diff options
Merge pull request #5 from FOSSEE/master
importing changes
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py | 115 |
1 files changed, 115 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py new file mode 100644 index 0000000..0a43def --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py @@ -0,0 +1,115 @@ +from manimlib.imports import *
+
+class DifferentPoint(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+
+ text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$")
+ self.add_fixed_in_frame_mobjects(text3d)
+
+ text3d.to_corner(UL)
+
+ text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
+
+ self.play(Write(text3d))
+ self.wait(1)
+
+ limit_func = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_func_copy1 = limit_func.copy()
+ limit_func_copy2 = limit_func.copy()
+
+ limit_func_x = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_func_y = ParametricSurface(
+ lambda u, v: np.array([
+ 3*np.sin(u)*np.cos(v),
+ 3*np.sin(u)*np.sin(v),
+ (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))
+ ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
+ resolution=(15, 32)).scale(1)
+
+ limit_x =ParametricFunction(
+ lambda u : np.array([
+ u,
+ 0,
+ 1
+ ]),color="#006400",t_min=-3,t_max=3,
+ )
+
+ limit_y =ParametricFunction(
+ lambda u : np.array([
+ 0,
+ u,
+ -1
+ ]),color="#000080",t_min=-3,t_max=3,
+ )
+
+ plane_x = Polygon(np.array([-3,0,-2]),np.array([3,0,-2]),np.array([3,0,2]),np.array([-3,0,2]),np.array([-3,0,-2]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
+ plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ plane_y = Polygon(np.array([0,-3,-2]),np.array([0,3,-2]),np.array([0,3,2]),np.array([0,-3,2]),np.array([0,-3,-2]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
+ plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)
+
+ origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))
+
+ origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
+ origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))
+
+ self.set_camera_orientation(phi=80 * DEGREES, theta = 0*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(3.7*UP)
+
+ self.add_fixed_in_frame_mobjects(axis[2])
+ self.add_fixed_orientation_mobjects(axis[0])
+ self.add_fixed_orientation_mobjects(axis[1])
+
+ self.play(ShowCreation(limit_func))
+
+ self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
+
+ self.play(ShowCreation(plane_x))
+ self.add_fixed_in_frame_mobjects(plane_x_text)
+ self.wait()
+ self.play(ReplacementTransform(limit_func, limit_func_x))
+ self.play(FadeOut(plane_x), FadeOut(plane_x_text), ShowCreation(origin_x))
+ self.add_fixed_orientation_mobjects(origin_x_text)
+ self.play(ShowCreation(limit_x))
+
+ self.move_camera(phi=80* DEGREES,theta=15*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(limit_x), ReplacementTransform(limit_func_x, limit_func_copy1))
+ self.play(ShowCreation(plane_y))
+ self.add_fixed_in_frame_mobjects(plane_y_text)
+ self.wait()
+ self.play(ReplacementTransform(limit_func_copy1, limit_func_y))
+ self.play(FadeOut(plane_y), FadeOut(plane_y_text), ShowCreation(origin_y))
+ self.add_fixed_orientation_mobjects(origin_y_text)
+ self.play(ShowCreation(limit_y))
+
+ self.move_camera(phi=80* DEGREES,theta=75*DEGREES)
+ self.wait(3)
+
+ self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(limit_y), ReplacementTransform(limit_func_y, limit_func_copy2))
+ self.wait(2)
+
\ No newline at end of file |