From 5ee6f0880a95632e35fc7b7d001d2f2aa6d2bc0c Mon Sep 17 00:00:00 2001 From: nishanpoojary Date: Sat, 4 Jul 2020 12:39:49 +0530 Subject: Add files via upload --- .../file4_partial_deriv_example.py | 246 +++++++++++++++++++++ 1 file changed, 246 insertions(+) create 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 new file mode 100644 index 0000000..0a5832d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py @@ -0,0 +1,246 @@ +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"$z = f(x,y) = 2 - x^2 - y^2$", color = BLUE_C).scale(0.6).move_to(np.array([3*LEFT +3*UP])) + surface_eqn[0].set_color(PINK) + + 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"$z = f(x,y) = 2 - x^2 - y^2$", color = BLUE_C ).scale(0.6).move_to(np.array([3*LEFT +3*UP])) + surface_eqn[0].set_color(PINK) + + 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