diff options
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py | 19 |
1 files changed, 9 insertions, 10 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py index 2c2a9de..2c1d668 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py @@ -1,7 +1,7 @@ from manimlib.imports import* #---- visualization of geometric proof of Lagrange multiplier -class GeometricProof(ThreeDScene): +class firstScene(ThreeDScene): def construct(self): axes = ThreeDAxes().scale(0.7).rotate(math.radians(180)) label_x = TextMobject("$x$").shift(4*RIGHT).fade(0.4) #---- x axis @@ -12,19 +12,18 @@ class GeometricProof(ThreeDScene): 1*np.sin(u)*np.cos(v), 1*np.sin(u)*np.sin(v), -1*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E]).scale(1).shift([-1.5,-1.5,0]) + ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI).set_color(GREEN).scale(1).shift([-1.5,-1.5,0]) d = Dot([-2,-2.55,0],color = '#800000') - a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g at maxima - a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- g parallel to f at maxima + a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g + a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- f parallel to g - b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- g parallel to f at minima - b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g at minima + b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- f parallel to g + b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g qd = Dot(color = '#800000').shift(1.2*LEFT+0.6*DOWN) - #---- level curves l1 = Line([-1,-3.1,0],[-4,-3.1,0],color = PINK).rotate(-0.3).fade(0.6) l2 = Line([-0.9,-2.9,0],[-4,-2.9,0],color = PINK).rotate(-0.3).fade(0.6) l3= Line([-0.8,-2.7,0],[-4,-2.7,0],color = PINK).rotate(-0.3).fade(0.6) @@ -48,7 +47,6 @@ class GeometricProof(ThreeDScene): p_text= TextMobject("$P$").shift([1.8,2.6,0]).scale(0.5) - #---- labelling of level curves l1_text = TextMobject("$w=$ 17").rotate(math.radians(180)).scale(0.4).shift(2.7*DOWN+4.36*LEFT) l2_text = TextMobject("$w=$ 16").rotate(math.radians(180)).scale(0.4).shift(2.46*DOWN+4.36*LEFT) l3_text = TextMobject("$w=$ 15").rotate(math.radians(180)).scale(0.4).shift(2.2*DOWN+4.36*LEFT) @@ -70,8 +68,9 @@ class GeometricProof(ThreeDScene): self.set_camera_orientation(phi=0 * DEGREES, theta = 90*DEGREES) self.add(axes) self.add(label_x) - self.add(label_y) - self.play(Write(surface)) + self.add(label_y) + self.wait(1) + self.add(surface) self.wait(1) self.play(ShowCreation(level_Curve)) self.wait(1) |