1 files changed, 145 insertions, 0 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
new file mode 100644
index 0000000..fcbc410
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
@@ -0,0 +1,145 @@
+from manimlib.imports import *
+
+class Sphere(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes() # creates a 3D Axis
+
+        text3d1 = TextMobject(r"$z = f(x,y) =  \sqrt{r^2 - x^2 - y^2}$")
+
+        text3d1.scale(0.7)
+
+        text3d1.to_corner(UL)
+
+        text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 
+        self.play(Write(text3d1))
+        self.wait(1)
+        
+        self.add_fixed_in_frame_mobjects(text3d1)
+
+        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/2,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],
+            resolution=(15, 32)).scale(1)
+
+
+        #Experiment with circles by changing difference value of u and v
+        '''
+        sphere_points = [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 u in range(0, 185, 5) for v in range(0, 365, 5)]
+
+        sphere_spheres = [Dot().move_to(pts) for pts in sphere_points]
+
+        sphere = VGroup(*sphere_spheres)
+        '''
+        
+        self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES)
+
+        self.add(axes)
+
+        axis = TextMobject(r"X",r"Y",r"Z")
+        axis[0].move_to(6*RIGHT)
+        axis[1].move_to(6*UP)
+        axis[2].move_to(np.array([0,0,3.7]))
+
+        self.add_fixed_orientation_mobjects(axis[2])
+        self.add_fixed_orientation_mobjects(axis[0])
+        self.add_fixed_orientation_mobjects(axis[1]) 
+
+        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]))
+
+        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)
+        point_x_y_z1_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_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)
+    
+        
+        self.play(ShowCreation(dot_x_y1))
+        self.add_fixed_orientation_mobjects(point_x_y1)
+        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))
+        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))
+        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))
+        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))
+        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]))
+    
+        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)
+        point_x_y_z2_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_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)
+       
+        
+        self.play(ShowCreation(dot_x_y2))
+        self.add_fixed_orientation_mobjects(point_x_y2)
+        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))
+        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))
+        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))
+        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))
+        self.add_fixed_orientation_mobjects(point_x_y_z2_5)
+
+        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, 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]
+
+            sphere_points2 = [np.array([2*np.sin((u+5)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+5)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+5)*DEGREES)]) for v in range(0, 370, 10)]
+            sphere_dots2 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points2]
+
+            sphere_points3 = [np.array([2*np.sin((u+10)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+10)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+10)*DEGREES)]) for v in range(0, 370, 10)]
+            sphere_dots3 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points3]
+
+            sphere_final = sphere_final + sphere_dots1 + sphere_dots2 + sphere_dots3
+
+            sphere_dots = sphere_dots1 + sphere_dots2 + sphere_dots3
+   
+            sphere_with_dots = VGroup(*sphere_dots)
+            self.play(ShowCreation(sphere_with_dots))
+
+        sphere_final_with_dots = VGroup(*sphere_final)
+        
+        
+        self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait(3)
+        self.play(ReplacementTransform(sphere_final_with_dots, sphere))
+        self.wait(5)
+\ No newline at end of file