diff options
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py | 49 |
1 files changed, 30 insertions, 19 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py index 742d6b5..a1396fc 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py @@ -1,41 +1,52 @@ from manimlib.imports import* import math as m -class firstScene(ThreeDScene): + class Constraints(ThreeDScene): def construct(self): - axes = ThreeDAxes() - 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 - - #---- constraint g(x,y) + axes = ThreeDAxes().rotate(m.radians(75)) + label_x = TextMobject("$x$").shift([-5.5,1,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([1,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + cylinder = ParametricSurface( lambda u, v: np.array([ np.cos(TAU * u), np.sin(TAU * u), - 2 * (v) - ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).rotate(m.radians(-40),RIGHT).shift([0.5,0.5,0]).scale(0.8) - - #---- constraint h(x,y) + 2 * (1-1.5*v) + ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).shift([0.5,0.5,-0.13]).scale(1) + plane = ParametricSurface( lambda u, v: np.array([ u, v, u+v - ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(2).fade(0.3) - - figure = VGroup(cylinder,plane).rotate(m.radians(-45),DOWN).scale(1.5) + ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(4).fade(0.3) + + c = Circle(color='#FF00FF',fill_opacity=0.3).shift([0.7,-1.3,0.4]).rotate(2.5,UP).scale(1.32) + + f_text = TextMobject("$f(x,y)=x^2+y^2+z^2$",color = '#FFA074').scale(0.6).to_corner(UL) + g_text = TextMobject("$g(x,y)=x^2+y^2+1$",color = '#FFA074').scale(0.6).to_corner(UL) + h_text = TextMobject("$h(x,y)=x+y-z=1$",color = '#FFA074').scale(0.6).to_corner(UL) + + + + self.set_camera_orientation(phi=65*DEGREES,theta=95*DEGREES) - self.set_camera_orientation(phi=65*DEGREES,theta=45*DEGREES) self.add(axes) self.add(label_x) self.add(label_y) - self.wait(1) + self.wait(1) + self.add_fixed_in_frame_mobjects(f_text) + self.play(Write(c)) + self.wait(1) + self.play(FadeOut(f_text)) + self.wait(1) + self.add_fixed_in_frame_mobjects(g_text) self.play(Write(cylinder)) - self.play(Write(plane)) self.wait(1) - self.begin_ambient_camera_rotation(rate=0.4) + self.play(FadeOut(g_text)) self.wait(1) + self.add_fixed_in_frame_mobjects(h_text) + self.play(Write(plane)) self.wait(1) - self.play(FadeOut(label_x),FadeOut(label_y)) - self.wait(1) + self.play(FadeOut(h_text)) self.wait(1) |