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diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/README.md b/FSF-2020/approximations-and-optimizations/Critical-Points/README.md deleted file mode 100644 index f0747bb..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/README.md +++ /dev/null @@ -1,32 +0,0 @@ -<h1><div align=”center”><b>SubTopic: Critical Points</b></h1></div> -<br/></br> - -<tab>file1_Critical_Point_of_a_function - - -<br/></br> -<br/></br> - -<tab>file2_Traces_and_Tangent - - -<br/></br> -<br/></br> - -<tab>file3_Tangent_plane_at_extrema_of_a_function - - -<br/></br> -<br/></br> - -<tab>file4_Types_of_critical_points - - -<br/></br> -<br/></br> - -<tab>file5_f(x,y)=(y-x)(1-2x-3y) - -%3D(y-x)(1-2x-3y).gif?raw=true) -<br/></br> -<br/></br> diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.gif b/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.gif Binary files differdeleted file mode 100644 index ca3989c..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py deleted file mode 100644 index e8cb08d..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py +++ /dev/null @@ -1,77 +0,0 @@ -from manimlib.imports import* -import math as m - -#---- case 1: parial derivatives exist at critical point of the function -class firstScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- f(x,y) = e^(-10x^2-10y^2) - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - m.exp(-10*u**2-10*v**2) - ]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [TEAL_E,TEAL_D,TEAL_C,TEAL_B]).fade(0.6).scale(3.5).shift([0,0,1.5]) - - l1 = Line([0,0,3.75],[0,0,0],color = '#800000') - - d = Dot([0,0,3.75],color = '#800000') #---- critical point - - d_text = TextMobject("$\\frac{\\partial f}{\\partial x}=\\frac{\\partial f}{\\partial y} = 0$").scale(0.8).to_corner(UL) - - f_text = TextMobject("Critical Point ",color = YELLOW).shift(3.4*UP).scale(0.5) - - self.set_camera_orientation(phi = 45*DEGREES, theta = 40*DEGREES) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.add_fixed_in_frame_mobjects(d_text) - self.begin_ambient_camera_rotation(rate = 0.2) - self.play(Write(surface)) - self.wait(1) - self.play(Write(l1)) - self.play(Write(d)) - self.wait(1) - self.add_fixed_in_frame_mobjects(f_text) - self.wait(3) - self.play(FadeOut(f_text),FadeOut(surface),FadeOut(axes),FadeOut(d_text),FadeOut(d),FadeOut(l1),FadeOut(label_x),FadeOut(label_y)) - - -#---- case 2: parial derivatives do not exist at critical point of the function -class secondScene(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- g(x,y)= |x|+|y| - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - abs(u)+abs(v) - ]),u_min = -1.5, u_max = 1.5, v_min = -1.5, v_max = 1.5, checkerboard_colors = [TEAL_E,TEAL_D,TEAL_C,TEAL_B]) - - d2 = Dot([0,0,0],color = '#800000') #---- critical point - - d2_text = TextMobject("$\\frac{\\partial f}{\\partial x}$ and/or $\\frac{\\partial f}{\\partial y}$ does not exist").scale(0.7).to_corner(UL) - - g_text = TextMobject("Critical Point",color = YELLOW).shift(1.2*RIGHT).scale(0.6) - - self.set_camera_orientation(phi = 60*DEGREES, theta = 40*DEGREES) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.add_fixed_in_frame_mobjects(d2_text) - self.begin_ambient_camera_rotation(rate = 0.2) - self.wait(1) - self.play(Write(surface2)) - self.wait(1) - self.play(Write(d2)) - self.wait(1) - self.add_fixed_in_frame_mobjects(g_text) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.gif b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.gif Binary files differdeleted file mode 100644 index 84acf2e..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py deleted file mode 100644 index 4b020e1..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py +++ /dev/null @@ -1,88 +0,0 @@ -from manimlib.imports import* -import math as m - -#---- tangent to the trace with x constant -class firstScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes().scale(1) - label_x = TextMobject("$x$").shift([5.8,-0.5,0]) - label_y = TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5) - - #---- graph of f(x,y) = -x^2-y^2 - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(1.5).shift([0,0,2]).rotate(0.2) - - #---- curve(trace) along y axis - curve = ParametricSurface( - lambda u, v: np.array([ - u*0.4, - v, - -v**2 - ]),v_min =-1 , v_max =1 , u_min = -0.1, u_max = 0.1).scale(1.6).shift([0.02,0.1,2.3]).set_color("#800000").rotate(0.1) - - d = Dot(color =YELLOW).shift([-0.05,-0.2,2.3]) #---- critical point - - x_text = TextMobject("Tangent to the trace with $x$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL) - - tangent_line = Line([-0.05,-1.5,2.3],[-0.05,1.5,2.3],color = '#228B22') - - self.add(axes) - self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES) - self.begin_ambient_camera_rotation(rate = 0.1) - self.add(label_x) - self.add(label_y) - self.play(Write(surface)) - self.add_fixed_in_frame_mobjects(x_text) - self.add(curve) - self.wait(1) - self.play(Write(tangent_line),Write(d)) - self.wait(1) - - - -#---- tangent to the trace with y constant -class secondScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes().scale(1) - label_x = TextMobject("$x$").shift([5.8,-0.5,0]) - label_y = TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5) - - #---- graph of f(x,y) = -x^2-y^2 - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,2]).rotate(0.2) - - #---- curve(trace) along x axis - curve = ParametricSurface( - lambda u, v: np.array([ - u, - v*0.4, - -u**2 - ]),v_min = -0.1, v_max = 0.1, u_min = -1, u_max = 1).scale(1.6).shift([0.07,0.1,2.3]).set_color("#800000") - - d = Dot(color = YELLOW).shift([0,-0.2,2.3]) #---- critical point - - tangent_line = Line(color = '#228B22').scale(1).shift([0,-0.2,2.3]).rotate(m.radians(190),LEFT) - - y_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL) - - self.add(axes) - self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES) - self.add(label_x) - self.add(label_y) - self.begin_ambient_camera_rotation(rate = 0.1) - self.play(Write(surface)) - self.add_fixed_in_frame_mobjects(y_text) - self.add(curve) - self.wait(1.5) - self.play(Write(tangent_line),Write(d)) - self.wait(0.5) diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.gif b/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.gif Binary files differdeleted file mode 100644 index 14fb318..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py deleted file mode 100644 index e674113..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py +++ /dev/null @@ -1,73 +0,0 @@ -from manimlib.imports import* - -#---- tangent plane to minima of the function -class firstScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- parabola: f(x,y) = x**2 + y**2 - parabola = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_E,GREEN_D,GREEN_C,GREEN_B], resolution = (20, 20)).scale(1) - - d = Dot(np.array([0,0,0]), color = '#800000') # ---- critical point - - tangent_plane = Rectangle(fill_color = '#C0C0C0', fill_opacity = 0.3).move_to(ORIGIN).fade(0.7) # ----tangent plane - - parabola_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL) - - self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES) - self.begin_ambient_camera_rotation(rate = 0.2) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.add_fixed_in_frame_mobjects(parabola_text) - self.wait(1) - self.play(Write(parabola)) - self.play(ShowCreation(d)) - self.wait(1) - self.play(ShowCreation(tangent_plane)) - self.wait(2) - self.play(FadeOut(parabola_text),FadeOut(parabola),FadeOut(tangent_plane),FadeOut(d),FadeOut(label_x),FadeOut(label_y),FadeOut(axes)) - - -#---- tangent plane to maxima of the function -class secondScene(ThreeDScene): - def construct(self): - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #----parabola: g(x,y) = -x**2-y**2 - parabola = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [BLUE_E,BLUE_D,BLUE_C,BLUE_B], resolution = (20, 20)).scale(1) - - d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point - - tangent_plane = Rectangle(fill_color = '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN).fade(0.7) #---- tangent plane - - parabola_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL) - - self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES) - self.begin_ambient_camera_rotation(rate = 0.2) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.add_fixed_in_frame_mobjects(parabola_text) - self.wait(1) - self.play(Write(parabola)) - self.play(ShowCreation(d)) - self.wait(1) - self.play(ShowCreation(tangent_plane)) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.gif b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.gif Binary files differdeleted file mode 100644 index 91e7084..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py deleted file mode 100644 index 656fb68..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py +++ /dev/null @@ -1,134 +0,0 @@ -from manimlib.imports import* - - -#---- Relative Maxima -class firstScene(ThreeDScene): - def construct(self): - - r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA') - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #----graph of the function f(x,y) = -x**2-y**2 - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E]).scale(1.5).shift([0,0,-0.51]).fade(0.3) - - f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL) - - d = Dot(color = "#800000").shift([0,0,0]) #---- critical point - - self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES) - self.add_fixed_in_frame_mobjects(r_text) - self.wait(1) - self.play(FadeOut(r_text)) - self.begin_ambient_camera_rotation(rate = 0.1) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.play(Write(surface),Write(d)) - self.add_fixed_in_frame_mobjects(f_text) - self.wait(2) - self.play(FadeOut(axes),FadeOut(surface),FadeOut(f_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y)) - - -#---- Relative Minima -class secondScene(ThreeDScene): - def construct(self): - - r2_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA') - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #----graph of the function g(x,y) = x**2+y**2 - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors =[TEAL_B,TEAL_C,TEAL_D,TEAL_E]).scale(1.5).shift([0,0,0.55]).fade(0.1) - - d = Dot(color = "#800000").shift([0,0,0]) #---- critical point - - g_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL) - - self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES) - self.add_fixed_in_frame_mobjects(r2_text) - self.wait(1) - self.play(FadeOut(r2_text)) - self.begin_ambient_camera_rotation(rate = 0.1) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.play(Write(surface),Write(d)) - self.add_fixed_in_frame_mobjects(g_text) - self.wait(2) - self.play(FadeOut(axes),FadeOut(surface),FadeOut(g_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y)) - - - -#---- Saddle Point -class thirdScene(ThreeDScene): - def construct(self): - - r3_text = TextMobject("Saddle Point", color = '#87CEFA') - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- graph of function h(x,y) = -x^2 + y^2 - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1,checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0]) - - #---- curve(trace) along x axis - curve_x = ParametricSurface( - lambda u, v: np.array([ - u*0.4, - v, - v**2 - ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.34]).scale(1.5).set_color("#800000") - - #---- curve(trace) along y axis - curve_y = ParametricSurface( - lambda u, v: np.array([ - u, - v*0.4, - -u**2 - ]),v_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color("#800000") - - d = Dot(color = GREEN).shift([0,0,0.1]) #---- critical point - - h_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) - - self.add_fixed_in_frame_mobjects(r3_text) - self.wait(1) - self.set_camera_orientation(phi = 50 * DEGREES,theta = 45 * DEGREES) - self.play(FadeOut(r3_text)) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.begin_ambient_camera_rotation(rate = 0.3) - self.add_fixed_in_frame_mobjects(h_text) - self.play(Write(surface)) - self.wait(1) - self.add(curve_y) - self.add(d) - self.wait(1) - self.play(FadeOut(curve_y)) - self.wait(1) - self.add(curve_x) - self.wait(1) - self.add(d) - self.wait(1) diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).gif b/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).gif Binary files differdeleted file mode 100644 index 4bc92f8..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).py b/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).py deleted file mode 100644 index 41c3b61..0000000 --- a/FSF-2020/approximations-and-optimizations/Critical-Points/file5_f(x,y)=(y-x)(1-2x-3y).py +++ /dev/null @@ -1,29 +0,0 @@ -from manimlib.imports import* - -#---- visualization of the function -class ExampleAnimation(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- f(x,y) = (y-x)(1-2x-3y) - surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - (v-u)*(1-2*u-3*v) - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D, PURPLE_E]).scale(1).fade(0.2).shift([0.2,0.2,0]) - - f_text = TextMobject("$f(x,y) = (y-x)(1-2x-3y)$").to_corner(UL) - - self.set_camera_orientation(phi = 60 * DEGREES, theta = 75 * DEGREES) - self.begin_ambient_camera_rotation(rate=0.1) - self.add_fixed_in_frame_mobjects(f_text) - self.wait(1) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.wait(1) - self.play(Write(f)) - self.wait(4) diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.gif b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.gif Binary files differdeleted file mode 100644 index 2b8bf5f..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py deleted file mode 100644 index 4c17f90..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file1_Tangent_Plane.py +++ /dev/null @@ -1,50 +0,0 @@ -from manimlib.imports import* - -#---- tangent plane is parallel to the surface of the funtion at a point -class firstScene(ThreeDScene): - def construct(self): - - s1_text=TextMobject("Suppose, the point $(x,y)$ lies on the surface of the function.").scale(0.5).shift(2*UP) - s2_text=TextMobject("When zooming on that point, the surface would appear more and more like a plane.").scale(0.5).shift(1*UP) - s3_text=TextMobject("This plane is called the tangent plane.").scale(0.5) - - #---- graph of function f(x,y) = -x^2-y^2 - - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E]).shift([0,0,0]).scale(1) - - - d = Dot([0,0,0],color = '#800000') #---- critical point - - r = Rectangle(color = PURPLE,fill_opacity=0.2).shift([0.1,0,0]).scale(0.3) #---- tangent plane - - s = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E]).shift([0,0,0]).scale(3.5) - - d2 = Dot([0,0,2.5],color = '#800000') #---- changing position of critical point - - r2 = Rectangle(color = PURPLE,fill_opacity=0.5).shift([0.1,0,2.5]).scale(0.3) #---- changing position of tangent plane - - self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES) - self.add_fixed_in_frame_mobjects(s1_text) - self.add_fixed_in_frame_mobjects(s2_text) - self.add_fixed_in_frame_mobjects(s3_text) - self.wait(2) - self.play(FadeOut(s1_text)) - self.play(FadeOut(s2_text)) - self.play(FadeOut(s3_text)) - self.wait(1) - self.play(Write(f)) - self.play(Write(d)) - self.play(Write(r)) - self.wait(2) - self.play(ReplacementTransform(f,s),ReplacementTransform(d,d2),ReplacementTransform(r,r2)) - self.wait(2) 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 984db16..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py +++ /dev/null @@ -1,34 +0,0 @@ -from manimlib.imports import* - -class TangenttoSurface(ThreeDScene): - - def construct(self): - axes = ThreeDAxes() - - #----f(x,y): x**2+y**2 - p = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u**2+v**2 - ]),v_min = -1,v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_C,GREEN_D], - resolution = (20, 20)).scale(1) - self.set_camera_orientation(phi = 75*DEGREES) - - h_text = TextMobject("The graph tends to coincide with its tangent plane").scale(0.5).to_corner(UL) - d = Dot([0,0,0],color ='#800000') #----critical point - r = Rectangle(height = 2,breadth = 1,color = YELLOW).scale(0.5) #----tangent plane to critical point - line1 = DashedLine(color=RED).shift(4*UP+1.3*RIGHT).rotate(1.571,UP).scale(1.2) - line2 = DashedLine(color=RED).shift(4*UP-1.3*RIGHT).rotate(1.571,UP).scale(1.2) - - r2 = Rectangle(height = 2, breadth = 1,color = GREEN, fill_opacity=0.3).scale(0.5) - - self.add(axes) - self.play(Write(r)) - self.play(Write(p),Write(d)) - self.play(ShowCreation(line1),ShowCreation(line2)) - self.wait(2) - - self.play(FadeOut(line1),FadeOut(line2),ReplacementTransform(p,r2)) - self.add_fixed_in_frame_mobjects(h_text) - self.wait(1) diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file3_non_differentiable_function.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file3_non_differentiable_function.py deleted file mode 100644 index 13bd73e..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file3_non_differentiable_function.py +++ /dev/null @@ -1,30 +0,0 @@ -from manimlib.imports import* -import math - -#---- tangent plane does not exists for f(x,y): sqrt(x**2+y**2) at origin - -class TangenttoSurface(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - #----f(x,y): sqrt(x**2+y**2) - p = ParametricSurface( - lambda u, v: np.array([ - u, - v, - math.sqrt(u**2+v**2) - ]),v_min = -1,v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_C,TEAL_D], - resolution = (20, 20)).scale(1) - - self.set_camera_orientation(phi = 75 * DEGREES) - - d = Dot([0,0,0],color = '#800000') #----critical point - d_text = TextMobject("$(0,0)$").scale(0.5).shift(0.2*DOWN) - f_text = TextMobject("$f$ is not differentiable at origin").scale(0.5).to_corner(UL) - - self.begin_ambient_camera_rotation(rate=0.1) - self.add(axes) - self.play(Write(p),Write(d)) - self.add_fixed_in_frame_mobjects(d_text) - self.add_fixed_in_frame_mobjects(f_text) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py deleted file mode 100644 index d129213..0000000 --- a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py +++ /dev/null @@ -1,62 +0,0 @@ -from manimlib.imports import* - -class TangenttoSurface(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - #----graph of first function f(x,y) = -x**2-y**2 - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_D, YELLOW_E], - resolution = (20, 20)).scale(1) - f_text = TextMobject("Tangent plane at relative maxima").to_corner(UL).scale(0.5) - - #----graph of second function f(x,y) = -x**2+y**2 - f2 = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_D, RED_E], - resolution = (20, 20)).scale(1) - f2_text = TextMobject("Tangent plane at saddle point").to_corner(UL).scale(0.5) - - #----graph of third function f(x,y) = x**2+y**2 - f3 = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u**2+v**2 - ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_D, GREEN_E], - resolution = (20, 20)).scale(1) - f3_text = TextMobject("Tangent plane at relative minima").to_corner(UL).scale(0.5) - - self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) - d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point - - r = Rectangle(height = 2,breadth = 1,color = PURPLE).scale(0.5) - - self.begin_ambient_camera_rotation(rate = 0.3) - self.add(axes) - self.play(Write(f),Write(d)) - self.wait(1) - self.add_fixed_in_frame_mobjects(f_text) - self.play(ShowCreation(r)) - self.wait(1) - self.play(FadeOut(r),FadeOut(f),FadeOut(d),FadeOut(f_text)) - self.wait(1) - self.play(Write(f2),Write(d)) - self.wait(1) - self.add_fixed_in_frame_mobjects(f2_text) - self.play(ShowCreation(r)) - self.wait(1) - self.play(FadeOut(r),FadeOut(f2),FadeOut(d),FadeOut(f2_text)) - self.wait(1) - self.play(Write(f3),Write(d)) - self.wait(1) - self.add_fixed_in_frame_mobjects(f3_text) - self.play(ShowCreation(r)) - self.wait(1) diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.gif b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.gif Binary files differdeleted file mode 100644 index 3471e4d..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.py b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.py deleted file mode 100644 index 84052cc..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file1_Second_order_partial_derivatives.py +++ /dev/null @@ -1,78 +0,0 @@ -from manimlib.imports import* - -#---- graphs of second-order partial derivatives of a function -class SurfacesAnimation(ThreeDScene): - def construct(self): - - axes = ThreeDAxes() - x_label = TextMobject('$x$').shift([5,0.5,0]) #---- x axis - y_label = TextMobject('$y$').shift([0.5,4,0]).rotate(-4.5) #---- y axis - - #---- surface of function: f(x,y) = (x^2+y^2)^2 - surface_f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - ((u**2)+(v**2))**2 - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[GREEN_D, GREEN_E]).scale(1) - - #---- surface of second-order partial derivative f_xx - surface_fxx = ParametricSurface( - lambda u, v: np.array([ - u, - v, - (3*u**2)+(v**2) - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[YELLOW_D, YELLOW_E]).shift([0,0,0]).scale(0.6) - - #---- surface of second-order partial derivative f_yy - surface_fyy = ParametricSurface( - lambda u, v: np.array([ - u, - v, - (u**2)+(3*v**2) - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[PURPLE_D, PURPLE_E]).scale(0.6).shift([0,0,0]) - - #---- surface of second-order partial derivative f_xy = f_yx - surface_fxy = ParametricSurface( - lambda u, v: np.array([ - u, - v, - 8*u*v - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[TEAL_D, TEAL_E]).scale(0.6) - - f_text= TextMobject("$f(x,y) = (x^2+y^2)^2$",color = GREEN).scale(0.7).to_corner(UL) - - fxx_text= TextMobject("$f_{xx} = 12x^2+4y^2$ (Concavity along x axis)",color = YELLOW).scale(0.5).to_corner(UL) - - fyy_text= TextMobject("$f_{yy} = 4x^2+12y^2$(Concavity along y axis)",color = PURPLE).scale(0.5).to_corner(UL) - - fxy_text= TextMobject("$f_{xy} = f_{yx} = 8xy$ (Twisting of the function)",color = TEAL).scale(0.5).to_corner(UL) - - - self.set_camera_orientation(phi = 40 * DEGREES, theta = 45 * DEGREES) - self.begin_ambient_camera_rotation(rate = 0.1) - self.add_fixed_in_frame_mobjects(f_text) - self.add(axes) - self.add(x_label) - self.add(y_label) - self.wait(1) - self.play(Write(surface_f)) - self.wait(2) - self.play(FadeOut(f_text)) - - - self.play(ReplacementTransform(surface_f,surface_fxx)) - - self.add_fixed_in_frame_mobjects(fxx_text) - self.wait(2) - self.play(FadeOut(fxx_text)) - - self.play(ReplacementTransform(surface_fxx,surface_fyy)) - self.add_fixed_in_frame_mobjects(fyy_text) - self.wait(2) - self.play(FadeOut(fyy_text)) - - self.play(ReplacementTransform(surface_fyy,surface_fxy)) - self.move_camera(phi = 35 * DEGREES, theta = 80 * DEGREES) - self.add_fixed_in_frame_mobjects(fxy_text) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file2_Degenerate_Hessian_Matrix.py b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file2_Degenerate_Hessian_Matrix.py deleted file mode 100644 index c1e3516..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file2_Degenerate_Hessian_Matrix.py +++ /dev/null @@ -1,52 +0,0 @@ -from manimlib.imports import* - -class firstscene(Scene): - def construct(self): - - h_text = TextMobject("Degenerate Hessian Matrix", color = RED).scale(1).shift(UP) - - - f_text = TextMobject("$f(x,y) = 2x^3+y^3$", color = TEAL).scale(1).to_corner(UL) - c_text = TextMobject("Critical Point: $(0,0)$", color = TEAL).scale(1).next_to(f_text).shift(DOWN+4.3*LEFT) - m_text = TextMobject("\\begin{equation*} D_2(x,y)= \\begin{vmatrix} 12x\\space & 0\\space \\\\ 0 & 6y \\end{vmatrix} \\end{equation*}",color = YELLOW) - d_text = TextMobject("\\begin{equation*} D_2(0,0)= \\begin{vmatrix} 0 \\space & 0\\space \\\\ 0 & 0 \\end{vmatrix} \\end{equation*}",color = PURPLE) - - - t_text = TextMobject("$D_2 = 0$(Inconclusive)", color = TEAL).scale(1).shift(2*DOWN) - - self.play(ShowCreation(h_text)) - self.wait(1) - self.play(FadeOut(h_text)) - self.wait(1) - self.play(ShowCreation(f_text)) - self.wait(1) - self.play(ShowCreation(c_text)) - self.wait(1) - self.play(ShowCreation(m_text)) - self.wait(2) - self.play(ReplacementTransform(m_text,d_text)) - self.wait(1) - self.play(ShowCreation(t_text)) - self.wait(2) - - -class SecondScene(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - (2*u**3)+v**3 - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[TEAL_C,YELLOW_D,BLUE_E], - resolution=(20, 20)).scale(1) - - self.set_camera_orientation(phi=25 * DEGREES,theta = 80*DEGREES) - self.begin_ambient_camera_rotation(rate=0.1) - - f_text = TextMobject("$f(x,y) = 2x^3+y^3$",color = ORANGE).shift(2*DOWN+2*RIGHT).scale(0.8) - self.add_fixed_in_frame_mobjects(f_text) - self.add(axes) - self.play(Write(f)) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file3_Nondegenerate_Hessian_Matrix.py b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file3_Nondegenerate_Hessian_Matrix.py deleted file mode 100644 index 3056842..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file3_Nondegenerate_Hessian_Matrix.py +++ /dev/null @@ -1,145 +0,0 @@ -from manimlib.imports import* - -class firstScene(Scene): - def construct(self): - - e_text = TextMobject("Case 3: One positive and one negative eigenvalue", color = YELLOW).scale(1).shift(3*UP+1*LEFT) - f_text = TextMobject("$f(x,y) = x^2-2y^2-2x$").scale(0.8).next_to(e_text).shift(6*LEFT+DOWN) - c_text = TextMobject("Critical Point: $(1,0)$").scale(0.8).next_to(f_text).shift(DOWN+4*LEFT) - d_text = TextMobject("\\begin{equation*} D_2(1,0)= \\begin{vmatrix} 2 \\space & 0\\space \\\\ 0 & -4 \\end{vmatrix} \\end{equation*}",color = GREEN).scale(0.9) - - t_text = TextMobject("$D_2 = -8<0$ (Saddle Point)", color = BLUE).scale(0.9).shift(2*DOWN) - - self.play(ShowCreation(e_text)) - self.wait(1) - self.play(ShowCreation(f_text)) - self.wait(1) - self.play(ShowCreation(c_text)) - self.wait(1) - self.play(ShowCreation(d_text)) - self.wait(1) - self.play(ShowCreation(t_text)) - self.wait(2) - -class SaddlePoint(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - u**2-2*v**2-2*u - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[RED_C,PURPLE_D,YELLOW_E], - resolution=(20, 20)).scale(1) - - self.set_camera_orientation(phi=35 * DEGREES,theta=80*DEGREES) - self.begin_ambient_camera_rotation(rate=0.4) - - f_text = TextMobject("$f(x,y) = x^2-2y^2-2x$",color = GREEN).shift(2*DOWN+2*RIGHT).scale(0.8) - self.add_fixed_in_frame_mobjects(f_text) - self.add(axes) - self.play(Write(f)) - self.wait(3) - - -class secondScene(Scene): - def construct(self): - - h_text = TextMobject("NonDegenerate Hessian Matrix", color = GREEN).scale(1).shift(UP) - e_text = TextMobject("Case 1: Two positive eigenvalues", color = PINK).scale(1).shift(3*UP+2*LEFT) - f_text = TextMobject("$f(x,y) = 2x^2+3y^2-2yx$",color = TEAL).scale(0.8).next_to(e_text).shift(6*LEFT+DOWN) - c_text = TextMobject("Critical Point: $(0,0)$",color = TEAL).scale(0.8).next_to(f_text).shift(DOWN+4.5*LEFT) - d_text = TextMobject("\\begin{equation*} D_2(0,0)= \\begin{vmatrix} 4 \\space & -2\\space \\\\ -2 & 6 \\end{vmatrix} \\end{equation*}",color = PINK).scale(0.9) - - t_text = TextMobject("$D_2 = 20>0$ (Relative Maxima or Relative Minima)", color = YELLOW).scale(0.9).shift(1*DOWN) - tm_text = TextMobject("$D_1 = \\frac{\\partial^2 f}{\\partial x^2} =4 >0$ (Relative Minima)", color = YELLOW).scale(0.9).shift(2*DOWN) - - - self.play(ShowCreation(h_text)) - self.wait(1) - self.play(FadeOut(h_text)) - self.wait(1) - self.play(ShowCreation(e_text)) - self.wait(1) - self.play(ShowCreation(f_text)) - self.wait(1) - self.play(ShowCreation(c_text)) - self.wait(1) - self.play(ShowCreation(d_text)) - self.wait(1) - self.play(ShowCreation(t_text)) - self.wait(1) - self.play(ShowCreation(tm_text)) - self.wait(2) - self.play(FadeOut(e_text),FadeOut(f_text),FadeOut(c_text),FadeOut(d_text),FadeOut(t_text),FadeOut(tm_text)) - -class Minima(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - 2*u**2+3*v**2-2*v*u - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[BLUE_C,YELLOW_D,GREEN_E], - resolution=(20, 20)).scale(1) - - self.set_camera_orientation(phi=10 * DEGREES,theta=90*DEGREES) - self.begin_ambient_camera_rotation(rate=0.2) - - f_text = TextMobject("$f(x,y) = 2x^2+3y^2-2yx$",color = PURPLE).shift(2*DOWN+3*RIGHT).scale(0.8) - self.add_fixed_in_frame_mobjects(f_text) - self.add(axes) - self.play(Write(f)) - self.wait(2) - - -class thirdScene(Scene): - def construct(self): - - - e_text = TextMobject("Case 2: Two negative eigenvalues", color = RED).scale(1).shift(3*UP+2*LEFT) - f_text = TextMobject("$f(x,y) = -x^2-4y^2$",color = BLUE).scale(0.8).next_to(e_text).shift(6*LEFT+DOWN) - c_text = TextMobject("Critical Point: $(0,0)$",color = BLUE).scale(0.8).next_to(f_text).shift(DOWN+3.8*LEFT) - d_text = TextMobject("\\begin{equation*} D_2(0,0)= \\begin{vmatrix} -2 \\space & 0\\space \\\\ 0 & -8 \\end{vmatrix} \\end{equation*}",color = TEAL).scale(0.9) - - t_text = TextMobject("$D_2 = 16>0$ (Relative Maxima or Relative Minima)" ).scale(0.9).shift(1*DOWN) - tm_text = TextMobject("$D_1 = \\frac{\\partial^2 f}{\\partial x^2} =-2 <0$ (Relative Maxima)").scale(0.9).shift(2*DOWN) - - - self.play(ShowCreation(e_text)) - self.wait(1) - self.play(ShowCreation(f_text)) - self.wait(1) - self.play(ShowCreation(c_text)) - self.wait(1) - self.play(ShowCreation(d_text)) - self.wait(1) - self.play(ShowCreation(t_text)) - self.wait(1) - self.play(ShowCreation(tm_text)) - self.wait(2) - self.play(FadeOut(e_text),FadeOut(f_text),FadeOut(c_text),FadeOut(d_text),FadeOut(t_text),FadeOut(tm_text)) - - -class Maxima(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - f = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -u**2-4*v**2 - ]),v_min=-1,v_max=1,u_min=-1,u_max=1,checkerboard_colors=[BLUE_C,PURPLE_D,TEAL_E], - resolution=(20, 20)).scale(1) - - self.set_camera_orientation(phi=75 * DEGREES) - self.begin_ambient_camera_rotation(rate=0.4) - - f_text = TextMobject("$f(x,y) = -x^2-4y^2$",color = YELLOW).shift(2*DOWN+3*RIGHT).scale(0.8) - self.add_fixed_in_frame_mobjects(f_text) - self.add(axes) - self.play(Write(f)) - self.wait(1) - self.move_camera(phi=30*DEGREES,theta=45*DEGREES,run_time=5) - self.wait(2) diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif Binary files differdeleted file mode 100644 index 129fedc..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif +++ /dev/null diff --git a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py b/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py deleted file mode 100644 index d3084e2..0000000 --- a/FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py +++ /dev/null @@ -1,120 +0,0 @@ -from manimlib.imports import* - -#---- contour diagram animation -class ContourDiagram(ThreeDScene): - def construct(self): - - heading = TextMobject("CONTOUR DIAGRAM", color = YELLOW).scale(1) - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis - - #---- surface of a paraboloid - surface = ParametricSurface( - lambda u, v: np.array([ - np.cos(v)*u, - np.sin(v)*u, - u**2 - ]),v_min = -2, v_max = 2, u_min = -2, u_max = 2, checkerboard_colors = [GREEN_B,GREEN_C,GREEN_D,GREEN_E]).shift([0,0,0]).scale(0.5) - - #---- first contour projection - contour1 = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2*(1 - 2.5*u) - ])).fade(0.5).scale(0.21).shift([0,0,1.01]) - - #---- first contour line - c_1 = Circle(color = BLUE).scale(0.21).shift([0,0,0]).rotate(0.1,DOWN) - - #------------------------------------------------- - - #---- second contour projection - contour2 = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2*(1 - 1.6*u) - ])).fade(0.5).scale(0.41).shift([0,0,0.3]).set_color(RED) - - #---- second contour line - c_2 = Circle(color = RED).scale(0.41).shift([0,0,0]).rotate(0.1,DOWN) - - #------------------------------------------------- - - #---- third contour projection - contour3 = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2*(1 - 1.5*u) - ])).fade(0.5).scale(0.61).shift([0,0,0.4]).set_color(YELLOW) - - #---- third contour line - c_3 = Circle(color = YELLOW).scale(0.61).shift([0,0,0]) - - #------------------------------------------------- - - #---- fourth contour projection - contour4 = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2*(1 - 1.5*u) - ])).fade(0.7).scale(0.81).shift([0,0,0.7]).set_color(PINK) - - #---- fourth contour line - c_4 = Circle(color = PINK).scale(0.81).shift([0,0,0]) - - #------------------------------------------------- - - #---- fifth contour projection - contour5 = ParametricSurface( - lambda u, v: np.array([ - np.cos(TAU * v), - np.sin(TAU * v), - 2*(1 - 1.5*u) - ])).fade(0.7).scale(1.01).shift([0,0,1]).set_color(PURPLE) - - #---- fifth contour line - c_5 = Circle(color = PURPLE).scale(1.01).shift([0,0,0]) - - c_text= TextMobject("Contour Lines").scale(0.5).shift(2*DOWN) - s = Square().scale(1.3) - - self.set_camera_orientation(phi = 75 * DEGREES, theta = 10 * DEGREES) - self.add_fixed_in_frame_mobjects(heading) - self.wait(1) - self.play(FadeOut(heading)) - self.wait(1) - self.add(axes) - self.add(label_x) - self.add(label_y) - self.play(Write(surface)) - self.wait(1) - self.add(contour1) - self.wait(1) - self.play(Write(c_1)) - self.play(ReplacementTransform(contour1,contour2)) - self.wait(1) - self.play(Write(c_2)) - self.play(ReplacementTransform(contour2,contour3)) - self.wait(1) - self.play(Write(c_3)) - self.play(ReplacementTransform(contour3,contour4)) - self.wait(1) - self.play(Write(c_4)) - self.play(ReplacementTransform(contour4,contour5)) - self.wait(1) - self.play(Write(c_5)) - self.wait(1) - self.play(FadeOut(contour5),FadeOut(axes),FadeOut(label_x),FadeOut(label_y),FadeOut(surface),FadeOut(contour5),FadeOut(contour4),FadeOut(contour3),FadeOut(contour2),FadeOut(contour1)) - self.wait(1) - self.move_camera(phi=0 * DEGREES,theta= 90*DEGREES) - self.wait(1) - self.add_fixed_in_frame_mobjects(c_text) - self.wait(1) - self.play(ShowCreation(s),FadeOut(c_text)) - self.wait(1) |
%3d(y-x)(1-2x-3y).gif?id=ed86b5f6d84efe35cea6b63b4f7d6afce8cde4b7){kind=link}
