diff options
Diffstat (limited to 'FSF-2020/approximations-and-optimizations')
| -rw-r--r-- | FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py | 94 |
1 files changed, 55 insertions, 39 deletions
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 index f3c16d4..e8cb08d 100644 --- 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 @@ -1,61 +1,77 @@ from manimlib.imports import* import math as m - -class CriticalPoint(ThreeDScene): +#---- 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 - surface = ParametricSurface( #---- partial derivatives of the funtion exists + #---- 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]).fade(0.6).scale(3.5).shift([0,0,1.5]) - - surface2 = ParametricSurface( #---- partial derivatives of the funtion does not exists - 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]) + 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 of surface - - d2 = Dot([0,0,0],color = '#800000') #---- critical point of surface2 - - d_text = TextMobject("$\\frac{\\partial f}{\\partial x}=\\frac{\\partial f}{\\partial y} = 0$").scale(1).to_corner(UL) - - d2_text = TextMobject("$\\frac{\\partial f}{\\partial x}$ and/or $\\frac{\\partial f}{\\partial y}$ does not exist").scale(0.8).to_corner(UL) - - f_text = TextMobject("Critical Point of a function",color = YELLOW).shift([3,0,3.7]).scale(0.7) + d = Dot([0,0,3.75],color = '#800000') #---- critical point - g_text = TextMobject("Critical Point of a function",color = YELLOW).shift(1*DOWN).scale(0.5) - - self.set_camera_orientation(phi=75*DEGREES,theta=90*DEGREES) - self.add(axes) - self.begin_ambient_camera_rotation(rate=0.2) - self.play(Write(surface)) + 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.move_camera(phi=0 * DEGREES,theta = 90*DEGREES) - self.wait(2) self.add_fixed_in_frame_mobjects(f_text) - self.play(FadeOut(f_text),FadeOut(surface),FadeOut(axes),FadeOut(d_text),FadeOut(d),FadeOut(l1)) - self.wait(1) - self.set_camera_orientation(phi=75*DEGREES,theta=60*DEGREES) - self.add(axes) - self.begin_ambient_camera_rotation(rate=0.3) - self.add_fixed_in_frame_mobjects(d2_text) - self.wait(1) + 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)) - l1.fade(0.4) - self.play(Write(l1)) - self.play(Write(d2)) + self.wait(1) + self.play(Write(d2)) + self.wait(1) self.add_fixed_in_frame_mobjects(g_text) - self.wait(2) - + self.wait(2) |