updated after review

6 files changed, 102 insertions, 24 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md
index fe4d73a..5fa2146 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/README.md
@@ -1,8 +1,8 @@
-**file1_surface**
-![file1_surface](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.gif)
+**file1_area_under_func**
+![file1_area_under_func](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.gif)
 
-**file2_area_under_func**
-![file2_area_under_func](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_area_under_func.gif)
+**file2_volume_under_surface**
+![file2_volume_under_surface](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif)
 
 **file3_y_limit_dependent_on_x**
 ![file3_y_limit_dependent_on_x](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file3_y_limit_dependent_on_x.gif)
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_area_under_func.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.gif
index 223218b..223218b 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_area_under_func.gif
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_area_under_func.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.py
index 773840c..773840c 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_area_under_func.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.py
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.gif
deleted file mode 100644
index ae23a7b..0000000
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif
new file mode 100644
index 0000000..74c306d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.py
index a794f46..cd4060b 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_surface.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file2_volume_under_surface.py
@@ -5,11 +5,11 @@ class SurfacesAnimation(ThreeDScene):
     CONFIG = {
         "axes_config": {
             "x_min": 0,
-            "x_max": 8,
+            "x_max": 7,
             "y_min": 0,
-            "y_max": 8,
+            "y_max": 7,
             "z_min": 0,
-            "z_max": 6,
+            "z_max": 5,
             "a":1 ,"b": 6, "c":2 , "d":6,
             "axes_shift":-3*OUT + 5*LEFT,
             "x_axis_config": {
@@ -46,13 +46,16 @@ class SurfacesAnimation(ThreeDScene):
         self.setup_axes()
         self.set_camera_orientation(distance=35,
             phi=80 * DEGREES,
-            theta=-80 * DEGREES,
+            theta=-100 * DEGREES,
         )
         
         fn_text=TextMobject("$z=f(x,y)$").set_color(PINK)
         self.add_fixed_in_frame_mobjects(fn_text) 
         fn_text.to_edge(TOP,buff=MED_SMALL_BUFF)
         
+        riemann_sum_text=TextMobject(r"The volume approximated as\\ sum of cuboids",color=BLUE)
+        riemann_sum_text.to_corner(UR,buff=.2)
+        
         R=TextMobject("R").set_color(BLACK).scale(3)
         R.move_to(self.axes.input_plane,IN)
         self.add(R)
@@ -70,13 +73,26 @@ class SurfacesAnimation(ThreeDScene):
         )
         
         
-        self.begin_ambient_camera_rotation(rate=0.07)
+        self.begin_ambient_camera_rotation(rate=0.08)
         self.play(Write(surface))
-      #  self.play(LaggedStart(ShowCreation(surface)))
+     #   self.add(surface)
         
         self.get_lines()
-   #     self.play(FadeIn(self.axes.input_plane))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(riemann_sum_text)
+        self.play(Write(riemann_sum_text))
+        self.show_the_riemmann_sum(
+            lambda x,y : np.array([x,y,self.Func(x,y)]),
+            fill_opacity=1,
+            dl=.5,
+            start_color=BLUE,
+            end_color=BLUE_E,
+        )
+        self.play(FadeOut(surface))
         self.wait(3)
+        
+        
+        
       
     def get_surface(self,axes, func, **kwargs):
         config = {
@@ -101,9 +117,6 @@ class SurfacesAnimation(ThreeDScene):
         
     def get_lines(self):
         axes = self.axes
-        labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),       
-            axes.y_axis.n2p(axes.d)]
-        
         
         surface_corners=[]
         for x,y,z in self.region_corners:
@@ -112,23 +125,90 @@ class SurfacesAnimation(ThreeDScene):
         lines=VGroup()
         for start , end in zip(surface_corners,
         self.region_corners):
-            lines.add(self.draw_lines(start,end,"RED"))
+            lines.add(self.draw_lines(start,end,"#9CDCEB"))
+        
+        labels=[
+            (axes.a,0,0), 
+            (axes.b,0,0), 
+            (0,axes.d,0), 
+            (0,axes.c,0)
+        ]  
+        self.region_corners[-1]=self.region_corners[0]
+        for start , end in zip(labels,self.region_corners):
+            lines.add(self.draw_lines(start,end,"WHITE"))
             
-        for start , end in zip(labels,
-        self.region_corners):
-         #   lines.add(self.draw_lines(start,end,"BLUE"))
-         #   print (start,end)
-         pass
+       # self.add(lines)
         self.play(ShowCreation(lines))
         
-             
+              
     def draw_lines(self,start,end,color):
         start=self.axes.c2p(*start)
         end=self.axes.c2p(*end)
         line=DashedLine(start,end,color=color)
         
         return line
+        
+        
+    def show_the_riemmann_sum(
+        self,
+        surface,
+        x_min=None,
+        x_max=None,
+        y_min=None,
+        y_max=None,
+        dl=.5,
+        stroke_width=.5,
+        stroke_color=BLACK,
+        fill_opacity=1,
+        start_color=None,
+        end_color=None,
+        ):
+            x_min = x_min if x_min is not None else self.axes.a
+            x_max = x_max if x_max is not None else self.axes.b
+            y_min = y_min if y_min is not None else self.axes.c
+            y_max = y_max if y_max is not None else self.axes.d
             
+            if start_color is None:
+                start_color = BLUE
+            if end_color is None:
+                end_color = BLUE
+                
+            cuboids = VGroup()
+            x_range = np.arange(x_min, x_max, dl)
+            y_range = np.arange(y_min, y_max, dl)
+            colors = color_gradient([start_color, end_color], len(x_range))
+            for x, color in zip(x_range, colors):
+              for y in y_range:
+                  sample_base = np.array([x ,y ,0])
+                  sample_base_dl = np.array([x + dl, y + dl,0])
+                  sample_input = np.array([x +0.5*dl, y +0.5*dl,0])
+                  
+                  base_point = self.axes.c2p(*sample_base)
+                  base_dx_point = self.axes.c2p(*sample_base_dl) 
+                  
+                  surface_val= surface(*sample_input[:2])
+                  surface_point = self.axes.c2p(*surface_val)
+               
+                  points = VGroup(*list(map(VectorizedPoint, [
+                      base_point,
+                      surface_point,
+                      base_dx_point
+                  ])))
+                    
+                #  self.add(points)
+                  cuboid = Prism(dimensions=[dl,dl,surface_val[-1]])
+                  cuboid.replace(points, stretch=True)
+             
+                  cuboid.set_fill(color, opacity=fill_opacity)
+                  cuboid.set_stroke(stroke_color, width=stroke_width)
+                  cuboids.add(cuboid)
+            
+            self.play(ShowCreation(cuboids),run_time=6)
+           # self.add(cuboids)
+            
+  
+#-------------------------------------------------------  
+    #customize 3d axes       
     def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
         config = dict(self.axes_config)
         config.update(kwargs)
@@ -165,7 +245,7 @@ class SurfacesAnimation(ThreeDScene):
         axes.input_plane = input_plane
 
         self.region_corners=[ 
-        input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
+        input_plane.get_corner(pos) for pos in (DL,DR,UL,UR)]
         
         return axes
         
@@ -232,5 +312,3 @@ class SurfacesAnimation(ThreeDScene):
         return axes    
         
     
-
-#uploaded by Somnath Pandit.FSF2020_Double_Integral