extended animation

2 files changed, 60 insertions, 21 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.gif
index e165a15..6a57cab 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.gif
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py
index 13211e9..fc56306 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file3_constructing_vector_field.py
@@ -3,10 +3,10 @@ from manimlib.imports import *
 
 class VectorFields(GraphScene):
     CONFIG = {
-        "x_min" : -2,
-        "x_max" : 2,
-        "y_min" : -2,
-        "y_max" : 2,
+        "x_min" : -4,
+        "x_max" : 4,
+        "y_min" : -4,
+        "y_max" : 4,
         "graph_origin": ORIGIN+2.5*LEFT,
         "x_axis_width": 7,
         "y_axis_height": 7,
@@ -18,15 +18,15 @@ class VectorFields(GraphScene):
             "min_magnitude": 0,
             "max_magnitude": 4,
             "colors": [GREEN,GREEN,YELLOW,RED],
-            "length_func": lambda norm : .6*sigmoid(norm),
+            "length_func": lambda n: n/2.5,
             "opacity": .75,
             "vector_config": {
                 "stroke_width":6,
-                "max_stroke_width_to_length_ratio":6
+                "max_stroke_width_to_length_ratio":4
             },
         },
         
-        "a":-1.5 ,"b": 2, "c": -1.5 ,"d": 2,
+        "a":-3.5 ,"b": 4, "c": -3.5 ,"d": 4,
     }  
 
     def construct(self):
@@ -35,27 +35,30 @@ class VectorFields(GraphScene):
         self.X=X ;self.Y=Y
         
         self.setup_axes(animate=False)
-        
-        vector_field=self.get_vector_field(
-            lambda v: np.array([
+        vector_function = lambda v: np.array([
             (v[0]-self.graph_origin[0])*(v[1]-self.graph_origin[1]),  
             -(v[0]-self.graph_origin[0]),  
             0,
             ])
-        ) 
+            
+        vector_field=self.get_vector_field(
+            vector_function,
+            colors= [GREEN]
+        )
         
         self.show_points()
         self.wait(.5)
         self.show_func_machine()
         self.wait(1)
         self.produce_vectors(vector_field)
+        self.wait(.5)
+        self.scale_down_vectors(vector_function)
         self.wait(2)
     
     
     
-        
     def show_points(self):
-        dn=.5
+        dn=1
         x_vals=np.arange(self.a,self.b,dn)
         y_vals=np.arange(self.c,self.d,dn)
         dots=VGroup()
@@ -84,7 +87,9 @@ class VectorFields(GraphScene):
         ).set_color_by_gradient(
             *self.default_vector_field_config["colors"]
         ).next_to(machine,IN)
-        self.add(machine,machine_label)
+        
+        machine=VGroup(machine,machine_label)
+        self.add(machine)
         
         self.func_machine=machine
         
@@ -92,6 +97,7 @@ class VectorFields(GraphScene):
     def produce_vectors(self,vector_field):
         count,i=3,0
         self.run_time=1
+        non_scaled_vectors=VGroup()
         for dot in self.dots:
             if i==count:
                 self.run_time=.05
@@ -99,8 +105,11 @@ class VectorFields(GraphScene):
             vect= vector_field.get_vector(position)
             self.go_to_machine(dot)
             self.take_vec_from_machine(vect,position)
+            non_scaled_vectors.add(vect)
             i+=1
             
+        self.non_scaled_vectors=non_scaled_vectors
+                
     def go_to_machine(self,dot):
         if self.run_time>.5:
          self.play(ApplyMethod(
@@ -113,14 +122,19 @@ class VectorFields(GraphScene):
         
     def take_vec_from_machine(self,vect,position):
         vect.next_to(self.func_machine,DOWN,buff=.1)
+        
         if self.run_time>.5:
+          point_coord=TexMobject(
+            "(x_i,y_i)"
+          ).next_to(self.dot,RIGHT,buff= .01).scale(.75)
+          input_point=VGroup(point_coord, self.dot)
           self.play(
             ApplyMethod(
-            self.dot.shift,DOWN,
+            input_point.shift,DOWN,
             run_time=self.run_time
           )),
           self.play(
-            FadeOut(self.dot),
+            FadeOut(input_point),
             run_time=.2
           )
           self.play(
@@ -130,15 +144,40 @@ class VectorFields(GraphScene):
         else:
             self.remove(self.dot)
             self.add(vect)
-            self.wait(.1)
+            self.wait(1.0/15)
  
         self.play(
-            ApplyMethod(
-            vect.move_to,position
-            ),
+            vect.move_to,position,
             run_time=self.run_time
         )
-        
+    
+    def scale_down_vectors(self,vector_function):
+        scale_down_text=TextMobject(
+            r"Vectors are rescaled\\ for clarity\\ and \\",
+            r"colors are used to \\ indicate magnitudes",
+            stroke_width=1.2
+        )
+        scale_down_text[0][:7].set_color(BLUE)
+        scale_down_text[1].set_color_by_gradient(
+            *self.default_vector_field_config["colors"]
+        )
+        scale_down_text.to_corner(UR).shift(DOWN)
+        scaled_vector_field= self.get_vector_field(
+            vector_function,
+            length_func= lambda norm : .75*sigmoid(norm)
+        )
+        for vector in self.non_scaled_vectors:
+            scaled_vect= scaled_vector_field.get_vector(vector.get_center())
+            vector.target= scaled_vect
+            
+        self.play(FadeOut(self.func_machine))
+        self.play(Write(scale_down_text))
+        self.wait(1.2) 
+        self.play(LaggedStartMap(
+            MoveToTarget, self.non_scaled_vectors,
+            run_time=3
+        ))   
+            
     def get_vector_field(self,func,**kwargs):
         config = dict()
         config.update(self.default_vector_field_config)