From 38fc15ed3749f7bf9140a45e7c5f210b3d4fc3c5 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Wed, 24 Jun 2020 05:01:53 +0530 Subject: Rename FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py to FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py --- ...e2_Tangent_plane_approximation_visualization.py | 74 ---------------------- ...e2_Tangent_plane_approximation_visualization.py | 74 ++++++++++++++++++++++ 2 files changed, 74 insertions(+), 74 deletions(-) delete mode 100644 FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py deleted file mode 100644 index d1ecf8c..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py +++ /dev/null @@ -1,74 +0,0 @@ -from manimlib.imports import* - -#---- tangent plane is parallel to the x-y plane -class MaximaScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes().scale(1.2) - label_x= TextMobject("$x$").shift([5.4,-0.5,0]) #---- x axis - label_y= TextMobject("$y$").shift([-0.5,5.2,0]).rotate(-4.5) #---- y axis - - #---- graph of the function - s = ParametricSurface( - lambda u, v: np.array([ - 1.5*np.cos(u)*np.cos(v), - 1.5*np.cos(u)*np.sin(v), - 1.5*np.sin(u) - ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[BLUE_B,BLUE_C,BLUE_D,BLUE_E]).scale(1.5).shift([-0.8,0.5,1.5]) - - d1 = Dot([0.2,2.01,2.24],color = '#800000').rotate(1.1,LEFT) #---- point(x_0,y_0) - d1_copy = Dot([1.1,2.2,-0.45],color = '#800000') #---- projection of point(x_0,y_0) on x-y plane - d1_text = TextMobject("$(x_0,y_0)$",color = "#8B0000").scale(0.4).shift(1.3*RIGHT+1.1*UP) - - d2 = Dot([1.1,2.2,2.7],color = '#800000').rotate(1,LEFT) #---- point(x,y) - d2_copy = Dot([0.1,1.95,0.4],color = '#800000') #---- projection of point(x,y) on x-y plane - d2_text = TextMobject("$(x,y)$",color = "#8B0000").scale(0.4).shift(0.6*RIGHT+0.8*UP) - - t_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2.9]) #---- tangent plane - - t_text= TextMobject("Tangent Plane",color = RED).scale(0.5).shift(0.3*RIGHT+1.3*UP).rotate(math.radians(5),LEFT) - - l1 = Line([1.1,2.2,2.6],[1.1,2.2,-0.45]).fade(0.2) - l2 = Line([0.1,1.95,2.05],[0.1,1.95,0.4]).fade(0.2) - - a1 = Line([0.1,1.95,0.4],[1.1,2.2,-0.45],color ="#00FF7F") - a_x = Line([0.1,1.95,0.4],[1.7,1.95,0.4],color ="#9400D3") - a_y = Line([0.1,1.95,0.4],[0.1,2.75,0.4],color ="#8B4513") - a2 = Line([1.7,1.95,0.4],[1.7,2.75,0.4]) - a3 = Line([0.1,2.75,0.4],[1.7,2.75,0.4]) - - #---- transition of tangent plane - - t2_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2]) - t3_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([1.1,2.5,2]) - t4_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([0.9,2.35,0.4]) - - #------------------------------------------- - self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES) - self.wait(1) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.play(Write(s)) - self.wait(1) - self.play(Write(d1)) - self.add_fixed_in_frame_mobjects(d1_text) - self.play(ShowCreation(t_plane)) - self.add_fixed_in_frame_mobjects(t_text) - self.wait(1) - self.play(FadeOut(t_text),Write(d2)) - self.add_fixed_in_frame_mobjects(d2_text) - self.wait(1) - self.play(Write(l1),Write(l2)) - self.play(Write(d2_copy),Write(d1_copy)) - self.wait(1) - self.play(Write(a1),Write(a_x),Write(a_y)) - self.wait(1) - self.play(Write(a2),Write(a3)) - self.wait(1) - self.play(ReplacementTransform(t_plane,t2_plane)) - self.wait(1) - self.play(ReplacementTransform(t2_plane,t3_plane)) - self.wait(1) - self.play(ReplacementTransform(t3_plane,t4_plane)) - self.wait(1) diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py new file mode 100644 index 0000000..d1ecf8c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py @@ -0,0 +1,74 @@ +from manimlib.imports import* + +#---- tangent plane is parallel to the x-y plane +class MaximaScene(ThreeDScene): + def construct(self): + + axes = ThreeDAxes().scale(1.2) + label_x= TextMobject("$x$").shift([5.4,-0.5,0]) #---- x axis + label_y= TextMobject("$y$").shift([-0.5,5.2,0]).rotate(-4.5) #---- y axis + + #---- graph of the function + s = ParametricSurface( + lambda u, v: np.array([ + 1.5*np.cos(u)*np.cos(v), + 1.5*np.cos(u)*np.sin(v), + 1.5*np.sin(u) + ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[BLUE_B,BLUE_C,BLUE_D,BLUE_E]).scale(1.5).shift([-0.8,0.5,1.5]) + + d1 = Dot([0.2,2.01,2.24],color = '#800000').rotate(1.1,LEFT) #---- point(x_0,y_0) + d1_copy = Dot([1.1,2.2,-0.45],color = '#800000') #---- projection of point(x_0,y_0) on x-y plane + d1_text = TextMobject("$(x_0,y_0)$",color = "#8B0000").scale(0.4).shift(1.3*RIGHT+1.1*UP) + + d2 = Dot([1.1,2.2,2.7],color = '#800000').rotate(1,LEFT) #---- point(x,y) + d2_copy = Dot([0.1,1.95,0.4],color = '#800000') #---- projection of point(x,y) on x-y plane + d2_text = TextMobject("$(x,y)$",color = "#8B0000").scale(0.4).shift(0.6*RIGHT+0.8*UP) + + t_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2.9]) #---- tangent plane + + t_text= TextMobject("Tangent Plane",color = RED).scale(0.5).shift(0.3*RIGHT+1.3*UP).rotate(math.radians(5),LEFT) + + l1 = Line([1.1,2.2,2.6],[1.1,2.2,-0.45]).fade(0.2) + l2 = Line([0.1,1.95,2.05],[0.1,1.95,0.4]).fade(0.2) + + a1 = Line([0.1,1.95,0.4],[1.1,2.2,-0.45],color ="#00FF7F") + a_x = Line([0.1,1.95,0.4],[1.7,1.95,0.4],color ="#9400D3") + a_y = Line([0.1,1.95,0.4],[0.1,2.75,0.4],color ="#8B4513") + a2 = Line([1.7,1.95,0.4],[1.7,2.75,0.4]) + a3 = Line([0.1,2.75,0.4],[1.7,2.75,0.4]) + + #---- transition of tangent plane + + t2_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2]) + t3_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([1.1,2.5,2]) + t4_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([0.9,2.35,0.4]) + + #------------------------------------------- + self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES) + self.wait(1) + self.add(axes) + self.add(label_x) + self.add(label_y) + self.play(Write(s)) + self.wait(1) + self.play(Write(d1)) + self.add_fixed_in_frame_mobjects(d1_text) + self.play(ShowCreation(t_plane)) + self.add_fixed_in_frame_mobjects(t_text) + self.wait(1) + self.play(FadeOut(t_text),Write(d2)) + self.add_fixed_in_frame_mobjects(d2_text) + self.wait(1) + self.play(Write(l1),Write(l2)) + self.play(Write(d2_copy),Write(d1_copy)) + self.wait(1) + self.play(Write(a1),Write(a_x),Write(a_y)) + self.wait(1) + self.play(Write(a2),Write(a3)) + self.wait(1) + self.play(ReplacementTransform(t_plane,t2_plane)) + self.wait(1) + self.play(ReplacementTransform(t2_plane,t3_plane)) + self.wait(1) + self.play(ReplacementTransform(t3_plane,t4_plane)) + self.wait(1) -- cgit