diff options
| -rw-r--r-- | FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py | 82 |
1 files changed, 51 insertions, 31 deletions
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 index b066d04..e674113 100644 --- 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 @@ -1,53 +1,73 @@ from manimlib.imports import* -class TangentPlane(ThreeDScene): +#---- 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: x**2+y**2 - parabola1 = ParametricSurface( + #---- 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) + ]),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) - #----parabola: -x**2-y**2 - parabola2 = 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) - - self.set_camera_orientation(phi=75 * DEGREES) - self.begin_ambient_camera_rotation(rate=0.2) - - d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point - r = Rectangle(fill_color= '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN).fade(0.7) #----tangent plane + d = Dot(np.array([0,0,0]), color = '#800000') # ---- critical point - parabola1_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL) + tangent_plane = Rectangle(fill_color = '#C0C0C0', fill_opacity = 0.3).move_to(ORIGIN).fade(0.7) # ----tangent plane - parabola2_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL) + 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_fixed_in_frame_mobjects(parabola2_text) + self.add(label_x) + self.add(label_y) + self.add_fixed_in_frame_mobjects(parabola_text) self.wait(1) - self.play(Write(parabola1)) + self.play(Write(parabola)) self.play(ShowCreation(d)) self.wait(1) - self.play(ShowCreation(r)) + self.play(ShowCreation(tangent_plane)) self.wait(2) - self.play(FadeOut(parabola2_text),FadeOut(parabola1),FadeOut(r),FadeOut(d)) + 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 - self.wait(1) - self.add_fixed_in_frame_mobjects(parabola1_text) - self.wait(1) - self.play(Write(parabola2)) + #----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(r)) - self.wait(1) + self.play(ShowCreation(tangent_plane)) + self.wait(2) |