diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file3_input-output2.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file3_input-output2.py | 136 |
1 files changed, 136 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file3_input-output2.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file3_input-output2.py new file mode 100644 index 0000000..b02e60b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Gradient/Gradient_file3_input-output2.py @@ -0,0 +1,136 @@ +from manimlib.imports import * +import numpy as np + + +def function(coordinate): + x,y = coordinate[:2] + return np.array([ + 0.4*(-x*np.sin((x**2+y**2)))/1*(x**2 + y**2), + 0.4*(-y*np.sin((x**2+y**2)))/1*(x**2 + y**2), + 0, + ]) + + +def function_two(coordinate): + x,y = coordinate[:2] + return np.array([ + 6*x*y/(x**2+y**2+1)**2, + -3*(x**2 -y**2 +1)/(x**2+y**2+1)**2, + 0, + ]) + +def function_three(coordinate): + x,y = coordinate[:2] + return np.array([ + np.exp(x)*np.cos(y), + -np.exp(x)*np.sin(y), + 0, + ]) + + +class Second(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + self.add(axes) + self.set_camera_orientation(phi=45*DEGREES,theta=60*DEGREES,distance=40) + self.begin_ambient_camera_rotation(rate=0.05) + + surface = ParametricSurface( + lambda u, v: np.array([ + 0.4*u, + 0.4*v, + 0.4*np.cos(np.sqrt((u**2)+(v**2))) + ]),u_min=-10,u_max=10, v_min=-10,v_max=10, checkerboard_colors = (["#1C6E8C", "#1C6E8C"]), stroke_color = "#1C6E8C").fade(0.7) + + text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7).set_stroke(width = 1.2) + text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7).set_stroke(width = 1.2) + field = VectorField(function, x_min = -4, x_max = 4, y_min = -4, y_max = 4, colors = (["#CC2936", "#4D8B31","#FFAD05"])) + + + self.add_fixed_in_frame_mobjects(text_func) + self.play(ShowCreation(surface)) + self.wait(3) + self.stop_ambient_camera_rotation() + self.move_camera(phi=0*DEGREES, theta=0*DEGREES) + + self.play(FadeIn(field),FadeOut(text_func)) + self.add_fixed_in_frame_mobjects(text_field) + self.wait() + self.play(FadeOut(surface), FadeOut(axes)) + self.wait() + + +class Third(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + self.add(axes) + self.set_camera_orientation(phi=45*DEGREES,theta=60*DEGREES,distance=40) + self.begin_ambient_camera_rotation(rate=0.2) + + + + + surface_two = ParametricSurface( + lambda x, y: np.array([ + x, + y, + -3*y/(x**2+y**2+1) + ]),u_min=-2,u_max=2, v_min=-2,v_max=2).set_color(BLUE_E).fade(0.7).scale(1.7) + + text_func = TexMobject(r"f = \frac{-3y}{x^{2} + y^{2} +1}").shift(4.8*LEFT+3*UP).scale(0.7) + text_field = TexMobject(r"\nabla", r"f = \begin{bmatrix}\frac{\partial f}{\partial x}\\\frac{\partial f}{\partial y}\end{bmatrix}").shift(4.8*LEFT+3*UP).scale(0.7) + text_field_a = TexMobject(r"\nabla", r" f = \begin{bmatrix} \frac{6xy}{(x^{2} + y^{2} + 1)^{2}}\\-3\frac{x^{2} - y^{2} + 1}{(x^{2} + y^{2} + 1)^{2}}\end{bmatrix}").shift(4.8*LEFT+3*UP).scale(0.7) + + field_two = VectorField(function_two, x_min = -3, x_max = 3, y_min = -3, y_max = 3, colors = (["#CC2936", "#4D8B31","#FFAD05"])) + text_field[0].set_color("#CC2936") + text_field_a[0].set_color("#CC2936") + + + + self.add_fixed_in_frame_mobjects(text_func) + self.play(ShowCreation(surface_two)) + self.wait(3) + self.stop_ambient_camera_rotation() + self.move_camera(phi=0*DEGREES, theta=0*DEGREES) + + self.play(FadeIn(field_two),FadeOut(text_func)) + self.add_fixed_in_frame_mobjects(text_field) + self.wait() + self.play(FadeOut(surface_two)) + self.wait() + + + +class Fourth(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + self.add(axes) + self.set_camera_orientation(phi=45*DEGREES,theta=60*DEGREES,distance=100) + self.begin_ambient_camera_rotation(rate=0.2) + + surface = ParametricSurface( + lambda u, v: np.array([ + u, + v, + np.exp(u)*np.cos(v) + ]),u_min=-3,u_max=3, v_min=-3,v_max=3).set_color(BLUE_E).fade(0.7) + + text_func = TexMobject(r"\textbf{Input: Function}").shift(4.4*LEFT+3.3*UP).scale(0.7) + text_field = TexMobject(r"\textbf{Output: Vector Field}").shift(4.4*LEFT+3.3*UP).scale(0.7) + field = VectorField(function_three, x_min = -3, x_max = 3, y_min = -3, y_max = 3) + + + self.add_fixed_in_frame_mobjects(text_func) + self.play(ShowCreation(surface)) + self.wait(3) + + self.stop_ambient_camera_rotation() + self.move_camera(phi=0*DEGREES, theta=0*DEGREES) + + self.play(FadeIn(field),FadeOut(text_func)) + self.add_fixed_in_frame_mobjects(text_field) + self.wait() + self.add_fixed_in_frame_mobjects(text_field_a) + self.play(ReplacementTransform(text_field, text_field_a)) + self.play(FadeOut(surface)) + self.wait()
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