Merge pull request #92 from nishanpoojary/master

Updated gifs and scripts

1 files changed, 36 insertions, 68 deletions

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
index 86239ae..fcbc410 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
@@ -4,28 +4,24 @@ class Sphere(ThreeDScene):
     def construct(self):

         axes = ThreeDAxes() # creates a 3D Axis

 

-        text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")

-        text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, \sqrt{r^2 - x^2 - y^2})$")

-        self.add_fixed_in_frame_mobjects(text3d)

-        text3d.scale(0.7)

+        text3d1 = TextMobject(r"$z = f(x,y) =  \sqrt{r^2 - x^2 - y^2}$")

+

         text3d1.scale(0.7)

-        text3d.to_corner(UL)

+

         text3d1.to_corner(UL)

-        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

         text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 

-        self.play(Write(text3d))

+        self.play(Write(text3d1))

         self.wait(1)

         

-        self.play(Transform(text3d,text3d1))

         self.add_fixed_in_frame_mobjects(text3d1)

-        self.play(FadeOut(text3d))

 

         sphere = ParametricSurface(

             lambda u, v: np.array([

                 2*np.sin(u)*np.cos(v),

                 2*np.sin(u)*np.sin(v),

                 2*np.cos(u)

-            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

             resolution=(15, 32)).scale(1)

 

 

@@ -53,8 +49,8 @@ class Sphere(ThreeDScene):
 

         dot_x_y1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,0]))

         dot_x_y_z1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,1.414]))

-        dot_x_y_z_1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,-1.414]))

-        line1 = DashedLine(np.array([-1,1,-1.414]), np.array([-1,1,1.414]), color = YELLOW_C)

+

+        line1 = DashedLine(np.array([-1,1,0]), np.array([-1,1,1.414]), color = YELLOW_C)

 

         point_x_y1 = TexMobject("(-1,1,0)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,0])).scale(0.5)

         point_x_y_z1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

@@ -62,38 +58,32 @@ class Sphere(ThreeDScene):
         point_x_y_z1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

         point_x_y_z1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

         point_x_y_z1_5 = TexMobject("(-1,1,1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

-

-        point_x_y_z_1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

-        point_x_y_z_1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

-        point_x_y_z_1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

-        point_x_y_z_1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

-        point_x_y_z_1_5 = TexMobject("(-1,1,-1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

-

+    

         

         self.play(ShowCreation(dot_x_y1))

         self.add_fixed_orientation_mobjects(point_x_y1)

-        self.play(ShowCreation(dot_x_y_z1), ShowCreation(dot_x_y_z_1), ShowCreation(line1))

-        self.add_fixed_orientation_mobjects(point_x_y_z1, point_x_y_z_1)

+        self.play(ShowCreation(dot_x_y_z1), ShowCreation(line1))

+        self.add_fixed_orientation_mobjects(point_x_y_z1)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2), ReplacementTransform(point_x_y_z_1,point_x_y_z_1_2))

-        self.add_fixed_orientation_mobjects(point_x_y_z1_2, point_x_y_z_1_2)

+        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_2)

 

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3), ReplacementTransform(point_x_y_z_1_2,point_x_y_z_1_3))

-        self.add_fixed_orientation_mobjects(point_x_y_z1_3, point_x_y_z_1_3)

+        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_3)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4), ReplacementTransform(point_x_y_z_1_3,point_x_y_z_1_4))

-        self.add_fixed_orientation_mobjects(point_x_y_z1_4, point_x_y_z_1_4)

+        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_4)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5), ReplacementTransform(point_x_y_z_1_4,point_x_y_z_1_5))

-        self.add_fixed_orientation_mobjects(point_x_y_z1_5, point_x_y_z_1_5)

+        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_5)

         

 

 

         dot_x_y2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,0]))

         dot_x_y_z2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,1.87]))

-        dot_x_y_z_2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,-1.87]))

-        line2 = DashedLine(np.array([0.5,-0.5,-1.87]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)

+    

+        line2 = DashedLine(np.array([0.5,-0.5,0]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)

 

         point_x_y2 = TexMobject("(0.5,-0.5,0)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,0])).scale(0.5)

         point_x_y_z2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

@@ -101,41 +91,35 @@ class Sphere(ThreeDScene):
         point_x_y_z2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

         point_x_y_z2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

         point_x_y_z2_5 = TexMobject("(0.5,-0.5,1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

-

-        point_x_y_z_2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

-        point_x_y_z_2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

-        point_x_y_z_2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

-        point_x_y_z_2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

-        point_x_y_z_2_5 = TexMobject("(0.5,-0.5,-1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

-

+       

         

         self.play(ShowCreation(dot_x_y2))

         self.add_fixed_orientation_mobjects(point_x_y2)

-        self.play(ShowCreation(dot_x_y_z2), ShowCreation(dot_x_y_z_2), ShowCreation(line2))

-        self.add_fixed_orientation_mobjects(point_x_y_z2, point_x_y_z_2)

+        self.play(ShowCreation(dot_x_y_z2), ShowCreation(line2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2), ReplacementTransform(point_x_y_z_2,point_x_y_z_2_2))

-        self.add_fixed_orientation_mobjects(point_x_y_z2_2, point_x_y_z_2_2)

+        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_2)

 

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3), ReplacementTransform(point_x_y_z_2_2,point_x_y_z_2_3))

-        self.add_fixed_orientation_mobjects(point_x_y_z2_3, point_x_y_z_2_3)

+        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_3)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4), ReplacementTransform(point_x_y_z_2_3,point_x_y_z_2_4))

-        self.add_fixed_orientation_mobjects(point_x_y_z2_4, point_x_y_z_2_4)

+        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_4)

         self.wait(0.5)

-        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5), ReplacementTransform(point_x_y_z_2_4,point_x_y_z_2_5))

-        self.add_fixed_orientation_mobjects(point_x_y_z2_5, point_x_y_z_2_5)

+        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_5)

 

-        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5), FadeOut(point_x_y_z_1_5), FadeOut(dot_x_y1), FadeOut(dot_x_y_z1), FadeOut(dot_x_y_z_1), FadeOut(line1))

-        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5), FadeOut(point_x_y_z_2_5), FadeOut(dot_x_y2), FadeOut(dot_x_y_z2), FadeOut(dot_x_y_z_2), FadeOut(line2))

+        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5))

+        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5))

         

 

 

 

         sphere_final = []

     

-        for u in range(0, 180, 15): 

+        for u in range(0, 90, 15): 

             sphere_points1 = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for v in range(0, 370, 10)]

             sphere_dots1 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points1]

 

@@ -158,20 +142,4 @@ class Sphere(ThreeDScene):
         self.begin_ambient_camera_rotation(rate=0.5)

         self.wait(3)

         self.play(ReplacementTransform(sphere_final_with_dots, sphere))

-        self.wait(5)

-        

-

-

-

-

-

-

-        

-

-

-

-

-        

-        

-

-        

+        self.wait(5)
\ No newline at end of file