diff options
Diffstat (limited to 'FSF-2020')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py | 80 |
1 files changed, 52 insertions, 28 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py index a097a96..2a1a750 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py @@ -1,53 +1,77 @@ from manimlib.imports import* - -class firstScene(ThreeDScene): - +#---- visualization of the differential dz between two points on the surface of the function +class differentialdz(ThreeDScene): def construct(self): - - axes = ThreeDAxes().rotate(1.571) + + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.3,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + surface = ParametricSurface( lambda u, v: np.array([ u, v, u**2+v**2 - ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").fade(0.6).scale(2).shift(3*UP+1*LEFT) + ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").shift([0,2.5,0.3]).scale(1.2) #----surface z = f(x,y) + - d = Dot([1.4,1.75,1],color = '#00FFFF').rotate(1.571,UP) - d2 = Dot([2,2,1],color = '#00FFFF').rotate(1.571,UP) + + plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(-1*RIGHT+3*UP).fade(0.9) #---- x-y plane + + d = Dot([1,2,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface + d2 = Dot([2,2.9,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface p1 = TextMobject("$P_1$",color ='#ADFF2F').scale(0.6).shift(2*RIGHT+1*UP) - p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.9*UP) + p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.4*UP) - l = DashedLine(color = '#800000').rotate(1.571,UP).scale(1).shift(1.7*UP+1.6*RIGHT) - l2 = DashedLine(color = '#800000').rotate(1.571,UP).scale(0.8).shift(2.26*UP+1.2*RIGHT) - l_text = TextMobject("$(x_1,y_1)$",color = '#ADFF2F').scale(0.6).shift(2*RIGHT+1.6*DOWN) - l2_text = TextMobject("$(x_2,y_2)$",color = '#ADFF2F').scale(0.6).shift(2.7*RIGHT+1.2*DOWN) + l1 = DashedLine(color = '#00BFFF').scale(1.6).shift(3.5*UP+3.25*LEFT).rotate(1.571) + l2 = DashedLine(color = '#00BFFF').scale(1).shift(4*UP+2*LEFT).rotate(1.571) - a = Arrow(color = '#FFFACD').scale(0.7).rotate(1.38,RIGHT).shift(2.5*LEFT+3.1*UP) + label_dz= TextMobject("$dz$").scale(0.4).shift(5.3*RIGHT+0.4*UP) - a_text = TextMobject("$dz$",color='#800000').scale(0.5).shift(2.3*RIGHT+0.5*UP) - plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(1*RIGHT+3*UP).fade(0.9) + l3 = Line(color = '#FFDAB9').scale(0.8).shift(1.95*UP+0.7*RIGHT).rotate(1.571,DOWN).fade(0.2) + l4 = Line(color = '#FFDAB9').scale(0.6).shift(2.86*UP+0.9*RIGHT).rotate(1.571,DOWN).fade(0.2) - label = TextMobject("$z = f(x,y)$").scale(0.6).shift(3.5*RIGHT+1.8*UP) - + line_y1 = DashedLine(color = '#00BFFF').scale(1.3).shift(0.82*UP+3.25*RIGHT).rotate(1.571) + line_y2 = DashedLine(color = '#00BFFF').scale(1.7).shift(1.2*UP+2.8*RIGHT).rotate(1.571) + + label_dy= TextMobject("$dy$").scale(0.6).shift(3*RIGHT+0.8*DOWN).rotate(math.radians(90)) + + line_x1 = DashedLine(color = '#00BFFF').scale(1.5).shift(2.2*UP+1.6*RIGHT).rotate(1.571,RIGHT) + line_x2 = DashedLine(color = '#00BFFF').scale(1.2).shift(2.9*UP+1.6*RIGHT).rotate(1.571,RIGHT) + + label_dx= TextMobject("$dx$").scale(0.4).shift(-0.4*UP+2.5*RIGHT) + + label = TextMobject("$f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP) + + + self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) self.add(axes) - self.set_camera_orientation(phi=75*DEGREES,theta=-10*DEGREES) - self.wait(1) + self.add(label_x) + self.add(label_y) self.play(Write(plane)) - self.play(Write(surface)) + self.play(Write(surface)) self.add_fixed_in_frame_mobjects(label) self.wait(1) - self.play(ShowCreation(l),ShowCreation(l2),Write(d),Write(d2)) - self.wait(1) + self.play(Write(d),Write(d2)) self.add_fixed_in_frame_mobjects(p1) self.add_fixed_in_frame_mobjects(p2) self.wait(1) - self.add_fixed_in_frame_mobjects(l_text) - self.add_fixed_in_frame_mobjects(l2_text) - self.play(ShowCreation(a)) + self.play(Write(l1)) + self.play(Write(l2)) + self.add_fixed_in_frame_mobjects(label_dz) + self.wait(1) + self.play(Write(l3)) + self.play(Write(l4)) + self.wait(1) + self.play(Write(line_y1)) + self.play(Write(line_y2)) + self.play(ShowCreation(label_dy)) + self.wait(1) + self.play(Write(line_x1)) + self.play(Write(line_x2)) + self.add_fixed_in_frame_mobjects(label_dx) self.wait(1) - self.add_fixed_in_frame_mobjects(a_text) - self.wait(2) |