diff options
| -rw-r--r-- | FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py | 172 |
1 files changed, 99 insertions, 73 deletions
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 index 42703ba..656fb68 100644 --- 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 @@ -1,108 +1,134 @@ -from manimlib.imports import * +from manimlib.imports import* + - -class MaximaScene(ThreeDScene): +#---- Relative Maxima +class firstScene(ThreeDScene): def construct(self): - axes = ThreeDAxes() - + r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA') - f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL) - #----graph of first function f(x,y) = -x**2-y**2 - f = ParametricSurface( + 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], - resolution = (20, 20)).scale(1.5).shift([0,0,-0.51]).fade(0.3) - - d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point - - self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) + ]),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.play(Write(f),Write(d)) + 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(f),FadeOut(f_text),FadeOut(d)) - -class SaddlePoint(ThreeDScene): + 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("Saddle Point",color ='#87CEFA') + r2_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA') + axes = ThreeDAxes() - - #----graph of third 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 = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0]) - - #---- trace along y axis - a = ParametricSurface( - lambda u, v: np.array([ - u, - v, - v**2 - ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.36]).scale(1.5).set_color(GREEN) - - #---- trace along x axis - b = ParametricSurface( + 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_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color(GREEN) - - d = Dot(color = '#800000').shift([0,0,0.1]) #---- critical point - - f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL) + 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.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) self.play(FadeOut(r2_text)) - self.add(axes) - self.begin_ambient_camera_rotation(rate=0.4) - self.add_fixed_in_frame_mobjects(f2_text) - self.play(Write(f2)) - self.add(b) - self.wait(1) - self.add(a) - self.wait(3) - self.add(d) + 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) - - -class MinimaScene(ThreeDScene): + 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("Relative Minimum at ORIGIN",color ='#87CEFA') + + r3_text = TextMobject("Saddle Point", color = '#87CEFA') + axes = ThreeDAxes() - - f3_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL) - - #----graph of third function f(x,y) = x**2+y**2 - f3 = ParametricSurface( + 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 =[TEAL_B,TEAL_C,TEAL_D,TEAL_E], - resolution = (20, 20)).scale(1.5).shift([0,0,0.55]).fade(0.1) + -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]) - self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES ) - d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point + #---- 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.play(Write(f3),Write(d)) - self.add_fixed_in_frame_mobjects(f3_text) - self.wait(2) + 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) |