1 files changed, 211 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Greens Theorem/GreensTheorem_file3_line-int-sum.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Greens Theorem/GreensTheorem_file3_line-int-sum.py
new file mode 100644
index 0000000..c5280e1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Greens Theorem/GreensTheorem_file3_line-int-sum.py
@@ -0,0 +1,211 @@
+from manimlib.imports import *
+
+def field_func(coordinate):
+	x,y = coordinate[:2]
+	return np.array([
+					-x, 
+					-y,
+					0
+				])
+
+
+class LineIntegral(MovingCameraScene, Scene):
+	def setup(self):
+		MovingCameraScene.setup(self)
+		Scene.setup(self)
+
+	def get_pending(self,path,proportion,dx=0.01):
+		if proportion < 1:
+			coord_i = path.point_from_proportion(proportion)
+			coord_f = path.point_from_proportion(proportion+dx)
+		else:
+			coord_i = path.point_from_proportion(proportion-dx)
+			coord_f = path.point_from_proportion(proportion)
+		line = Line(coord_i,coord_f)
+		angle = line.get_angle()
+		return angle
+
+	def construct(self):
+		axes_config = {"x_min": -6,
+					"x_max": 6,
+					"y_min": -6,
+					"y_max": 6,
+					"z_axis_config": {},
+					"z_min": -1,
+					"z_max": 1,
+					"z_normal": DOWN,
+					"light_source": 9 * DOWN + 7 * LEFT + 10 * OUT,
+					"number_line_config": {
+						"include_tip": False,
+						},
+					}
+
+		axes = Axes(**axes_config)
+		c_sym = TexMobject(r"C").move_to(4.8*RIGHT+1.3*UP)
+
+
+		final_eq = TexMobject(r"\oint_{C} \vec F \cdot \vec dr", r" = \sum_{i = 1}^{n} \oint_{C_{i}} \vec F \cdot \vec dr ").shift(3*DOWN).set_color("#EDF2EF").scale(1.5)
+		final_eq[0].set_color("#D1D646")
+		
+		text = TexMobject(r"\oint_{C} \vec F . dr",r" = \oint_{C_{1}} \vec F . dr ",r"+ \oint_{C_{2}} \vec F . dr",r" + \oint_{C_{3}} \vec F . dr + \oint_{C_{4}} \vec F . dr + ...", r" + \oint_{C_n} \vec F \cdot \vec dr ").shift(3*DOWN).set_color("#EDF2EF").scale(0.7)
+		text[0].set_color("#D1D646")
+
+		vector_field = VectorField(field_func, x_min = -15, x_max = 15, y_min = -15, y_max = 15).fade(0.5)
+		boundary = Ellipse(width = 9, height = 3).set_color("#32908F")
+		start_angle = self.get_pending(boundary, 0)
+
+		pointer = Triangle(fill_opacity = 1).set_height(0.25).set_color(YELLOW_E)
+		pointer.set_fill(YELLOW_E)
+		pointer.move_to(boundary.get_start())
+		pointer.rotate(- PI / 2)
+		pointer.save_state()
+		pointer.rotate(start_angle, about_point=pointer.get_center())
+
+		split_1 = Line(boundary.get_center()+1.5*UP, boundary.get_center()+1.5*DOWN).set_color("#32908F")
+		split_2 = Line(boundary.get_center()+4.5*LEFT, boundary.get_center()+4.5*RIGHT).set_color("#32908F")
+
+		surface_3 = ParametricSurface(
+			self.surface,
+			u_min=-3,
+			u_max=3,
+			v_min=-3,
+			v_max=3,
+			fill_color=BLACK,
+			checkerboard_colors=[BLACK, BLACK],
+			stroke_color="#32908F",
+			stroke_width = 1.5,
+			resolution = [4,4]
+		).set_fill(opacity=0.2).scale(1.5).set_stroke(width = 1.5)
+
+		surface_4 = ParametricSurface(
+			self.surface,
+			u_min=-3,
+			u_max=3,
+			v_min=-3,
+			v_max=3,
+			fill_color=BLACK,
+			checkerboard_colors=[BLACK, BLACK],
+			stroke_color="#32908F",
+			stroke_width = 1.5,
+			resolution = [16,16]
+		).set_fill(opacity=0.2).scale(1.5).set_stroke(width = 1.5)
+
+		surface_5 = ParametricSurface(
+			self.surface,
+			u_min=-3,
+			u_max=3,
+			v_min=-3,
+			v_max=3,
+			fill_color=BLACK,
+			checkerboard_colors=[BLACK, BLACK],
+			stroke_color="#32908F",
+			stroke_width = 1.5,
+			resolution = [32,32]
+		).set_fill(opacity=0.2).scale(1.5).set_stroke(width = 1.5)
+		surface_6 = ParametricSurface(
+			self.surface,
+			u_min=-3,
+			u_max=3,
+			v_min=-3,
+			v_max=3,
+			fill_color=BLACK,
+			checkerboard_colors=[BLACK, BLACK],
+			stroke_color="#32908F",
+			stroke_width = 1.5,
+			resolution = [64,64]
+		).set_fill(opacity=0.2).scale(1.5).set_stroke(width = 1.5)
+
+		dot = Dot()
+		dot_1 = Dot()
+		dot_2 = Dot()
+
+
+		pointer = Triangle(fill_opacity = 1).set_height(0.25).set_color("#75485E")
+		pointer.set_fill("#75485E")
+		pointer.move_to(boundary.get_start())
+		pointer.rotate(- PI / 2)
+		pointer.save_state()
+		pointer.rotate(start_angle, about_point=pointer.get_center())
+
+		pointer_b2 = Triangle(fill_opacity = 1).set_height(0.25).set_color(YELLOW_E)
+		pointer_b2.set_fill(YELLOW_E)
+		pointer_b2.move_to(boundary.get_start())
+		pointer_b2.rotate(- PI / 2)
+		pointer_b2.save_state()
+		pointer_b2.rotate(start_angle, about_point=pointer_b2.get_center())
+
+
+		# labels
+		labels_1 = VGroup( TexMobject(r"C_{1}").move_to(np.array([0, 3, 0])),
+							TexMobject(r"C_{2}").move_to(np.array([0, -3, 0]))).scale(0.7)
+		labels_2 = VGroup( TexMobject(r"C_{1}").move_to(np.array([-2.25, 2.5, 0])),
+							TexMobject(r"C_{2}").move_to(np.array([-2.25, -2.5, 0])),
+							TexMobject(r"C_{3}").move_to(np.array([2.25, -2.5, 0])),
+							TexMobject(r"C_{4}").move_to(np.array([2.25, 2.5, 0]))).scale(0.7)
+
+		og = VGroup(boundary, split_1, split_2, labels_1, labels_2)
+
+
+		self.add(vector_field, boundary, pointer, text[0], c_sym)
+		def update_rotate_move(mob,alpha):
+			pointer.restore()
+
+			angle = self.get_pending(boundary,alpha)
+
+			pointer.move_to(boundary.point_from_proportion(alpha))
+			pointer.rotate(angle, about_point=pointer.get_center())
+
+		self.play(
+			UpdateFromAlphaFunc(pointer,update_rotate_move),
+			run_time=3,
+			)
+		self.wait()
+		self.play(Indicate(text[0]))
+		self.wait(2)
+		self.play(ShowCreation(text[1]), FadeIn(split_2), ShowCreation(text[2]), ShowCreation(labels_1), FadeOut(pointer), FadeOut(c_sym))
+		self.play(Indicate(text[1]), Indicate(text[2]))
+		self.wait(2)
+		self.play(FadeIn(split_1), ShowCreation(text[3]), ReplacementTransform(labels_1, labels_2))
+		self.play(Indicate(text[1]), Indicate(text[2]), Indicate(text[3]))
+		self.wait(2)
+		self.play(FadeOut(og), ShowCreation(surface_3))
+		self.play(FadeOut(surface_3), ShowCreation(surface_4))
+		self.play(FadeOut(surface_4), ShowCreation(surface_5))
+		self.play(FadeOut(surface_5), ShowCreation(surface_6), ShowCreation(text[4]))
+		self.wait(2)
+		self.play(ReplacementTransform(text, final_eq))
+		self.wait()
+		self.play(Indicate(final_eq))
+		self.wait()
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+	@staticmethod
+	def surface(t, v):
+		return np.array([
+		v*np.sin(t),
+		np.cos(t),
+		0
+	])
+
+