Merge pull request #1 from mohan-padmapriya/edit_two

Code for subtopic one: Gradient

7 files changed, 382 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py
new file mode 100644
index 0000000..cd754cd
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file1_missile-example.py
@@ -0,0 +1,37 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		np.sin(x-y),
+		np.exp(y),
+		0
+	])
+def func(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		-2*x,
+		y,
+		0])
+
+class Missiles(GraphScene):
+	def construct(self):
+
+		field = VectorField(function)
+		#path = ParametricFunction(lambda x: -2*x)
+
+		dot = SVGMobject("miss").move_to(DL).scale(0.09).set_color(WHITE).rotate(PI/4 + PI)
+		path = ArcBetweenPoints(dot.get_center(), UP+0.2*LEFT)
+
+		self.play(FadeIn(field))
+		self.wait()
+		self.play(FadeIn(dot))
+		self.wait()
+		self.play(MoveAlongPath(dot, path))
+		self.play(ApplyMethod(dot.rotate, PI/4), rate = 0.2)
+		self.play(ApplyMethod(dot.move_to, 3.5*UP), rate = 0.3)
+		#self.play(ApplyMethod(dot.move_to, 3.5*UP))
+		#self.add_fixed_in_frame_mobjects(text_field)
+		self.wait()
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py
new file mode 100644
index 0000000..7a95867
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file2_gradient-example-1.py
@@ -0,0 +1,43 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		0.4*x,
+		0.4*y,
+		0.4*np.cos(np.sqrt((x**2)+(y**2))
+	)])
+
+class ThreeDVector(ThreeDScene):
+	def construct(self):
+		axes = ThreeDAxes()
+		self.add(axes)
+		self.set_camera_orientation(phi=45*DEGREES,theta=60*DEGREES,distance=40)
+		self.begin_ambient_camera_rotation(rate=0.5)
+
+		surface = ParametricSurface(
+			lambda u, v: np.array([
+				0.4*u,
+				0.4*v,
+				0.4*np.cos(np.sqrt((u**2)+(v**2)))
+			]),u_min=-20,u_max=20, v_min=-10,v_max=10).set_color(BLUE_E).fade(0.7)
+
+		text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7)
+		text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7)
+		
+		
+		self.add_fixed_in_frame_mobjects(text_func)
+		self.play(ShowCreation(surface))
+		self.wait(3)
+
+		field = VectorField(function)
+		self.play(FadeIn(field), FadeOut(text_func))
+		self.add_fixed_in_frame_mobjects(text_field)
+		self.wait()
+		self.play(FadeOut(surface))
+		self.wait()
+
+
+
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py
new file mode 100644
index 0000000..e37581d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file3_gradient-example-2.py
@@ -0,0 +1,39 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		x,
+		y,
+		x**2  - y**2
+	])
+
+class ThreeDVector_three(ThreeDScene):
+	def construct(self):
+		axes = ThreeDAxes()
+		self.add(axes)
+		self.set_camera_orientation(phi=45*DEGREES,theta=85*DEGREES,distance=40)
+		self.begin_ambient_camera_rotation(rate=0.5)
+
+		surface = ParametricSurface(
+			lambda x, y: np.array([
+			x,
+			y,
+			x**2  - y**2
+		]),u_min=-2,u_max=2, v_min=-1.5,v_max=1.5).set_color(BLUE_E).fade(0.7).scale(1.7)
+
+		text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7)
+		text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7)
+		
+		self.add_fixed_in_frame_mobjects(text_func)
+		self.play(ShowCreation(surface))
+		self.wait(3)
+
+		field = VectorField(function)
+		self.play(FadeIn(field), FadeOut(text_func))
+		self.add_fixed_in_frame_mobjects(text_field)
+		self.wait()
+		self.play(FadeOut(surface))
+		self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py
new file mode 100644
index 0000000..e9c8fd0
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4-multidimensional-gradient.py
@@ -0,0 +1,113 @@
+from manimlib.imports import *
+import numpy as np
+
+
+class Hills(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes(
+            number_line_config={
+                "color": GREEN,
+                "include_tip": False,
+                "exclude_zero_from_default_numbers": True,
+            }
+        )
+        self.add(axes)
+
+        self.set_camera_orientation(phi=45*DEGREES,theta=45*DEGREES,distance=40)
+        #self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait()
+
+        cylinder_1 = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            7*u*v/np.exp(u**2+v**2)
+            ]),u_min=-3,u_max=3, v_min=-1,v_max=-0.95).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5)
+        cylinder = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            7*u*v/np.exp(u**2+v**2)
+            ]),u_min=-3,u_max=3, v_min=-3,v_max=3).set_color(YELLOW_E).rotate(PI/2).shift(LEFT).fade(0.5)     
+        text_one = TexMobject(r"\textrm{Single variable functions slope up and down}")
+        #name = TexMobject(r"\textrm{PROBE}").next_to(text_one, DOWN, buff = SMALL_BUFF).scale(0.7)
+        text_one_a = TexMobject(r"\textrm{Position }", r" \rightarrow ").next_to(text_one, DOWN, buff = SMALL_BUFF)
+        probe = Sphere(radius = 0.2).next_to(text_one_a, RIGHT).set_color(BLUE_E)
+        text_one_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe, RIGHT, buff = SMALL_BUFF)
+        name = TextMobject("PROBE").next_to(probe, DOWN, buff = SMALL_BUFF).scale(0.5)
+        text = VGroup(text_one, text_one_a, probe, text_one_b, name).to_edge(UP+1.5*LEFT).scale(0.5)
+
+        text_two = TexMobject(r"\textrm{Multivariable functions slope in infinitely many directions!}")
+        #name_two = TexMobject(r"\textrm{PROBE2.0}").next_to(text_two, DOWN, buff = SMALL_BUFF).scale(0.7)
+        text_two_a = TexMobject(r"\textrm{Position, Direction }", r" \rightarrow ").next_to(text_two, DOWN, buff = SMALL_BUFF)
+        probe_two = Sphere(radius = 0.2).next_to(text_two_a, RIGHT).set_color(PURPLE_E)
+        text_two_b = TexMobject(r" \rightarrow ", r"\textrm{ slope }").next_to(probe_two, RIGHT, buff = SMALL_BUFF)
+        name_two = TextMobject("PROBE2.0").next_to(probe_two, DOWN, buff = SMALL_BUFF).scale(0.5)
+        two = VGroup(text_two, text_two_a, probe_two, text_two_b, name_two).to_edge(UP+LEFT).scale(0.5).shift(3.5*LEFT)
+
+
+
+
+
+
+        self.play(ShowCreation(cylinder_1))
+        self.wait()
+        self.add_fixed_in_frame_mobjects(text)
+        self.wait(3.5)
+        self.play(FadeOut(text))
+        self.play(ReplacementTransform(cylinder_1, cylinder))
+        self.wait()
+        self.add_fixed_in_frame_mobjects(two)
+        self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait(4)
+
+class OneMore(ThreeDScene, GraphScene):
+    def setup(self):
+        GraphScene.setup(self)
+        ThreeDScene.setup(self)
+
+    def construct(self):
+        axes = ThreeDAxes(
+            number_line_config={
+                "color": GREEN,
+                "include_tip": False,
+                "exclude_zero_from_default_numbers": True,
+            }
+        )
+        self.add(axes)
+
+        self.set_camera_orientation(phi=90*DEGREES,theta=90*DEGREES,distance=40)
+        #self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait()
+
+        shape = ParametricSurface(
+            lambda u, v: np.array([
+            u,
+            v,
+            2 - u**2 - v**2,
+            ]),u_min=0,u_max =0.01, v_min=-2,v_max=2).set_color(GREEN_C)
+
+        shape_A = ParametricSurface(
+            lambda u, v: np.array([
+            0*u,
+            0,
+            v,
+            ]),u_min=-2,u_max = 2, v_min=-2,v_max=2).set_color(GREEN_C)
+
+
+        '''
+        path = self.get_graph(lambda u,v: np.array([
+            u,
+            2 - u**2 - v**2]), u_min=-2,u_max=2, v_min=-2,v_max=2)
+        location = np.array([-2,-2, -2]) #location: Point
+        dot = Dot(location)
+        '''
+
+        self.play(ShowCreation(shape))
+        self.add(shape_A)
+        #self.play(ShowCreation(path), ShowCreation(dot))
+        #self.play(MoveAlongPath(dot, path))
+        #self.wait(3)
+        self.play(ApplyMethod(shape.fade, 0.5))
+        self.begin_ambient_camera_rotation(rate = 0.5)
+        self.wait(3)
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py
new file mode 100644
index 0000000..7c0ef54
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file4_gradient-example-3.py
@@ -0,0 +1,40 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		x,
+		y,
+		1/np.cos(x*y),
+	])
+
+class ThreeDVector(ThreeDScene):
+	def construct(self):
+		axes = ThreeDAxes()
+		self.add(axes)
+		self.set_camera_orientation(phi=45*DEGREES,theta=45*DEGREES,distance=40)
+		self.begin_ambient_camera_rotation(rate=0.5)
+
+		surface = ParametricSurface(
+			lambda x, y: np.array([
+			x,
+			y,
+			1/np.cos(x*y),
+		]),u_min=-1.15,u_max=1.15, v_min=-1.15,v_max=1.15).set_color(BLUE_E).fade(0.7).scale(1.4)
+
+		text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.3)
+		text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7)
+		
+		self.add_fixed_in_frame_mobjects(text_func)
+		self.play(ShowCreation(surface))
+		self.wait(2)
+
+		field = VectorField(function).scale(0.7)
+		self.play(FadeIn(field), FadeOut(text_func))
+		self.add_fixed_in_frame_mobjects(text_field)
+		self.wait()
+
+		self.play(FadeOut(surface))
+		self.wait(2)
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py
new file mode 100644
index 0000000..803ea4a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file5_steepest-ascent-analogy.py
@@ -0,0 +1,71 @@
+from manimlib.imports import *
+import numpy as np
+
+class Rules(ThreeDScene):
+
+	def setup(self):
+		ThreeDScene.setup(self)
+
+	def construct(self):
+		axes = ThreeDAxes()#.scale(0.8)#.shift(2*RIGHT, 2*DOWN)
+		self.set_camera_orientation(phi=PI/3 + 10*DEGREES,theta=-PI/4 + 25*DEGREES,distance=60)
+
+		plane = Polygon(np.array([4,4,0]), np.array([4, -4, 0]), np.array([-4, -4, 0]), np.array([-4, 4, 0]), color = BLACK, fill_color = YELLOW_E, fill_opacity = 0.3)
+
+		path_one = Line(start = ORIGIN, end = np.array([3, 0, 0])).set_color(BLUE_E)
+		path_one_text = TexMobject(r"\textrm{3 steps in the x direction}").shift(2*DOWN+3.5*LEFT).scale(0.5).set_color(BLUE_E)
+		path_two_text = TexMobject(r"\textrm{2 steps in the y direction}").next_to(path_one_text, DOWN, buff = SMALL_BUFF).scale(0.5).set_color(GREEN_C)
+		path_three_text = TexMobject(r"\textrm{2 steps in the z direction}").next_to(path_two_text, DOWN, buff = SMALL_BUFF).scale(0.5).set_color(PURPLE_E)
+		obj = TextMobject("Objective: ", "Maximise points for a set number of steps").scale(0.8).to_edge(UP+LEFT)
+
+		steps = TexMobject(r"\textrm{Total steps = 7}").to_edge(RIGHT, buff = LARGE_BUFF).set_color(YELLOW_E).scale(0.7).shift(1*UP)
+		points_one = TexMobject(r"\textrm{Total points = 13}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E)
+		question = TexMobject(r"\textrm{Change direction to score more points?}").shift(2*DOWN+2.5*RIGHT).scale(0.9)
+
+		path_two = Line(start = np.array([3, 0, 0]), end = np.array([3, 2, 0])).set_color(GREEN_C)
+		path_three = Line(start = np.array([3, 2, 0]), end = np.array([3, 2, 2])).set_color(PURPLE_E)
+		total = Line(start = np.array([0, 0, 0]), end = np.array([3, 2, 2])).set_color(YELLOW_E)
+		projection_total = Line(start = np.array([0, 0, 0]), end = np.array([3, 2, 0]))
+		paths = VGroup(path_one, path_two, path_three, path_one_text, path_two_text, path_three_text)
+
+		total_one = VGroup(total, projection_total)
+
+		total_two = Line(start = np.array([0, 0, 0]), end = np.array([4, 1, 2])).set_color(YELLOW_E)
+		projection_total_two = Line(start = np.array([0, 0, 0]), end = np.array([4, 1, 0])) 
+		points_two = TexMobject(r"\textrm{Total points = 12}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E)
+
+		total_three = Line(start = np.array([0, 0, 0]), end = np.array([1, 4, 2])).set_color(YELLOW_E)
+		projection_total_three = Line(start = np.array([0, 0, 0]), end = np.array([1, 4, 0]))
+		points_three = TexMobject(r"\textrm{Total points = 15}").next_to(steps, DOWN, buff = SMALL_BUFF).scale(0.7).set_color(YELLOW_E)
+
+		everything = VGroup(axes, plane, path_one, path_two, path_three, total, projection_total, total_two, projection_total_two, total_three, projection_total_three)
+		everything.scale(0.7).shift(2*LEFT+1*DOWN)
+		self.add_fixed_in_frame_mobjects(obj)
+		self.add(axes, plane)
+		self.wait()
+		self.add_fixed_in_frame_mobjects(path_one_text)
+		self.play(ShowCreation(path_one))
+		self.wait()
+		self.add_fixed_in_frame_mobjects(path_two_text)
+		self.play(ShowCreation(path_two))
+		self.wait()
+		self.add_fixed_in_frame_mobjects(path_three_text)
+		self.play(ShowCreation(path_three))
+		self.add_fixed_in_frame_mobjects(steps, points_one)
+		self.wait()
+		self.play(ShowCreation(total))
+		self.play(ReplacementTransform(total.copy(), projection_total))
+		self.wait()
+		self.play(FadeOut(paths))
+		self.add_fixed_in_frame_mobjects(question)
+		self.wait()
+		self.play(ReplacementTransform(total, total_two), ReplacementTransform(projection_total, projection_total_two))
+		self.play(FadeOut(points_one))
+		self.add_fixed_in_frame_mobjects(points_two)
+		self.wait()
+		self.play(ReplacementTransform(total_two, total_three), ReplacementTransform(projection_total_two, projection_total_three))
+		self.play(FadeOut(points_two))
+		self.add_fixed_in_frame_mobjects(points_three)
+		self.wait()
+
+
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py
new file mode 100644
index 0000000..255a0eb
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/gradient/file6-maximum.py
@@ -0,0 +1,39 @@
+from manimlib.imports import *
+import numpy as np
+
+
+def function(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+		x,
+		y,
+		2 - x**2 - y**2
+	])
+
+class ThreeDVector_one(ThreeDScene):
+	def construct(self):
+		axes = ThreeDAxes()
+		self.add(axes)
+		self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES,distance=40)
+		self.begin_ambient_camera_rotation(rate=0.5)
+
+		surface = ParametricSurface(
+			lambda x, y: np.array([
+			x,
+			y,
+			2 - x**2 - y**2
+		]),u_min=-2,u_max=2, v_min=-2,v_max=2).set_color(RED_E).fade(0.7)
+
+		probe = Sphere(radius = 0.2).set_color(PURPLE_E)
+		probe_one = Sphere(radius = 0.1).set_color(PURPLE_E).move_to(np.array([0,0,2.1]))
+		text_one_b = TexMobject(r" \textrm{ reads 0 at local maximum }").next_to(probe, RIGHT, buff = SMALL_BUFF)
+		name = TextMobject("PROBE2.0 ").next_to(probe, DOWN, buff = SMALL_BUFF).scale(0.5)
+		text = VGroup(probe, text_one_b, name).to_edge(1.5*UP+0.5*LEFT).scale(0.5) 
+		
+
+		self.play(ShowCreation(surface))
+		self.add(probe_one)
+		field = VectorField(function).scale(0.8)
+		self.play(FadeIn(field))
+		self.add_fixed_in_frame_mobjects(text)
+		self.wait(3)