diff options
Diffstat (limited to 'FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations')
5 files changed, 0 insertions, 176 deletions
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) |
