diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py | 177 |
1 files changed, 177 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..86239ae --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py @@ -0,0 +1,177 @@ +from manimlib.imports import *
+
+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.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.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],
+ 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]))
+ 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)
+
+ 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)
+
+ 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.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.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.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.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)
+
+
+
+ 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)
+
+ 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)
+
+ 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.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.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.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.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(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))
+
+
+
+
+ sphere_final = []
+
+ for u in range(0, 180, 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)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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