From b2542c71573f8bae8f7c82b3f38fc550dadb2af6 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 09:36:29 +0530
Subject: Update README.md
---
.../geometry-of-planes-and-curves/arc-length-and-curvature/README.md | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
(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 f5313c9..a2a86e6 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
@@ -1,4 +1,4 @@
-**file1_simple_visualization.py**
+**file1_simple_visualization.py**
**file2_circle_curvature.py**
@@ -7,5 +7,5 @@
**file3_curvature_intuition.gif**
-**file4_different_curvature_single_curve.py**
+**file4_different_curvature_single_curve.py**
--
cgit
From 7a7bab3efc3a4c8d02905466b686be050b536c87 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 09:44:47 +0530
Subject: Update README.md
---
.../geometry-of-planes-and-curves/space-curves/README.md | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md
index 18516b7..42f5df1 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md
@@ -1,7 +1,7 @@
-**file1_parametric_ellipse.py**
+**file1_parametric_ellipse.py**
-**file2_parametric_helix.py**
+**file2_parametric_helix.py**
**file3_circletosphere.py**
--
cgit
From d01408565b129dc85ef36d0448302ca612221ab6 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 10:19:41 +0530
Subject: Update README.md
---
.../general-parametric-curves/README.md | 8 ++++----
1 file changed, 4 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/general-parametric-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md
index be358ac..8a47a0e 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md
@@ -1,11 +1,11 @@
-**file1_parametric_circle..py**
+**file1_parametric_circle..py**
-**file2_cycloid_manim.py**
+**file2_cycloid_manim.py**
-**file3_brachistochrone.py**
+**file3_brachistochrone.py**
-**file4_helix_visualization.py**
+**file4_helix_visualization.py**
--
cgit
From 6e1fd99eaf81433196d4f33018307a684b53d304 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 10:20:58 +0530
Subject: Update README.md
---
.../velocity-and-differentiability/README.md | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
index 8092cf7..b08375b 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
@@ -1,5 +1,5 @@
-**file1_smooth_curves.gif**
+**file1_smooth_curves.gif**
-**file2_tangent_space_curve.py**
+**file2_tangent_space_curve.py**
--
cgit
From 3e6832a776041727478a6928ad41100b21794c23 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 10:51:43 +0530
Subject: Create README.md
---
.../tnb-frame-and-serret-frenet-formulae/README.md | 5 +++++
1 file changed, 5 insertions(+)
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
(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
new file mode 100644
index 0000000..fe09907
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
@@ -0,0 +1,5 @@
+**file1_prescribed_plane.gif**
+
+
+**file2_TNB_frame.gif**
+
--
cgit
From d8de81420dd15a86e1e45fe937e3bf3d75c065b3 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 10:54:57 +0530
Subject: Update README.md
---
.../equations-of-planes-and-lines/README.md | 8 ++++----
1 file changed, 4 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/equations-of-planes-and-lines/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md
index d6b89ef..29d2f6a 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md
@@ -1,14 +1,14 @@
**file1_line_eqn.py**
-**file2_point_normal_form_plane.py**
+**file2_point_normal_form_plane.py**
-**file3_intercept_form_plane.py**
+**file3_intercept_form_plane.py**
-**file4_3d_plane.py**
+**file4_3d_plane.py**
-**file5_vector_form_line.py**
+**file5_vector_form_line.py**
--
cgit
From 950344546229095d1c2019e1305e682959b9fafd Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 13:11:09 +0530
Subject: Update README.md
---
.../geometry-of-planes-and-curves/arc-length-and-curvature/README.md | 3 ---
1 file changed, 3 deletions(-)
(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 a2a86e6..a2f71d7 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
@@ -4,8 +4,5 @@
**file2_circle_curvature.py**
-**file3_curvature_intuition.gif**
-
-
**file4_different_curvature_single_curve.py**
--
cgit
From 28cb4d37575ed5a4dd3630e21f72431101075991 Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 13:12:07 +0530
Subject: Delete README.md
---
.../tnb-frame-and-serret-frenet-formulae/README.md | 5 -----
1 file changed, 5 deletions(-)
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
(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
deleted file mode 100644
index fe09907..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
+++ /dev/null
@@ -1,5 +0,0 @@
-**file1_prescribed_plane.gif**
-
-
-**file2_TNB_frame.gif**
-
--
cgit
From 6725b1f2f29dd2165364856905b31d83aa8daeab Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Wed, 24 Jun 2020 13:12:26 +0530
Subject: Update README.md
---
.../velocity-and-differentiability/README.md | 3 ---
1 file changed, 3 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
index b08375b..bc571c6 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md
@@ -1,5 +1,2 @@
-**file1_smooth_curves.gif**
-
-
**file2_tangent_space_curve.py**
--
cgit
From 69c003a243ea5f36e52e8010c4fa63fef7d7bbb4 Mon Sep 17 00:00:00 2001
From: vishal786-commits
Date: Wed, 24 Jun 2020 13:23:04 +0530
Subject: Create file4_surface.py
---
.../surface-integrals/file4_surface.py | 237 +++++++++++++++++++++
1 file changed, 237 insertions(+)
create mode 100644 FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
new file mode 100644
index 0000000..3c2e145
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
@@ -0,0 +1,237 @@
+from manimlib.imports import *
+
+class Surf(ThreeDScene):
+
+ CONFIG = {
+ "axes_config": {
+ "x_min": 0,
+ "x_max": 8,
+ "y_min": 0,
+ "y_max": 8,
+ "z_min": 0,
+ "z_max": 6,
+ "a":2 ,"b": 6, "c":1 , "d":6,
+ "axes_shift":-3*OUT + 5*LEFT,
+ "x_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "y_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "z_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "num_axis_pieces": 1,
+ },
+ "default_graph_style": {
+ "stroke_width": 2,
+ "stroke_color": WHITE,
+ },
+ "default_surface_config": {
+ "fill_opacity": 0.5,
+ "checkerboard_colors": [LIGHT_GREY],
+ "stroke_width": 0.5,
+ "stroke_color": WHITE,
+ "stroke_opacity": 0.5,
+ },
+ "Func": lambda x,y: 2+y/4+np.sin(x)
+ }
+
+
+ def construct(self):
+
+ self.setup_axes()
+ self.set_camera_orientation(distance=35,
+ phi=80 * DEGREES,
+ theta=-80 * DEGREES,
+ )
+
+ fn_text=TextMobject("$S$").set_color(BLUE)
+ self.add_fixed_in_frame_mobjects(fn_text)
+ fn_text.to_edge(TOP,buff=MED_SMALL_BUFF)
+
+ R=TextMobject("D").set_color(BLACK).scale(3)
+ R.move_to(self.axes.input_plane,IN)
+ self.add(R)
+
+ #get the surface
+ surface= self.get_surface(
+ self.axes, lambda x , y:
+ self.Func(x,y)
+ )
+ surface.set_style(
+ fill_opacity=0.8,
+ fill_color=YELLOW,
+ stroke_width=0.8,
+ stroke_color=WHITE,
+ )
+
+
+ self.begin_ambient_camera_rotation(rate=0.05)
+ self.play(Write(surface))
+ # self.play(LaggedStart(ShowCreation(surface)))
+
+ self.get_lines()
+ # self.play(FadeIn(self.axes.input_plane))
+ self.wait(2)
+ self.stop_ambient_camera_rotation()
+ self.wait(1)
+
+ def get_surface(self,axes, func, **kwargs):
+ config = {
+ "u_min": axes.c,
+ "u_max": axes.d,
+ "v_min": axes.a,
+ "v_max": axes.b,
+ "resolution": (
+ (axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
+ (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
+ ),
+ }
+
+ config.update(self.default_surface_config)
+ config.update(kwargs)
+ return ParametricSurface(
+ lambda x,y : axes.c2p(
+ x, y, func(x, y)
+ ),
+ **config
+ )
+
+ def get_lines(self):
+ axes = self.axes
+ labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),
+ axes.y_axis.n2p(axes.d)]
+
+
+ surface_corners=[]
+ for x,y,z in self.region_corners:
+ surface_corners.append([x,y,self.Func(x,y)])
+
+ lines=VGroup()
+ for start , end in zip(surface_corners,
+ self.region_corners):
+ lines.add(self.draw_lines(start,end,"WHITE"))
+
+ for start , end in zip(labels,
+ self.region_corners):
+ # lines.add(self.draw_lines(start,end,"BLUE"))
+ # print (start,end)
+ pass
+ self.play(ShowCreation(lines))
+
+
+ def draw_lines(self,start,end,color):
+ start=self.axes.c2p(*start)
+ end=self.axes.c2p(*end)
+ line=DashedLine(start,end,color=color)
+
+ return line
+
+ def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
+ config = dict(self.axes_config)
+ config.update(kwargs)
+ axes = ThreeDAxes(**config)
+ axes.set_stroke(width=2)
+
+ if include_numbers:
+ self.add_axes_numbers(axes)
+
+ if include_labels:
+ self.add_axes_labels(axes)
+
+ # Adjust axis orientation
+ axes.x_axis.rotate(
+ 90 * DEGREES, RIGHT,
+ about_point=axes.c2p(0, 0, 0),
+ )
+ axes.y_axis.rotate(
+ 90 * DEGREES, UP,
+ about_point=axes.c2p(0, 0, 0),
+ )
+
+ # Add xy-plane
+ input_plane = self.get_surface(
+ axes, lambda x, t: 1e-5
+ )
+ input_plane.set_style(
+ fill_opacity=0.5,
+ fill_color=TEAL,
+ stroke_width=0,
+ stroke_color=WHITE,
+ )
+
+ axes.input_plane = input_plane
+
+ self.region_corners=[
+ input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
+
+ return axes
+
+
+ def setup_axes(self):
+ axes = self.get_three_d_axes(include_labels=True)
+ axes.add(axes.input_plane)
+ axes.scale(1)
+ # axes.center()
+ axes.shift(axes.axes_shift)
+
+ self.add(axes)
+ self.axes = axes
+
+ def add_axes_numbers(self, axes):
+ x_axis = axes.x_axis
+ y_axis = axes.y_axis
+ tex_vals_x = [
+ ("a", axes.a),
+ ("b", axes.b),
+ ]
+ tex_vals_y=[
+ ("c", axes.c),
+ ("d", axes.d)
+ ]
+ x_labels = VGroup()
+ y_labels = VGroup()
+ for tex, val in tex_vals_x:
+ label = TexMobject(tex)
+ label.scale(1)
+ label.next_to(x_axis.n2p(val), DOWN)
+ x_labels.add(label)
+ x_axis.add(x_labels)
+ x_axis.numbers = x_labels
+
+ for tex, val in tex_vals_y:
+ label = TexMobject(tex)
+ label.scale(1.5)
+ label.next_to(y_axis.n2p(val), LEFT)
+ label.rotate(90 * DEGREES)
+ y_labels.add(label)
+
+ y_axis.add(y_labels)
+ y_axis.numbers = y_labels
+
+ return axes
+
+ def add_axes_labels(self, axes):
+ x_label = TexMobject("X")
+ x_label.next_to(axes.x_axis.get_end(), RIGHT)
+ axes.x_axis.label = x_label
+
+ y_label = TextMobject("Y")
+ y_label.rotate(90 * DEGREES, OUT)
+ y_label.next_to(axes.y_axis.get_end(), UP)
+ axes.y_axis.label = y_label
+
+ z_label = TextMobject("Z")
+ z_label.rotate(90 * DEGREES, RIGHT)
+ z_label.next_to(axes.z_axis.get_zenith(), RIGHT)
+ axes.z_axis.label = z_label
+ for axis in axes:
+ axis.add(axis.label)
+ return axes
+ ######Code_by_Somnath_Pandit_https://github.com/panditsomnath10016git#########
+
+
--
cgit
From bd51f25304cd0305a20f448db306deb03cf1093c Mon Sep 17 00:00:00 2001
From: vishal786-commits
Date: Wed, 24 Jun 2020 13:23:36 +0530
Subject: Rename file4_surface.py to file5_surface.py
---
.../surface-integrals/file4_surface.py | 237 ---------------------
.../surface-integrals/file5_surface.py | 237 +++++++++++++++++++++
2 files changed, 237 insertions(+), 237 deletions(-)
delete mode 100644 FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
create mode 100644 FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.py
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
deleted file mode 100644
index 3c2e145..0000000
--- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file4_surface.py
+++ /dev/null
@@ -1,237 +0,0 @@
-from manimlib.imports import *
-
-class Surf(ThreeDScene):
-
- CONFIG = {
- "axes_config": {
- "x_min": 0,
- "x_max": 8,
- "y_min": 0,
- "y_max": 8,
- "z_min": 0,
- "z_max": 6,
- "a":2 ,"b": 6, "c":1 , "d":6,
- "axes_shift":-3*OUT + 5*LEFT,
- "x_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "y_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "z_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "num_axis_pieces": 1,
- },
- "default_graph_style": {
- "stroke_width": 2,
- "stroke_color": WHITE,
- },
- "default_surface_config": {
- "fill_opacity": 0.5,
- "checkerboard_colors": [LIGHT_GREY],
- "stroke_width": 0.5,
- "stroke_color": WHITE,
- "stroke_opacity": 0.5,
- },
- "Func": lambda x,y: 2+y/4+np.sin(x)
- }
-
-
- def construct(self):
-
- self.setup_axes()
- self.set_camera_orientation(distance=35,
- phi=80 * DEGREES,
- theta=-80 * DEGREES,
- )
-
- fn_text=TextMobject("$S$").set_color(BLUE)
- self.add_fixed_in_frame_mobjects(fn_text)
- fn_text.to_edge(TOP,buff=MED_SMALL_BUFF)
-
- R=TextMobject("D").set_color(BLACK).scale(3)
- R.move_to(self.axes.input_plane,IN)
- self.add(R)
-
- #get the surface
- surface= self.get_surface(
- self.axes, lambda x , y:
- self.Func(x,y)
- )
- surface.set_style(
- fill_opacity=0.8,
- fill_color=YELLOW,
- stroke_width=0.8,
- stroke_color=WHITE,
- )
-
-
- self.begin_ambient_camera_rotation(rate=0.05)
- self.play(Write(surface))
- # self.play(LaggedStart(ShowCreation(surface)))
-
- self.get_lines()
- # self.play(FadeIn(self.axes.input_plane))
- self.wait(2)
- self.stop_ambient_camera_rotation()
- self.wait(1)
-
- def get_surface(self,axes, func, **kwargs):
- config = {
- "u_min": axes.c,
- "u_max": axes.d,
- "v_min": axes.a,
- "v_max": axes.b,
- "resolution": (
- (axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
- (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
- ),
- }
-
- config.update(self.default_surface_config)
- config.update(kwargs)
- return ParametricSurface(
- lambda x,y : axes.c2p(
- x, y, func(x, y)
- ),
- **config
- )
-
- def get_lines(self):
- axes = self.axes
- labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),
- axes.y_axis.n2p(axes.d)]
-
-
- surface_corners=[]
- for x,y,z in self.region_corners:
- surface_corners.append([x,y,self.Func(x,y)])
-
- lines=VGroup()
- for start , end in zip(surface_corners,
- self.region_corners):
- lines.add(self.draw_lines(start,end,"WHITE"))
-
- for start , end in zip(labels,
- self.region_corners):
- # lines.add(self.draw_lines(start,end,"BLUE"))
- # print (start,end)
- pass
- self.play(ShowCreation(lines))
-
-
- def draw_lines(self,start,end,color):
- start=self.axes.c2p(*start)
- end=self.axes.c2p(*end)
- line=DashedLine(start,end,color=color)
-
- return line
-
- def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
- config = dict(self.axes_config)
- config.update(kwargs)
- axes = ThreeDAxes(**config)
- axes.set_stroke(width=2)
-
- if include_numbers:
- self.add_axes_numbers(axes)
-
- if include_labels:
- self.add_axes_labels(axes)
-
- # Adjust axis orientation
- axes.x_axis.rotate(
- 90 * DEGREES, RIGHT,
- about_point=axes.c2p(0, 0, 0),
- )
- axes.y_axis.rotate(
- 90 * DEGREES, UP,
- about_point=axes.c2p(0, 0, 0),
- )
-
- # Add xy-plane
- input_plane = self.get_surface(
- axes, lambda x, t: 1e-5
- )
- input_plane.set_style(
- fill_opacity=0.5,
- fill_color=TEAL,
- stroke_width=0,
- stroke_color=WHITE,
- )
-
- axes.input_plane = input_plane
-
- self.region_corners=[
- input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
-
- return axes
-
-
- def setup_axes(self):
- axes = self.get_three_d_axes(include_labels=True)
- axes.add(axes.input_plane)
- axes.scale(1)
- # axes.center()
- axes.shift(axes.axes_shift)
-
- self.add(axes)
- self.axes = axes
-
- def add_axes_numbers(self, axes):
- x_axis = axes.x_axis
- y_axis = axes.y_axis
- tex_vals_x = [
- ("a", axes.a),
- ("b", axes.b),
- ]
- tex_vals_y=[
- ("c", axes.c),
- ("d", axes.d)
- ]
- x_labels = VGroup()
- y_labels = VGroup()
- for tex, val in tex_vals_x:
- label = TexMobject(tex)
- label.scale(1)
- label.next_to(x_axis.n2p(val), DOWN)
- x_labels.add(label)
- x_axis.add(x_labels)
- x_axis.numbers = x_labels
-
- for tex, val in tex_vals_y:
- label = TexMobject(tex)
- label.scale(1.5)
- label.next_to(y_axis.n2p(val), LEFT)
- label.rotate(90 * DEGREES)
- y_labels.add(label)
-
- y_axis.add(y_labels)
- y_axis.numbers = y_labels
-
- return axes
-
- def add_axes_labels(self, axes):
- x_label = TexMobject("X")
- x_label.next_to(axes.x_axis.get_end(), RIGHT)
- axes.x_axis.label = x_label
-
- y_label = TextMobject("Y")
- y_label.rotate(90 * DEGREES, OUT)
- y_label.next_to(axes.y_axis.get_end(), UP)
- axes.y_axis.label = y_label
-
- z_label = TextMobject("Z")
- z_label.rotate(90 * DEGREES, RIGHT)
- z_label.next_to(axes.z_axis.get_zenith(), RIGHT)
- axes.z_axis.label = z_label
- for axis in axes:
- axis.add(axis.label)
- return axes
- ######Code_by_Somnath_Pandit_https://github.com/panditsomnath10016git#########
-
-
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.py
new file mode 100644
index 0000000..3c2e145
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.py
@@ -0,0 +1,237 @@
+from manimlib.imports import *
+
+class Surf(ThreeDScene):
+
+ CONFIG = {
+ "axes_config": {
+ "x_min": 0,
+ "x_max": 8,
+ "y_min": 0,
+ "y_max": 8,
+ "z_min": 0,
+ "z_max": 6,
+ "a":2 ,"b": 6, "c":1 , "d":6,
+ "axes_shift":-3*OUT + 5*LEFT,
+ "x_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "y_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "z_axis_config": {
+ "tick_frequency": 1,
+ # "include_tip": False,
+ },
+ "num_axis_pieces": 1,
+ },
+ "default_graph_style": {
+ "stroke_width": 2,
+ "stroke_color": WHITE,
+ },
+ "default_surface_config": {
+ "fill_opacity": 0.5,
+ "checkerboard_colors": [LIGHT_GREY],
+ "stroke_width": 0.5,
+ "stroke_color": WHITE,
+ "stroke_opacity": 0.5,
+ },
+ "Func": lambda x,y: 2+y/4+np.sin(x)
+ }
+
+
+ def construct(self):
+
+ self.setup_axes()
+ self.set_camera_orientation(distance=35,
+ phi=80 * DEGREES,
+ theta=-80 * DEGREES,
+ )
+
+ fn_text=TextMobject("$S$").set_color(BLUE)
+ self.add_fixed_in_frame_mobjects(fn_text)
+ fn_text.to_edge(TOP,buff=MED_SMALL_BUFF)
+
+ R=TextMobject("D").set_color(BLACK).scale(3)
+ R.move_to(self.axes.input_plane,IN)
+ self.add(R)
+
+ #get the surface
+ surface= self.get_surface(
+ self.axes, lambda x , y:
+ self.Func(x,y)
+ )
+ surface.set_style(
+ fill_opacity=0.8,
+ fill_color=YELLOW,
+ stroke_width=0.8,
+ stroke_color=WHITE,
+ )
+
+
+ self.begin_ambient_camera_rotation(rate=0.05)
+ self.play(Write(surface))
+ # self.play(LaggedStart(ShowCreation(surface)))
+
+ self.get_lines()
+ # self.play(FadeIn(self.axes.input_plane))
+ self.wait(2)
+ self.stop_ambient_camera_rotation()
+ self.wait(1)
+
+ def get_surface(self,axes, func, **kwargs):
+ config = {
+ "u_min": axes.c,
+ "u_max": axes.d,
+ "v_min": axes.a,
+ "v_max": axes.b,
+ "resolution": (
+ (axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
+ (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
+ ),
+ }
+
+ config.update(self.default_surface_config)
+ config.update(kwargs)
+ return ParametricSurface(
+ lambda x,y : axes.c2p(
+ x, y, func(x, y)
+ ),
+ **config
+ )
+
+ def get_lines(self):
+ axes = self.axes
+ labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),
+ axes.y_axis.n2p(axes.d)]
+
+
+ surface_corners=[]
+ for x,y,z in self.region_corners:
+ surface_corners.append([x,y,self.Func(x,y)])
+
+ lines=VGroup()
+ for start , end in zip(surface_corners,
+ self.region_corners):
+ lines.add(self.draw_lines(start,end,"WHITE"))
+
+ for start , end in zip(labels,
+ self.region_corners):
+ # lines.add(self.draw_lines(start,end,"BLUE"))
+ # print (start,end)
+ pass
+ self.play(ShowCreation(lines))
+
+
+ def draw_lines(self,start,end,color):
+ start=self.axes.c2p(*start)
+ end=self.axes.c2p(*end)
+ line=DashedLine(start,end,color=color)
+
+ return line
+
+ def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
+ config = dict(self.axes_config)
+ config.update(kwargs)
+ axes = ThreeDAxes(**config)
+ axes.set_stroke(width=2)
+
+ if include_numbers:
+ self.add_axes_numbers(axes)
+
+ if include_labels:
+ self.add_axes_labels(axes)
+
+ # Adjust axis orientation
+ axes.x_axis.rotate(
+ 90 * DEGREES, RIGHT,
+ about_point=axes.c2p(0, 0, 0),
+ )
+ axes.y_axis.rotate(
+ 90 * DEGREES, UP,
+ about_point=axes.c2p(0, 0, 0),
+ )
+
+ # Add xy-plane
+ input_plane = self.get_surface(
+ axes, lambda x, t: 1e-5
+ )
+ input_plane.set_style(
+ fill_opacity=0.5,
+ fill_color=TEAL,
+ stroke_width=0,
+ stroke_color=WHITE,
+ )
+
+ axes.input_plane = input_plane
+
+ self.region_corners=[
+ input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
+
+ return axes
+
+
+ def setup_axes(self):
+ axes = self.get_three_d_axes(include_labels=True)
+ axes.add(axes.input_plane)
+ axes.scale(1)
+ # axes.center()
+ axes.shift(axes.axes_shift)
+
+ self.add(axes)
+ self.axes = axes
+
+ def add_axes_numbers(self, axes):
+ x_axis = axes.x_axis
+ y_axis = axes.y_axis
+ tex_vals_x = [
+ ("a", axes.a),
+ ("b", axes.b),
+ ]
+ tex_vals_y=[
+ ("c", axes.c),
+ ("d", axes.d)
+ ]
+ x_labels = VGroup()
+ y_labels = VGroup()
+ for tex, val in tex_vals_x:
+ label = TexMobject(tex)
+ label.scale(1)
+ label.next_to(x_axis.n2p(val), DOWN)
+ x_labels.add(label)
+ x_axis.add(x_labels)
+ x_axis.numbers = x_labels
+
+ for tex, val in tex_vals_y:
+ label = TexMobject(tex)
+ label.scale(1.5)
+ label.next_to(y_axis.n2p(val), LEFT)
+ label.rotate(90 * DEGREES)
+ y_labels.add(label)
+
+ y_axis.add(y_labels)
+ y_axis.numbers = y_labels
+
+ return axes
+
+ def add_axes_labels(self, axes):
+ x_label = TexMobject("X")
+ x_label.next_to(axes.x_axis.get_end(), RIGHT)
+ axes.x_axis.label = x_label
+
+ y_label = TextMobject("Y")
+ y_label.rotate(90 * DEGREES, OUT)
+ y_label.next_to(axes.y_axis.get_end(), UP)
+ axes.y_axis.label = y_label
+
+ z_label = TextMobject("Z")
+ z_label.rotate(90 * DEGREES, RIGHT)
+ z_label.next_to(axes.z_axis.get_zenith(), RIGHT)
+ axes.z_axis.label = z_label
+ for axis in axes:
+ axis.add(axis.label)
+ return axes
+ ######Code_by_Somnath_Pandit_https://github.com/panditsomnath10016git#########
+
+
--
cgit
From a865350d4775d430765d60cdaef021374c1435aa Mon Sep 17 00:00:00 2001
From: vishal786-commits
Date: Wed, 24 Jun 2020 13:31:40 +0530
Subject: Add files via upload
---
.../surface-integrals/file5_surface.gif | Bin 0 -> 7241572 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.gif
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.gif
new file mode 100644
index 0000000..27dcac8
Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/file5_surface.gif differ
--
cgit
From b5f5577b9a5fadd92febd2e9ead886469be4b0af Mon Sep 17 00:00:00 2001
From: vishal786-commits
Date: Wed, 24 Jun 2020 13:33:20 +0530
Subject: Update README.md
---
.../triple-and-surface-integrals/surface-integrals/README.md | 2 ++
1 file changed, 2 insertions(+)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/README.md
index a4a1c84..a1de8b5 100644
--- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/README.md
+++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/surface-integrals/README.md
@@ -6,3 +6,5 @@
**file4_pauseandponder.py**
+**file5_surface.py**
+
--
cgit
From ebfe7a6656b240aacffc4c92e873d4f3fed79971 Mon Sep 17 00:00:00 2001
From: vishal786-commits
Date: Wed, 24 Jun 2020 13:36:10 +0530
Subject: Update file4_cube_surface.py
---
.../flux/file4_cube_surface.py | 195 +++++++++++++++++++--
1 file changed, 176 insertions(+), 19 deletions(-)
(limited to 'FSF-2020/calculus-of-several-variables')
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
index 5963996..9301a00 100644
--- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
+++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
@@ -43,29 +43,186 @@ class cuber(ThreeDScene):
n1.rotate(PI/2,axis=RIGHT)
n1.shift(3*RIGHT+1.3*OUT+DOWN)
+ spaceloc = [[0,0,2],[1,0,2],[-1,0,2],[2,0,2],[-2,0,2],[3,0,2],[-3,0,2],
+ [0,1,2],[1,1,2],[-1,1,2],[2,1,2],[-2,1,2],[3,1,2],[-3,1,2],
+ [0,-1,2],[1,-1,2],[-1,-1,2],[2,-1,2],[-2,-1,2],[3,-1,2],[-3,-1,2],
+ [0,2,2],[1,2,2],[-1,2,2],[2,2,2],[-2,2,2],[3,2,2],[-3,2,2],
+ [0,-2,2],[1,-2,2],[-1,-2,2],[2,-2,2],[-2,-2,2],[3,-2,2],[-3,-2,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2],
+ [0,4,2],[1,4,2],[-1,4,2],[2,4,2],[-2,4,2],[3,4,2],[-3,4,2],
+ [0,4,2],[1,4,2],[-1,4,2],[2,4,2],[-2,4,2],[3,4,2],[-3,4,2],
+ [0,5,2],[1,5,2],[-1,5,2],[2,5,2],[-2,5,2],[3,5,2],[-3,5,2],
+ [0,5,2],[1,5,2],[-1,5,2],[2,5,2],[-2,5,2],[3,5,2],[-3,5,2],
+ [0,6,2],[1,6,2],[-1,6,2],[2,6,2],[-2,6,2],[3,6,2],[-3,6,2],
+ [0,1.5,2],[1,1.5,2],[-1,1.5,2],[2,1.5,2],[-2,1.5,2],[3,1.5,2],[-3,1.5,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2]]
+
+
+ veclist1=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)]
+
+
+
+
+
+ [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist1[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield1=VGroup(*veclist1)
+ [veclist1[i].shift(spaceloc[i]) for i in range(98)]
- self.set_camera_orientation(phi=75 * DEGREES,theta=-15*DEGREES)
+
+
+ veclist2=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)]
+
+
+
+
+
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist2[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield2=VGroup(*veclist2)
+ [veclist2[i].shift(spaceloc[i]) for i in range(98)]
+
+
+
+ veclist3=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()]
+
+
+
+
+
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist3[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield3=VGroup(*veclist3)
+ [veclist3[i].shift(spaceloc[i]) for i in range(98)]
+
+
+
+
+ veclist4=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()]
+
+
+
+
+
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist4[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield4=VGroup(*veclist4)
+ [veclist4[i].shift(spaceloc[i]) for i in range(98)]
+
+
+ vectorfield1.shift(1.5*DOWN)
+ vectorfield2.shift(IN+1.5*DOWN)
+ vectorfield3.shift(2*IN+1.5*DOWN)
+ vectorfield4.shift(3*IN+1.5*DOWN)
+
+ vectors=[vectorfield1,vectorfield2,vectorfield3,vectorfield4]
+ vectorfield=VGroup(*vectors)
+ vectorfield.scale(1.25)
+
+ fv=[Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ ]
+
+ spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5],[1.5,2,0.5],
+ [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1],[1.5,2,1],
+ [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5],[1.5,2,1.5],
+ [1.5,0.5,2],[1.5,1,2],[1.5,1.5,2],[1.5,2,2]]
+
+ [fv[i].rotate(PI/4,axis=RIGHT) for i in range(1)]
+ [fv[i].rotate(PI/6,axis=OUT) for i in range(16)]
+ [fv[i].rotate(PI/8,axis=DOWN) for i in range(16)]
+ [fv[i].shift(spaceloc2[i]) for i in range(16)]
+ fvfield=VGroup(*fv)
+ fvfield.shift(0.5*IN+2*DOWN)
+
+ flux=TextMobject("Flux through one side of the cube").set_color(ORANGE)
+ flux.shift(3*UP+1.5*LEFT)
+
+
+
+
+
+ self.set_camera_orientation(phi=70 * DEGREES,theta=-75*DEGREES)
self.play(ShowCreation(axes),ShowCreation(axis_label))
- self.play(ShowCreation(cube, run_time=3))
- self.begin_ambient_camera_rotation(rate=-0.2)
- # self.move_camera(phi=150*DEGREES,theta=-45*DEGREES, run_time=3)
+ self.play(ShowCreation(vectorfield))
+ self.add(fvfield)
+ self.begin_ambient_camera_rotation(rate=0.01)
+
+ self.play(ShowCreation(cube, run_time=1))
+
self.wait(1)
self.play(ShowCreation(sq3))
-
self.wait(1)
- self.play(ShowCreation(v1),ShowCreation(n1))
+ self.play(FadeOut(cube))
+ self.play(FadeOut(vectorfield))
+ self.add_fixed_in_frame_mobjects(flux)
+ # self.play(ShowCreation(flux))
self.wait(1)
- self.stop_ambient_camera_rotation()
- self.wait(2)
-
-
- # self.play(Write(t1))
- # self.play(Transform(vg,t1))
- # self.wait(3)
- # self.play(ReplacementTransform(t1,t2))
- # self.wait(3)
- # # self.move_camera(phi=50*DEGREES,theta=-45*DEGREES,run_time=3)
- # self.wait(8)
- # self.move_camera(phi=75 * DEGREES, run_time=3)
- # self.wait(3)
+ self.play(ShowCreation(v1),ShowCreation(n1))
+ self.wait(6)
+ # self.stop_ambient_camera_rotation()
+
--
cgit
From 82b3f04bc10d746282a618458797486e2096a28c Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Thu, 25 Jun 2020 03:06:20 +0530
Subject: tnb
---
.../file2_TNB_frame.gif | Bin 150050 -> 0 bytes
.../file2_tnb_frame.gif | Bin 0 -> 150050 bytes
.../file2_tnb_frame_manim.gif | Bin 0 -> 837251 bytes
.../file2_tnb_frame_manim.py | 125 +++++++++++++++++++++
4 files changed, 125 insertions(+)
delete mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_TNB_frame.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
(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.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.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
new file mode 100644
index 0000000..097652f
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_frame.gif 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.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
new file mode 100644
index 0000000..784b6a6
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_frame_manim.gif 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
new file mode 100644
index 0000000..ee5e717
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
@@ -0,0 +1,125 @@
+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), 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.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))
+
+ 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(ApplyMethod(point2.set_color, GRAY), FadeIn(point3))
+ self.play(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.add_fixed_in_frame_mobjects(bnm5)
+ self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5))
+ self.wait(2)
+
+ self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
--
cgit
From f97ad581d99f06f62389903c80ffdd6de982363b Mon Sep 17 00:00:00 2001
From: Saarth Deshpande
Date: Thu, 25 Jun 2020 03:08:34 +0530
Subject: Create README.md
---
.../tnb-frame-and-serret-frenet-formulae/README.md | 2 ++
1 file changed, 2 insertions(+)
create mode 100644 FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
(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
new file mode 100644
index 0000000..34885b2
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
@@ -0,0 +1,2 @@
+**file2_tnb_frame_manim.py**
+
--
cgit