From 975a74e11015394cd5ccfdd9edb2bd4863273cac Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sat, 4 Jul 2020 12:39:33 +0530 Subject: Delete file4_partial_deriv_example.py --- .../file4_partial_deriv_example.py | 246 --------------------- 1 file changed, 246 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py deleted file mode 100644 index 5712a62..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py +++ /dev/null @@ -1,246 +0,0 @@ -from manimlib.imports import * - -class PartialDerivX(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - paraboloid = ParametricSurface( - lambda u, v: np.array([ - 2*np.sin(u)*np.cos(v), - 2*np.sin(u)*np.sin(v), - -2*2*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE], - resolution=(15, 32)).scale(1) - - paraboloid_copy = paraboloid.copy() - - - paraboloid_x = ParametricSurface( - lambda u, v: np.array([ - 2*np.sin(u)*np.cos(v), - 2*np.sin(u)*np.sin(v), - -2*2*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE], - resolution=(15, 32)).scale(1) - - - parabola =ParametricFunction( - lambda u : np.array([ - u, - 0, - -(u*u) + 2 - ]),color="#006400",t_min=-2,t_max=2, - ) - - plane = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2) - plane_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3*RIGHT) - - surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP])) - surface_eqn[0].set_color(BLUE_C) - - line = Line(np.array([-2,0,0]), np.array([2,0,0]), color = RED_C) - - - 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.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES) - - self.play(Write(paraboloid)) - - self.add_fixed_in_frame_mobjects(surface_eqn) - #self.move_camera(phi=80* DEGREES,theta=95*DEGREES) - self.move_camera(phi=80* DEGREES,theta=45*DEGREES) - self.play(ShowCreation(plane)) - self.add_fixed_in_frame_mobjects(plane_text) - self.wait() - self.play(ReplacementTransform(paraboloid, paraboloid_x)) - self.play(FadeOut(plane), FadeOut(plane_text)) - self.play(ShowCreation(parabola), ShowCreation(line)) - - text1 = TextMobject("Moving small", r"$dx$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE) - - text2 = TextMobject("Observing change in function, keeping", r"$y$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - - slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT) - slope_text[0].set_color(BLUE_E) - slope_text.set_color_by_tex("\\partial",PINK) - slope_text.set_color_by_tex("f","#006400") - slope_text[5].set_color(RED_C) - - self.add_fixed_in_frame_mobjects(text1, text2) - self.wait() - self.add_fixed_in_frame_mobjects(slope_text) - #add_fixed_orientation_mobjects - - - dot = Dot().rotate(PI/2).set_color(RED_C) - alpha = ValueTracker(0) - vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5) - dot.add_updater(lambda m: m.move_to(vector.get_center())) - self.play( - ShowCreation(parabola), - GrowFromCenter(dot), - GrowArrow(vector) - ) - vector.add_updater( - lambda m: m.become( - self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5) - ) - ) - self.add(vector,dot) - self.play(alpha.increment_value, 1, run_time=10, rate_func=linear) - self.wait() - - - ''' - for i in np.arange(-2,2,0.2): - self.play(ReplacementTransform(Line(np.array([i,0,0]), np.array([i,0,-i*i + 2]), color = GREEN_C), Line(np.array([i+0.2,0,0]), np.array([i+0.2,0,-(i+0.2)**2 + 2]), color = GREEN_C))) - #self.wait() - ''' - - self.wait() - self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn)) - - #self.move_camera(phi=80* DEGREES,theta= 0*DEGREES) - self.play(ReplacementTransform(paraboloid_x, paraboloid_copy)) - self.wait() - - - def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1): - coord_i = curve.point_from_proportion(proportion) - coord_f = curve.point_from_proportion(proportion + dx) - reference_line = Line(coord_i,coord_f) - unit_vector = reference_line.get_unit_vector() * scale - vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = BLUE_E, buff=0) - return vector - - -class PartialDerivY(ThreeDScene): - def construct(self): - axes = ThreeDAxes() - - paraboloid = ParametricSurface( - lambda u, v: np.array([ - 2*np.sin(u)*np.cos(v), - 2*np.sin(u)*np.sin(v), - -2*2*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE], - resolution=(15, 32)).scale(1) - - paraboloid_copy = paraboloid.copy() - - - paraboloid_y = ParametricSurface( - lambda u, v: np.array([ - 2*np.sin(u)*np.cos(v), - 2*np.sin(u)*np.sin(v), - -2*2*np.sin(u)*np.sin(u)+2 - ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE], - resolution=(15, 32)).scale(1) - - - parabola =ParametricFunction( - lambda u : np.array([ - 0, - u, - -(u*u) + 2 - ]),color=YELLOW_C,t_min=-2,t_max=2, - ) - - plane = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2) - plane_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3*RIGHT) - - surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP])) - surface_eqn[0].set_color(BLUE_C) - - line = Line(np.array([0,-2,0]), np.array([0,2,0]), color = RED_C) - - 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.set_camera_orientation(phi=80 * DEGREES, theta = 45*DEGREES) - - self.play(Write(paraboloid)) - - self.add_fixed_in_frame_mobjects(surface_eqn) - #self.move_camera(phi=80* DEGREES,theta=5*DEGREES) - self.play(ShowCreation(plane)) - self.add_fixed_in_frame_mobjects(plane_text) - self.wait() - self.play(ReplacementTransform(paraboloid, paraboloid_y)) - self.play(FadeOut(plane), FadeOut(plane_text)) - self.play(ShowCreation(parabola), ShowCreation(line)) - - text1 = TextMobject("Moving small", r"$dy$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE) - - text2 = TextMobject("Observing change in function, keeping", r"$x$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) - - slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT) - slope_text[0].set_color("#006400") - slope_text.set_color_by_tex("\\partial",PINK) - slope_text.set_color_by_tex("f",YELLOW_C) - slope_text[5].set_color(RED_C) - - self.add_fixed_in_frame_mobjects(text1, text2) - self.wait() - self.add_fixed_in_frame_mobjects(slope_text) - - dot = Dot().rotate(PI/2).set_color(RED_C) - alpha = ValueTracker(0) - vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5) - dot.add_updater(lambda m: m.move_to(vector.get_center())) - self.play( - ShowCreation(parabola), - GrowFromCenter(dot), - GrowArrow(vector) - ) - vector.add_updater( - lambda m: m.become( - self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5) - ) - ) - self.add(vector,dot) - self.play(alpha.increment_value, 1, run_time=10, rate_func=linear) - self.wait() - - ''' - for i in np.arange(-2,2,0.2): - self.play(ReplacementTransform(Line(np.array([0,i,0]), np.array([0,i,-i*i + 2]), color = BLUE_C), Line(np.array([0,i+0.2,0]), np.array([0,i+0.2,-(i+0.2)**2 + 2]), color = BLUE_C))) - #self.wait() - ''' - - - self.wait() - self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn)) - - #self.move_camera(phi=80* DEGREES,theta= 90*DEGREES) - self.play(ReplacementTransform(paraboloid_y, paraboloid_copy)) - self.wait() - - def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1): - coord_i = curve.point_from_proportion(proportion) - coord_f = curve.point_from_proportion(proportion + dx) - reference_line = Line(coord_i,coord_f) - unit_vector = reference_line.get_unit_vector() * scale - vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = "#006400", buff=0) - return vector - - \ No newline at end of file -- cgit