diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py | 38 |
1 files changed, 13 insertions, 25 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py index da17aac..a01efb0 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py @@ -5,33 +5,26 @@ import math as m class ConstrainedExtrema(ThreeDScene): def construct(self): axes = ThreeDAxes().fade(0.4) - label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis - label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + 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( lambda u, v: np.array([ u, v, u**2+v**2+u**3-v**3 - ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.4) + ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.2) - c = Circle().set_color('#FF00FF').shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7) + c = Circle(color='#FF00FF',fill_opacity=0.3).shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7) minima = Dot(color = '#4169E1').shift([-0.5,0.5,1]).rotate(1.571,UP) - maxima = Dot(color = '#4169E1').shift([0.1,0,2.2]).rotate(1.571,UP) + maxima = Dot(color = '#4169E1').shift([0.1,0,2.2]).rotate(1.571,UP) - l1 = DashedLine([-0.5,0.5,0.9],[-0.5,0.5,0],color = '#F08080') - l2 = DashedLine([0.1,0,2.1],[0.1,0,0],color = '#F08080') - - c2 = Circle(fill_opacity= 0.5).shift([-0.3,0.2,0]).scale(0.4) - - minima_refl = Dot(color = '#4682B4').shift([-0.5,0.5,0]).rotate(1.571,UP) - maxima_refl = Dot(color = '#4682B4').shift([0.1,0,0]).rotate(1.571,UP) - - max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-1.7,0,0]).scale(0.5).shift(2.2*UP) - min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.5).shift(0.5*UP) - label_f = TextMobject("$z=f(x,y)$",color = '#8A2BE2').scale(0.5).shift(3*UP+3*RIGHT) - label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT) + max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').scale(0.6).shift(2.3*UP+2*LEFT) + min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.6).shift(0.5*UP) + label_f = TextMobject("$z=f(x,y)$",color=TEAL).scale(0.8).shift(3*UP+3*RIGHT) + label_g = TextMobject("g(x,y)=k",color = PURPLE).scale(0.5).shift(1.5*UP+0.8*LEFT) + self.add(axes) self.add(label_x) @@ -42,16 +35,11 @@ class ConstrainedExtrema(ThreeDScene): self.wait(2) self.play(Write(c)) self.wait(1) + self.add_fixed_in_frame_mobjects(label_g) + self.wait(1) self.play(Write(maxima)) self.add_fixed_in_frame_mobjects(max_text) self.wait(1) self.play(Write(minima)) self.add_fixed_in_frame_mobjects(min_text) - self.wait(1) - self.play(ShowCreation(l1),ShowCreation(l2)) - self.play(Write(c2)) - self.add_fixed_in_frame_mobjects(label_g) - self.wait(1) - self.play(Write(maxima_refl)) - self.play(Write(minima_refl)) - self.wait(1) + self.wait(1) |