diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and conservative fields/CurlTheorem_file3_measure-curl.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and conservative fields/CurlTheorem_file3_measure-curl.py | 82 |
1 files changed, 82 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and conservative fields/CurlTheorem_file3_measure-curl.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and conservative fields/CurlTheorem_file3_measure-curl.py new file mode 100644 index 0000000..e7a324d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and conservative fields/CurlTheorem_file3_measure-curl.py @@ -0,0 +1,82 @@ +from manimlib.imports import * + +def field_func(coordinate): + x,y = coordinate[:2] + return np.array([ + -y, + x, + 0 + ]) + + +class LineIntegral(MovingCameraScene, Scene): + def setup(self): + MovingCameraScene.setup(self) + Scene.setup(self) + + def get_pending(self,path,proportion,dx=0.01): + if proportion < 1: + coord_i = path.point_from_proportion(proportion) + coord_f = path.point_from_proportion(proportion+dx) + else: + coord_i = path.point_from_proportion(proportion-dx) + coord_f = path.point_from_proportion(proportion) + line = Line(coord_i,coord_f) + angle = line.get_angle() + return angle + + def construct(self): + + vector_field = VectorField(field_func) + vec_field_for_flow = VectorField(field_func, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5) + flow_rep = StreamLines( + field_func, + virtual_time=4, + min_magnitude=0, + max_magnitude=2, + dt = 0.1, + x_min = -1, x_max = 1, y_min = -1, y_max = 1, + ).set_color_by_gradient([BLUE_E, TEAL, WHITE]) + flow = AnimatedStreamLines( + flow_rep, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + ) + boundary = Circle(radius = 2).set_color("#7FFF00") + + start_angle = self.get_pending(boundary, 0) + + pointer = Triangle(fill_opacity = 1).set_height(0.25).set_color("#ffff00") + pointer.set_fill("#ffff00") + pointer.move_to(boundary.get_start()) + pointer.rotate(- PI / 2) + pointer.save_state() + pointer.rotate(start_angle, about_point=pointer.get_center()) + sym_1 = TexMobject(r"\oint \vec F \cdot \vec dr").next_to(pointer, RIGHT, buff = SMALL_BUFF).scale(0.7).set_color("#ffff00").add_background_rectangle() + sym_2 = TexMobject(r"\nabla \times \vec F").scale(0.7).set_color(TEAL).add_background_rectangle() + + self.play(ShowCreation(vector_field)) + self.wait() + self.add(flow) + self.play(Write(boundary), Write(sym_2)) + self.wait(2) + self.play(Write(pointer)) + def update_rotate_move(mob,alpha): + pointer.restore() + + angle = self.get_pending(boundary,alpha) + + pointer.move_to(boundary.point_from_proportion(alpha)) + pointer.rotate(angle, about_point=pointer.get_center()) + + + + self.play( + #self.camera_frame.scale,.25, + UpdateFromAlphaFunc(pointer,update_rotate_move), + run_time=3, + ) + self.play(Write(sym_1)) + self.wait() + + + |