diff options
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py | 72 |
1 files changed, 72 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py new file mode 100644 index 0000000..bbbf238 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Constraint_circle_with_contour_plot_of_the_surface_x^2+y^2+x^3-y^3.py @@ -0,0 +1,72 @@ +from manimlib.imports import* +import math as m + +#---- contour plot of the surface with constraint circle +class ContourScene(ThreeDScene): + def construct(self): + axes = ThreeDAxes().scale(0.7).rotate(m.radians(180)).fade(0.6) + label_x = TextMobject("$x$").shift(4*LEFT).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift(3.2*DOWN+0.2*RIGHT).rotate(m.radians(180)).fade(0.4) #---- y axis + + #---- surface of the function f(x,y) = x^2+y^2+x^3-y^3 + 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,-0.5,2.5]).set_color(TEAL).fade(0.5) + + + #---- contour plots of the surface of the function + + c0 = Circle(color = '#800000').scale(0.5).shift([0,-0.5,0]) + c1 = Circle(color = '#800000').scale(1).shift([0,-0.5,0]) + c2 = Circle(color = '#800000').scale(1.5).shift([0,-0.5,0]) + c3 = Circle(color = '#800000').scale(2).shift([0,-0.5,0]) + c4 = Circle(color = '#800000').scale(2.5).shift([0,-0.5,0]) + + #---- constraint circle + circle = Circle(color='#FF00FF',fill_opacity=0.3).shift([-0.5,-1.2,1.5]).rotate(1.9,UP).scale(0.8) + circle2 = Circle(color='#FF00FF',fill_opacity=0.3).shift([0.74,0.95,1.5]).rotate(1.9,UP).scale(0.8) + + maxima = Dot(color = '#4169E1').shift([0.7,0.15,1.5]) #---- point of maxima + minima = Dot(color = '#4169E1').shift([0.8,1.7,1.5]) #---- point of minima + + min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').scale(0.6).shift([-2,0.16,1.5]) + max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-2.3,-2.6,1.5]).scale(0.6).shift(0.5*UP) + + + #---- labelling contour curves + label_c0 = TextMobject("1",color = '#FFA074').shift([0.2,0.1,0.5]).scale(0.5) + label_c1 = TextMobject("2",color = '#FFA074').shift([0.2,-0.6,0.5]).scale(0.5) + label_c2 = TextMobject("3",color = '#FFA074').shift([0.2,-1.1,0.5]).scale(0.5) + label_c3 = TextMobject("4",color = '#FFA074').shift([0.2,-1.6,0.5]).scale(0.5) + label_c4 = TextMobject("5",color = '#FFA074').shift([0.2,-2.1,0.5]).scale(0.5) + + + self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES) + self.add(axes) + self.add(label_x) + self.add(label_y) + self.wait(1) + self.play(Write(surface)) + self.play(Write(circle)) + self.wait(1) + self.play(FadeOut(circle)) + self.wait(1) + self.move_camera(phi=0 * DEGREES, theta = 90*DEGREES) + self.wait(1) + self.play(Write(c0),Write(c1),Write(c2),Write(c3),Write(c4)) + self.play(FadeOut(surface)) + self.add_fixed_in_frame_mobjects(label_c0) + self.add_fixed_in_frame_mobjects(label_c1) + self.add_fixed_in_frame_mobjects(label_c2) + self.add_fixed_in_frame_mobjects(label_c3) + self.add_fixed_in_frame_mobjects(label_c4) + self.wait(1) + self.play(Write(circle2)) + self.wait(1) + self.play(Write(minima),Write(maxima)) + self.add_fixed_in_frame_mobjects(max_text) + self.add_fixed_in_frame_mobjects(min_text) + self.wait(1) |