Update file1_Visualization_of_dz.py

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)