From ac83cc7b152273a6f6bd823028e7dec75a6f9fd1 Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Wed, 1 Jul 2020 11:56:42 +0530 Subject: Added updated multivariable-limits-and-continuity folder --- .../file3_limit_approach_point_3d.py | 152 +++++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py') diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py new file mode 100644 index 0000000..f1007a4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py @@ -0,0 +1,152 @@ +from manimlib.imports import * + +class Limit(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + + text3d = TextMobject(r"$f(x,y) = \frac{x - y}{x - 1}$") + 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), + (3*np.sin(u)*np.cos(v) - 3*np.sin(u)*np.sin(v))/2*(3*np.sin(u)*np.cos(v) - 1) + ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1, + resolution=(15, 32)).scale(1) + + limit_y_x =ParametricFunction( + lambda u : np.array([ + u, + u, + 0 + ]),color=GREEN_D,t_min=-3,t_max=3, + ) + + limit_y_1 =ParametricFunction( + lambda u : np.array([ + u, + 1, + 1/2 + ]),color=BLUE_D,t_min=-3,t_max=3, + ) + + limit_y_x_2 =ParametricFunction( + lambda u : np.array([ + u, + u*u, + (u - u*u)/2*(u - 1) + ]),color=RED_D,t_min=-3,t_max=3, + ) + + limit_y_2_x =ParametricFunction( + lambda u : np.array([ + u, + 2 - u, + 1 + ]),color=YELLOW_D,t_min=-3,t_max=3, + ) + + plane_y_x = Polygon(np.array([-3,-3,-3]),np.array([3,3,-3]),np.array([3,3,3]),np.array([-3,-3,3]),np.array([-3,-3,-3]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.1) + plane_y_x_text = TextMobject(r"$y = x$", color = GREEN_C).move_to(np.array([5,0,3])) + + plane_y_1 = Polygon(np.array([-3,1,-3]),np.array([3,1,-3]),np.array([3,1,3]),np.array([-3,1,3]),np.array([-3,1,-3]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1) + plane_y_1_text = TextMobject(r"$y = 1$", color = BLUE_C).move_to(np.array([5,0,2.5])) + + + #Creating plane y = x^2 + ###### + y_x_2 = [] + y_x_2.append(np.array([2, 4, -3])) + y_x_2.append(np.array([2, 4, 3])) + y_x_2_1 = [np.array([i, i*i, 3]) for i in np.arange(1.9,-2.1, -0.1)] + + y_x_2 = y_x_2 + y_x_2_1 + + y_x_2.append(np.array([-2, 4, 3])) + y_x_2.append(np.array([-2, 4, -3])) + + y_x_2_2 = [np.array([i, i*i, -3]) for i in np.arange(-2,2.1, 0.1)] + + y_x_2 = y_x_2 + y_x_2_2 + #y_x_2.append(np.array([-3, 9, 0])) + + plane_y_x_2 = Polygon(*y_x_2, color = RED_C, fill_color = RED_C, fill_opacity = 0.1) + plane_y_x_2_text = TextMobject(r"$y = x^2$", color = RED_C).move_to(np.array([5,0,2])) + + ###### + + plane_y_2_x = Polygon(np.array([-3,5,-3]),np.array([3,-1,-3]),np.array([3,-1,3]),np.array([-3,5,3]),np.array([-3,5,-3]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.1) + plane_y_2_x_text = TextMobject(r"$y = 2 - x$", color = YELLOW_C).move_to(np.array([5,0,1.5])) + + line_1_1 = Line(np.array([1,1,-3]), np.array([1,1,3]), color = PINK) + + point = 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([1,1,0])) + point_text = TextMobject(r"$(1,1,0)$", color = WHITE).scale(0.7).move_to(np.array([1.8,1,0])) + + + + + self.set_camera_orientation(phi=70 * DEGREES, theta = -95*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.wait(2) + + self.play(ShowCreation(plane_y_x)) + self.add_fixed_orientation_mobjects(plane_y_x_text) + self.play(ShowCreation(limit_y_x)) + self.wait() + + self.play(ShowCreation(plane_y_1)) + self.add_fixed_orientation_mobjects(plane_y_1_text) + self.play(ShowCreation(limit_y_1)) + self.wait() + + self.play(ShowCreation(plane_y_x_2)) + self.add_fixed_orientation_mobjects(plane_y_x_2_text) + self.play(ShowCreation(limit_y_x_2)) + self.wait() + + self.play(ShowCreation(plane_y_2_x)) + self.add_fixed_orientation_mobjects(plane_y_2_x_text) + self.play(ShowCreation(limit_y_2_x)) + self.wait() + + self.play(ShowCreation(line_1_1)) + self.wait() + + self.play(ShowCreation(point)) + self.add_fixed_orientation_mobjects(point_text) + self.wait() + + self.play(FadeOut(plane_y_x_text), FadeOut(plane_y_1_text), FadeOut(plane_y_x_2_text), FadeOut(plane_y_2_x_text)) + + self.move_camera(phi=0* DEGREES,theta=-95*DEGREES) + self.wait(2) + self.play(FadeOut(plane_y_x), FadeOut(plane_y_1), FadeOut(plane_y_x_2), FadeOut(plane_y_2_x)) + self.wait(3) + + self.move_camera(phi=75* DEGREES,theta=-95*DEGREES) + self.wait(3) + + + \ No newline at end of file -- cgit