(FadeIn(VGroup(*[tgt2, nm2])))
+ self.wait(1)
+ self.play(FadeIn(VGroup(*[square, arrow, arrowText])))
+ self.wait(1)
+ self.play(FadeIn(unit2))
+ self.wait(1)
+ self.play(FadeIn(VGroup(*[tgt2text, nm2text])))
+ self.wait(1)
+ self.play(FadeIn(text1))
+ self.wait(1)
+ self.play(FadeIn(text2))
+ self.wait(2)
+ self.play(FadeOut(VGroup(*[tgt2text, nm2text, text1, text2, tgt, tgtText,nm, nmText,tgt2, nm2,square, arrow, arrowText,unit2])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
deleted file mode 100644
index 0d6fdcf..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
index 3ecd57c..56b7fbb 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
@@ -8,7 +8,9 @@ class GR(GraphScene):
"x_max": 6,
"y_min": -6,
"y_max": 10,
- "graph_origin": ORIGIN
+ "graph_origin": ORIGIN,
+ 'x_tick_frequency': 20,
+ 'y_tick_frequency': 20
}
def construct(self):
@@ -21,7 +23,7 @@ class GR(GraphScene):
tracker = ValueTracker(-3)
- text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
+ text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
dot1 = Dot((0,3,0), color = YELLOW)
dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1)
@@ -50,12 +52,18 @@ class GR(GraphScene):
circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
- curvature1 = VGroup(*[circle1, tgt1])
+ r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN)
+ r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6)
+
+ curvature1 = VGroup(*[circle1, tgt1, r1, r1label])
circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT)
tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP)
- curvature2 = VGroup(*[circle2, tgt2])
+ r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN)
+ r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6)
+
+ curvature2 = VGroup(*[circle2, tgt2, r2, r2label])
line = always_redraw(get_tangent_line)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
deleted file mode 100644
index 39656de..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif
deleted file mode 100644
index c028db4..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
deleted file mode 100644
index 5c68f69..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_basic.py
+++ /dev/null
@@ -1,31 +0,0 @@
-from manimlib.imports import *
-
-class tnb(ThreeDScene):
- def construct(self):
- t = TextMobject(r'T', color = YELLOW)
- n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
- b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
- frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
-
- text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
- curve = ParametricFunction(
- lambda t: np.array([
- np.sin(TAU*t),
- np.cos(TAU*t),
- 0
- ])
- ).scale(2.5)
- dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT)
- tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT)
- normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN)
- binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN)
- square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2)
- group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0]))
-
- self.add_fixed_in_frame_mobjects(text)
- self.add(curve, group)
- self.wait(1)
- self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2)
- self.begin_ambient_camera_rotation(rate = 0.5)
- self.wait(5)
- self.play(FadeOut(VGroup(*[text, curve, dot, tgt, normal, square, binormal])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif
new file mode 100644
index 0000000..eae8686
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py
new file mode 100644
index 0000000..80372ee
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py
@@ -0,0 +1,66 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+ def construct(self):
+ self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+
+ helix1 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE
+ )
+
+ helix2 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE
+ )
+
+ pointText = TextMobject(r'Consider an arbitrary point \\ on the given curve.').scale(0.8).shift(1.5*UP)
+ tgtText = TextMobject(r'Unit', ' tangent ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP)
+ tgtText.set_color_by_tex_to_color_map({
+ "tangent": YELLOW
+ })
+ normalText = TextMobject(r'Unit', ' normal ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP)
+ normalText.set_color_by_tex_to_color_map({
+ "normal": BLUE
+ })
+ planeText = TextMobject(r'$\overrightarrow{T}$ and $\overrightarrow{N}$ \\ prescribe a plane.').scale(0.8).shift(1.5*UP)
+ bnmText = TextMobject(r'The vector normal to this plane \\ is called the', ' binormal ', 'vector.').scale(0.8).shift(1.5*UP)
+ bnmText.set_color_by_tex_to_color_map({
+ "binormal": GREEN_E
+ })
+
+ dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+ tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+ nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0]))
+ bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+ plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+ point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+
+
+
+ helix = VGroup(*[helix1, helix2])
+ self.play(FadeIn(helix))
+ self.play(ApplyMethod(helix.scale, 4))
+ self.add_fixed_in_frame_mobjects(pointText)
+ self.play(FadeIn(dot1), FadeIn(pointText))
+ self.wait(2)
+ self.add_fixed_in_frame_mobjects(tgtText)
+ self.play(Write(tgt1), ReplacementTransform(pointText, tgtText))
+ self.wait(2)
+ self.add_fixed_in_frame_mobjects(normalText)
+ self.play(Write(nm1), ReplacementTransform(tgtText, normalText))
+ self.wait(2)
+ self.add_fixed_in_frame_mobjects(planeText)
+ self.play(FadeIn(plane1), ReplacementTransform(normalText, planeText))
+ self.wait(2)
+ self.add_fixed_in_frame_mobjects(bnmText)
+ self.add_fixed_in_frame_mobjects(bnm1)
+ self.play(ReplacementTransform(planeText, bnmText), Write(bnm1))
+ self.wait(2)
+ self.play(FadeOut(VGroup(*[helix, bnm1, bnmText, dot1, tgt1, nm1, plane1])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif
new file mode 100644
index 0000000..67aaea2
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py
new file mode 100644
index 0000000..c870210
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py
@@ -0,0 +1,36 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+ def construct(self):
+ t = TextMobject(r'T', color = YELLOW)
+ n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
+ b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
+ frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
+ f1 = TextMobject(r'$\overrightarrow{B}$ ', color = GREEN_E)
+ f2 = TextMobject(r' = $\overrightarrow{T}$', color = YELLOW).next_to(f1, RIGHT, buff=0.2)
+ f3 = TextMobject(r'$\times\overrightarrow{N}$', color = BLUE).next_to(f2, RIGHT, buff=0.1)
+ formula = VGroup(*[f1, f2, f3]).move_to(ORIGIN).shift(3*UP)
+
+ # text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
+ curve = ParametricFunction(
+ lambda t: np.array([
+ np.sin(TAU*t),
+ np.cos(TAU*t),
+ 0
+ ])
+ ).scale(2.5)
+ dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT)
+ tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT)
+ normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN)
+ binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN)
+ square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2)
+ group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0]))
+
+ self.add_fixed_in_frame_mobjects(formula)
+ self.add(curve, group)
+ self.wait(1)
+ self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2)
+ self.add_fixed_in_frame_mobjects(formula)
+ self.begin_ambient_camera_rotation(rate = 0.5)
+ self.wait(5)
+ self.play(FadeOut(VGroup(*[formula, curve, dot, tgt, normal, square, binormal])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
deleted file mode 100644
index 78e3aa3..0000000
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif and /dev/null differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
deleted file mode 100644
index 176cac5..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
+++ /dev/null
@@ -1,126 +0,0 @@
-from manimlib.imports import *
-
-class tnb(ThreeDScene):
- def construct(self):
- self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
-
- t = TextMobject(r'T', color = YELLOW)
- n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
- b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
- frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
-
- text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
-
- helix1 = ParametricFunction(
- lambda t: np.array([
- np.cos(TAU*t),
- np.sin(TAU*t),
- 0.4*t
- ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE
- )
-
- helix2 = ParametricFunction(
- lambda t: np.array([
- np.cos(TAU*t),
- np.sin(TAU*t),
- 0.4*t
- ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE
- )
-
- helix3 = ParametricFunction(
- lambda t: np.array([
- np.cos(TAU*t),
- np.sin(TAU*t),
- 0.4*t
- ]), t_min = -1.33*np.pi/3, t_max = -np.pi/3, color = WHITE
- )
-
- helix4 = ParametricFunction(
- lambda t: np.array([
- np.cos(TAU*t),
- np.sin(TAU*t),
- 0.4*t
- ]), t_min = -np.pi/3, t_max = -1.3*np.pi/6, color = WHITE
- )
-
- helix5 = ParametricFunction(
- lambda t: np.array([
- np.cos(TAU*t),
- np.sin(TAU*t),
- 0.4*t
- ]), t_min = -1.3*np.pi/6, t_max = 0, color = WHITE
- )
-
- helix_dot = Dot(radius = 0.16, color = RED)
-
- dot0 = Dot(np.array([np.cos(-2*np.pi/3), np.sin(-2*np.pi/3), -0.8*np.pi/3]), radius = 0.16, color=RED).shift(np.array([4.65,0,-0.8]))
- tgt0 = Arrow((0,0,0), (1,2,0), color = YELLOW).shift(dot0.get_center() - np.array([0.04,0.2,0]))
- nm0 = Arrow((0,0,0), (-2,1,0), color = BLUE).shift(dot0.get_center() + np.array([0.3,0,0]))
- bnm0 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(6.1*LEFT + 3*DOWN)
- plane0 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot0.get_center() + np.array([-0.35, 0.85, 0])).scale(1.2).rotate(65*DEGREES)
- point0 = VGroup(*[dot0, tgt0, nm0, bnm0, plane0]).scale(0.8).shift(np.array([1,0,0]))
-
- dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
- tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
- nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0]))
- bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(3.68*RIGHT+2.48*DOWN)
- plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
- point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,6.25,0]))
-
- dot2 = Dot(np.array([np.cos(-np.pi/6), np.sin(-np.pi/6), -0.2*np.pi/3]) - np.array([1.9,0,0]), radius=0.16,color=RED)
- tgt2 = Arrow((0,0,0), (1,-2,0), color = YELLOW).shift(dot2.get_center() + np.array([-0.2,0.2,0]))
- nm2 = Arrow((0,0,0), (2,1,0), color = BLUE).shift(dot2.get_center() + np.array([-0.2,-0.06,0]))
- bnm2 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(0.4*RIGHT + 0.16*DOWN)
- plane2 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot2.get_center() + np.array([0.92, -0.5, 0])).rotate(23*DEGREES).scale(1.2)
- point2 = VGroup(*[dot2, tgt2, nm2, bnm2, plane2])
-
- helix = VGroup(*[helix1, helix2, helix3, helix4, helix5])
- self.add_fixed_in_frame_mobjects(text)
- self.play(FadeIn(helix), FadeIn(text))
- self.play(ApplyMethod(helix.scale, 4))
- self.add_fixed_in_frame_mobjects(bnm0)
- self.play(FadeIn(point0))
- self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5))
-
- self.add_fixed_in_frame_mobjects(bnm1)
- self.play(FadeIn(point1))
- self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5))
-
- self.add_fixed_in_frame_mobjects(bnm2)
- self.play(FadeIn(point2))
- self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5))
-
- dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED)
- tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0]))
- nm3 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(helix_dot.get_center() + np.array([0.25,0,0]))
- bnm3 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.87*LEFT + 1.24*DOWN)
- plane3 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(helix_dot.get_center() + np.array([-0.5, 0.62, 0]))
- point3 = VGroup(*[dot3, tgt3, nm3, bnm3, plane3]).shift(np.array([0,0,0]))
-
- dot4 = Dot(np.array([np.cos(-np.pi/12), np.sin(-np.pi/12), -0.1*np.pi/3]) + np.array([-3.4,3.4,0]), radius = 0.16, color=RED)
- tgt4 = Arrow((0,0,0), (-2,-0.85,0), color = YELLOW).shift(dot4.get_center() - np.array([-0.05,0,0]))
- nm4 = Arrow((0,0,0), (0.8,-2,0), color = BLUE).shift(dot4.get_center() + np.array([-0.1,0.25,0]))
- bnm4 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(4.03*RIGHT + 0.5*DOWN)
- plane4 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot4.get_center() + np.array([-0.4,-1,0])).rotate(22*DEGREES).scale(1.2)
- point4 = VGroup(*[dot4, tgt4, nm4, bnm4, plane4])
-
- dot5 = Dot((1,0,0) + np.array([2.3,-1,1]))
- tgt5 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(dot5.get_center() - np.array([-0.05,0.2,0]))
- nm5 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(dot5.get_center() + np.array([0.25,0,0]))
- bnm5 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.34*LEFT+0.3*UP)
- plane5 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot5.get_center() + np.array([-0.5,0.5,0]))
- point5 = VGroup(*[tgt5, nm5, bnm5, plane5])
-
- self.add_fixed_in_frame_mobjects(bnm3)
- self.play(FadeIn(point3))
- self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5))
-
- self.add_fixed_in_frame_mobjects(bnm4)
- self.play(FadeIn(point4))
- self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5))
-
- self.add_fixed_in_frame_mobjects(bnm5)
- self.play(FadeIn(point5))
- self.wait(2)
-
- self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif
new file mode 100644
index 0000000..78e3aa3
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py
new file mode 100644
index 0000000..176cac5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py
@@ -0,0 +1,126 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+ def construct(self):
+ self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+
+ t = TextMobject(r'T', color = YELLOW)
+ n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
+ b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
+ frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
+
+ text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
+
+ helix1 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE
+ )
+
+ helix2 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE
+ )
+
+ helix3 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -1.33*np.pi/3, t_max = -np.pi/3, color = WHITE
+ )
+
+ helix4 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -np.pi/3, t_max = -1.3*np.pi/6, color = WHITE
+ )
+
+ helix5 = ParametricFunction(
+ lambda t: np.array([
+ np.cos(TAU*t),
+ np.sin(TAU*t),
+ 0.4*t
+ ]), t_min = -1.3*np.pi/6, t_max = 0, color = WHITE
+ )
+
+ helix_dot = Dot(radius = 0.16, color = RED)
+
+ dot0 = Dot(np.array([np.cos(-2*np.pi/3), np.sin(-2*np.pi/3), -0.8*np.pi/3]), radius = 0.16, color=RED).shift(np.array([4.65,0,-0.8]))
+ tgt0 = Arrow((0,0,0), (1,2,0), color = YELLOW).shift(dot0.get_center() - np.array([0.04,0.2,0]))
+ nm0 = Arrow((0,0,0), (-2,1,0), color = BLUE).shift(dot0.get_center() + np.array([0.3,0,0]))
+ bnm0 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(6.1*LEFT + 3*DOWN)
+ plane0 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot0.get_center() + np.array([-0.35, 0.85, 0])).scale(1.2).rotate(65*DEGREES)
+ point0 = VGroup(*[dot0, tgt0, nm0, bnm0, plane0]).scale(0.8).shift(np.array([1,0,0]))
+
+ dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+ tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+ nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0]))
+ bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(3.68*RIGHT+2.48*DOWN)
+ plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+ point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,6.25,0]))
+
+ dot2 = Dot(np.array([np.cos(-np.pi/6), np.sin(-np.pi/6), -0.2*np.pi/3]) - np.array([1.9,0,0]), radius=0.16,color=RED)
+ tgt2 = Arrow((0,0,0), (1,-2,0), color = YELLOW).shift(dot2.get_center() + np.array([-0.2,0.2,0]))
+ nm2 = Arrow((0,0,0), (2,1,0), color = BLUE).shift(dot2.get_center() + np.array([-0.2,-0.06,0]))
+ bnm2 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(0.4*RIGHT + 0.16*DOWN)
+ plane2 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot2.get_center() + np.array([0.92, -0.5, 0])).rotate(23*DEGREES).scale(1.2)
+ point2 = VGroup(*[dot2, tgt2, nm2, bnm2, plane2])
+
+ helix = VGroup(*[helix1, helix2, helix3, helix4, helix5])
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(FadeIn(helix), FadeIn(text))
+ self.play(ApplyMethod(helix.scale, 4))
+ self.add_fixed_in_frame_mobjects(bnm0)
+ self.play(FadeIn(point0))
+ self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5))
+
+ self.add_fixed_in_frame_mobjects(bnm1)
+ self.play(FadeIn(point1))
+ self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5))
+
+ self.add_fixed_in_frame_mobjects(bnm2)
+ self.play(FadeIn(point2))
+ self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5))
+
+ dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED)
+ tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0]))
+ nm3 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(helix_dot.get_center() + np.array([0.25,0,0]))
+ bnm3 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.87*LEFT + 1.24*DOWN)
+ plane3 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(helix_dot.get_center() + np.array([-0.5, 0.62, 0]))
+ point3 = VGroup(*[dot3, tgt3, nm3, bnm3, plane3]).shift(np.array([0,0,0]))
+
+ dot4 = Dot(np.array([np.cos(-np.pi/12), np.sin(-np.pi/12), -0.1*np.pi/3]) + np.array([-3.4,3.4,0]), radius = 0.16, color=RED)
+ tgt4 = Arrow((0,0,0), (-2,-0.85,0), color = YELLOW).shift(dot4.get_center() - np.array([-0.05,0,0]))
+ nm4 = Arrow((0,0,0), (0.8,-2,0), color = BLUE).shift(dot4.get_center() + np.array([-0.1,0.25,0]))
+ bnm4 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(4.03*RIGHT + 0.5*DOWN)
+ plane4 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot4.get_center() + np.array([-0.4,-1,0])).rotate(22*DEGREES).scale(1.2)
+ point4 = VGroup(*[dot4, tgt4, nm4, bnm4, plane4])
+
+ dot5 = Dot((1,0,0) + np.array([2.3,-1,1]))
+ tgt5 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(dot5.get_center() - np.array([-0.05,0.2,0]))
+ nm5 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(dot5.get_center() + np.array([0.25,0,0]))
+ bnm5 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.34*LEFT+0.3*UP)
+ plane5 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot5.get_center() + np.array([-0.5,0.5,0]))
+ point5 = VGroup(*[tgt5, nm5, bnm5, plane5])
+
+ self.add_fixed_in_frame_mobjects(bnm3)
+ self.play(FadeIn(point3))
+ self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5))
+
+ self.add_fixed_in_frame_mobjects(bnm4)
+ self.play(FadeIn(point4))
+ self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5))
+
+ self.add_fixed_in_frame_mobjects(bnm5)
+ self.play(FadeIn(point5))
+ self.wait(2)
+
+ self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif
new file mode 100644
index 0000000..6b4b438
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
new file mode 100644
index 0000000..c719a1d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
@@ -0,0 +1,23 @@
+from manimlib.imports import *
+
+class fs1(ThreeDScene):
+ def construct(self):
+
+
+ self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+ dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+ tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+ nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8)
+ bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+ plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+ point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+ t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN)
+ n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT)
+ b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1)
+ text = VGroup(*[t, n, b])
+ self.add_fixed_in_frame_mobjects(bnm1, text)
+ self.play(FadeIn(point1), FadeIn(bnm1), FadeIn(text))
+ self.wait()
+ self.play(TransformFromCopy(tgt1, nm1, run_time = 2))
+ self.wait(2)
+ self.play(FadeOut(VGroup(*[bnm1, text, point1, nm1])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif
new file mode 100644
index 0000000..ce367b6
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py
new file mode 100644
index 0000000..0261fed
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py
@@ -0,0 +1,28 @@
+from manimlib.imports import *
+
+class fs1(ThreeDScene):
+ def construct(self):
+
+
+ self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+ dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+ tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+ nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8)
+ bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+
+ bnms = Line((0,0,0), (0,0,1.6), color = GREEN_E).shift(np.array([3.1,5.2,0])).scale(0.6)
+ bnmsa = ArrowTip(color = GREEN_E).next_to(bnms, np.array([0,0,1]), buff = 0).rotate(45*DEGREES)
+ bns = VGroup(*[bnms, bnmsa])
+
+ plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+ point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+ t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN)
+ n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT)
+ b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1)
+ text = VGroup(*[t, n, b])
+ self.add_fixed_in_frame_mobjects(bnm1, text)
+ self.play(FadeIn(point1), FadeIn(text), FadeIn(bnm1))
+ self.wait()
+ self.play(TransformFromCopy(bnms, nm1, run_time = 3))
+ self.wait(2)
+ self.play(FadeOut(VGroup(*[bnms, text, point1, nm1, bnm1])))
--
cgit
From 0fe85fe7b505f92718d7401e065a50077a8de252 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 1 Jul 2020 13:01:29 +0530
Subject: Update README.md
---
.../geometry-of-planes-and-curves/arc-length-and-curvature/README.md | 3 +++
1 file changed, 3 insertions(+)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
index a2f71d7..10786d6 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
@@ -4,5 +4,8 @@
**file2_circle_curvature.py**
+**file3_curvature_interpretation.py**
+
+
**file4_different_curvature_single_curve.py**
--
cgit
From 564956f093a9aa612d07653ddf73163495321992 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 1 Jul 2020 13:04:06 +0530
Subject: Update README.md
---
.../tnb-frame-and-serret-frenet-formulae/README.md | 17 +++++++++++++----
1 file changed, 13 insertions(+), 4 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
index 766c91f..7874f43 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
@@ -1,6 +1,15 @@
-**file1_tnb_basic.py**
-
+**file1_tnb_creation.py**
+
-**file2_tnb_frame_manim.py**
-
+**file2_tnb_basic.py**
+
+
+**file3_tnb_frame_manim.py**
+
+
+**file4_fs1.py**
+
+
+**file5_fs2.py**
+
--
cgit
From 2fee7bc2a219755e6018d3c1a5fb995d8eccf287 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 1 Jul 2020 13:11:25 +0530
Subject: math error fix
---
.../file3_curvature_interpretation.gif | Bin 702280 -> 700862 bytes
.../file3_curvature_interpretation.py | 2 +-
2 files changed, 1 insertion(+), 1 deletion(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
index 39489b7..22a450a 100644
Binary files a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif and b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif differ
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
index cf6b032..d8dd0a4 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
@@ -20,7 +20,7 @@ class interpretation(Scene):
# self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText])))
tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES )
- nm2text = TextMobject(r'$\frac{dT}{dt} = \frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.6).shift(0.5*RIGHT+0.6*DOWN).rotate(-25*DEGREES)
+ nm2text = TextMobject(r'$\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.7).shift(0.7*RIGHT+0.8*DOWN).rotate(-25*DEGREES)
unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN)
self.play(FadeIn(VGroup(*[tgt, tgtText])))
--
cgit